So in the history of geometry, there are three classical geometric problems squaring the circle Trisecting an arbitrary angle and duplicating the cube We say that all of these are impossible to solve And in fact all of these were solved during the fourth century BC Wait, what? So let's talk about these problems a little bit the first one Duplicating the cube emerges as follows suppose you have a cube with a side length of a You want to find a cube with twice the volume? We'll have a side length of x where a cubed is to x cubed as one is to two And so the problem of duplicating the cube comes down to how can we find x? To solve this problem. We have to introduce some extra terms So the first important term here, which will show up many times in the history of mathematics is that of a mean proportional This is not a proportional that goes around bullying other Proportionals, but rather it emerges as follows given two quantities a and b. We can insert one Mean proportional by finding an x where a is to x as x is to b and You can see here that in this context the idea of a mean proportional is that it's someplace in the middle It's someplace between a and b Well the standard rule in math is anything you can do once you can do as many times as you want to so we've put one Mean proportional between a and b. Well, let's see if we can insert two mean Proportionals and we'll do that by finding x and y where a is to x as x is to y as y is to b and We can find three mean proportionals x y and z and so on so another term that will show up is the geometric mean and That comes from inserting one mean proportional So if we insert one mean proportional x between a and b we have a is to x as x is to b and in modern terms this gives us a over x is x over b or cross-multiplying a b is equal to x squared Consequently, we have the following result given a and b the mean proportional x satisfies x is the square root of a times b and x is also known as the geometric mean So this brings us to Hippocrates of Kios Kios is one of the many islands that make up Greece and Hippocrates of Kios shouldn't be confused with a much more famous contemporary Hippocrates of Kos Hippocrates of Kos was the physician Hippocrates of Kios was an mathematician We actually know quite a bit about the life of Hippocrates He lived around 430 BC and he was a merchant according to one story one of his ships was seized by pirates and He found out that its goods appeared in Athens and so he went to Athens to try and retrieve them This required dealing with the Athenian legal system, which took time So to keep himself entertained he attended some lectures in mathematics and after a while he said to himself Hippocrates you can do that and so he became the first person We know by name to be paid to be a teacher of mathematics Hippocrates also wrote the first known textbook on geometry, which he called the elements We'll talk about that more later Now Hippocrates considered the problem of finding two mean proportionals between a and b and his results are most easily understood if we rewrite this in a somewhat modernized format So this first proportionality a is to x as x is to y We can write that as a over x equals x over y and if we multiply both of these by a over x and Simplify a squared is to x squared as a is to y But wait, there's more if you look at the first and third ratios that says that a over x is equal to y over b So this means we can multiply one side by y over b and the other side by a over x Then simplify and this is a very interesting and important result Because of b is to a then a cubed is to x cubed as one is to two But this is exactly what we need to do in order to duplicate the cube And what that means is the problem of duplicating the cube can be solved by finding two mean Proportionals and it's worth pointing out that Hippocrates did a very mathematician thing He took one problem duplicating the cube and said it's the same as another problem inserting two mean proportionals Of course, he didn't have any idea of how to solve this problem of inserting two mean Proportionals, but it did offer two methods of attack on the same problem And in fact it led to one of the solutions So a little while later Monachmas who lived around 350 BC found a relationship between different lengths Associated with what we now call conic sections We'll talk about Monachmas's work with conic sections elsewhere But in modern terms we might describe Monachmas's results as follows for a parabola There is a parameter K where the distance to the vertex and the point satisfies the relationship K y equals x squared And we might view that as the equality of a rectangle with with K and height y With the square with the side of x and for what we call a rectangular hyperbola There is an area p squared where p squared is equal to x y Equivalently the area of a rectangle with one vertex on the hyperbola is equal to a particular square and Monachmas was able to use these relationships to find two mean Proportionals and because it was the same problem to duplicate the cube So later Greek writers described a general strategy for solving problems in geometry analysis and synthesis in Analysis we assume the problem already solved Then try to work towards a starting point Then in synthesis we begin at our starting point and work towards the solution So in this case suppose we've already solved the problem and we've already found those two mean Proportionals x and y so we already know a is to x as x is to y as y is to b Now if we take a look at these first two ratios that gives us a over x is x over y And if we cross multiply we find that a y equals x squared Which tells us these solutions x and y are going to be the ordnance of a parabola But wait, there's more if we take a look at the first and last ratios We have a over x equals y over b and cross multiplying gives us a b equal to x y Which means that x y are the ordnance of a hyperbola and what this means is that we can find these two mean proportionals by looking at a specific parabola and a specific hyperbola and Seeing where they intersect And so now comes the synthesis since duplicating the cube requires to a equal to b Let's construct the parabola b y equals x squared. Well, that's 2 a y equals x squared We'll also construct the hyperbola a b equals x y or 2 a squared equals x y Locate their intersection point which will give us x and y and Since we have 1 is to 2 as a cubed is to x cubed Then x will be the side of the cube with twice the volume of the cube with side a and that solves our problem


This is where the free world ends, and the communist dominion begins. This is the border between West Germany and Eastern Europe. Here is where Winston Churchill's simile of the iron curtain is made terrifyingly real. Hundreds of miles of high steel fence along the boundaries of East Germany and Czechoslovakia. It is from somewhere behind this steel barrier that attack would come should the communists employ armed force to press their dream of world domination. So it is that men of the United States Army patrolled the roads along the fence, on watch day and night, keeping their vigil in the air as well as on the ground. Reports flow back constantly to two United States cavalry regiments that are poised along the border of West Germany. Ready to hurl themselves at the foe should invasion come. Determined to slow his advance until the free world deploys its armed might. For this is the frontier of freedom. These men are the border watchers. One of the most honored unit insignias in the United States Army is the regimental crest of the Second Armored Cavalry Regiment, serving its country since 1836. Today, its motto, to sure pray, always ready, is more significant than ever. As the men who wear it carry their vigil into the skies. That is Czechoslovakia in the distance, occupied by armies of the Soviet Union. A totalitarian power that has used armed force to dominate its neighbors. It is lush countryside, a landscape painters delight, massive castles frown over sunny fields, and dark forests. The red-tiled roofs of ancient towns gleam like illustrations from a medieval storybook. Rolling metal lands, fertile soil for wheat and other crops, breathe a tranquil peace. Only the frontier fence mars the pastoral scene.  Ominous watchtowers, linked at regular intervals. A high steel barrier dips into forests and plies the mountains of the lower Bavarian Elves. Right to the summit of Cracky Peaks. Scarcely a stone's throw away from ski lodges that defiantly hug the slope. This evil partition sunders towns and villages. Below lies Eisenstein, riven apart by the border, which even runs through the railroad station. The locomotive is West German. The rails on the Czech side of town, called marked Eisenstein, lie rusting in disuse. On the ground, an iron barrier at the railroad station marks the division between two worlds. Even the waiting room inside is split in two. A chain runs across it, warning that passage beyond is forbidden an absurd yet sinister token of communist hostility and suspicion. The communist obsession with secrecy requires us to calm the enemy side for signs of suspicious activity. Vigilance is unceasing. Everyone is on constant alert. The helicopter crew must check with base every 10 minutes. Any delay is a cause for alarm. The roving patrols are backed up by a series of fixed observation points, operated on a 24-hour, 7-day basis by troops of the 2nd Armored Cavalry Regiment. Atop the tower, trained eyes constantly scan enemy territory. Women walking northeast of tower 2 seem to be checking fence, carrying on right shoulder 58 Papa automatic weapons. Still observing. The search is for anything out of the ordinary. Even slight changes in familiar scenes can be significant. Traffic on a road seldom used. A new building, a fresh clearing. An increase in personnel at a Czech watch tower. Whatever the activity reported by the observer, the sergeant in charge immediately phones it back to higher headquarters. 7-0-9-4-5-1. A photographic record of the activity is also made to be relayed back to base for study. The hundreds of miles of Czech border the 2nd Armored Cav must patrol. Its remoteness from regimental headquarters has required the establishment of semi-permanent base camps like this one, Camp Gates. Line troops of the regiment rotate monthly duty assignments here, sending out mounted patrols and the men who man the outposts. It is at the base camp that each jeep patrol is carefully debriefed. Sergeant Farber, on your patrol last night, did you or any member of your patrol enter into Czechoslovakia? No, sir. Did you have any use for your weapons? No, sir. Did you fire them? No, sir. Did you at any time, you or your men, enter into the 50-meter zone? Yes, sir. Point out on the map. We're in the 50-meter zone at this location, this location, and this location here. Were any of these points outside of your normal patrol route? No, sir. Then would you go into more detail on those personnel carriers which you spotted last night? Yes, sir. There were 13 personnel carriers, T-64s at this location loading on flat cars with approximately 30 men with them. About a platoon, then? Yes, sir. Could you tell whether or not they were Czech or Russian carriers? It was difficult to tell, sir, but I'm pretty sure they were Czechoslovakian. Very good. Thank you, Sergeant. Yes, sir. Cavalry means movement, and the border watchers must be ready to roll day or night. This constant readiness demands the highest quality of maintenance. The mechanics of the second cav perform prodigies of labor to keep equipment operational. The same sense of urgency motivates signal technicians. Operational standards are rigidly maintained by inspection teams from higher headquarters. C-M-M-I stands for command, maintenance, and management inspection. These experts seek one simple but vital goal, 100% operational readiness. Men as well as equipment must be kept in a high state of readiness. Repeated practice alerts called without warning train the troopers to move out fast but in perfect order without getting in one another's way. While this mechanized infantry squad enters its armored personnel carrier, tank crews mount their M-60A1 tanks. The main gun is unlocked. Tube and turret action are checked. The tank commander secures the radio antenna while the powerful diesel engine warms up. The steel giant stirs into motion. The convoy is rolling. It usually develops into a field training exercise in which combat elements take up defensive positions or engage in tactical maneuvers. Frequently, the maneuvers are large-scale, testing the operational readiness of major cavalry units such as squadrons. These operational readiness tests, ORTs, are carried out under simulated battlefield conditions. Attack and counterattack are executed with the aggressiveness and verve that are typically cavalry in style. The maneuvers are often joined by West German paramilitary troops whose job is border defense. They are called Bundesgrenschutz, BGS for short. Here they are acting as enemy soldiers, a role they frequently reverse with their American allies. Although live ammunition is not used, the mock skirmish is fought in deadly earnest. More than skill in skirmishing is at stake. And the nations allied to them in NATO. The performance of American troops is evaluated by umpires who roam the maneuver area. These men are officers or high-ranking non-cons of great experience. They grade the skill and teamwork of fighting units. Particular attention is paid to the leadership qualities shown by those in command. Their reports go back for study to the regimental command post in Nuremberg. This is where the headquarters of the Second Armored Cavalry Regiment is located. It is in a former SS Cassarne in which der Führer himself lived when he came to this ancient city to address Nazi party rallies. The famous stadium where the rallies were held stands empty nearby. Once it rang with marching boots as 100,000 stormtroopers crowded its vast area. From this podium, Hitler exhorted his followers and received their frenzied adulation. In disuse since the Nazi downfall, the stadium today is a bleak expanse of quiet desolation. A grim reminder of how fleeting are dreams of martial glory and world conquest. In vivid contrast, modern Nuremberg frogs with the light and noise of a busy metropolis. Nuremberg is one of West Germany's major metropolitan areas. Virtually leveled by Allied bombing raids, the famous speed evil city has been meticulously rebuilt. No sign of devastation remains. Nuremberg is a favorite of cavalry troopers on lead. Its glittering shops, excellent and inexpensive restaurants, many theaters and nightclubs offer ample diversion from the strain of border watching. The Second Armored Cavalry Regiment has a vigorous recreation program. It is often combined with the goal of improving community relations. The soccer game is being played by German and American teams. Sharing the border watch with the Second Cav is the 14th Armored Cavalry Regiment. It patrols a shorter stretch of border along East Germany running north. The northernmost section of the border is manned by British troops. Headquarters of the 14th is at Fulda. Since its squadrons are located close to the border, no advanced base camps are required. Border watch activity is carried out much like the Second Armored Cavalry Regiment. There are a series of fixed observation posts manned by troopers on 24-hour ships. Here too, the watch reports any and all activity on the East German side no matter how routine or slight. There is an added stimulus to observation. This area of Germany is known as the Fulda Gap. Peaceful in appearance, it is an historical invasion route from the East. So the border watchers keep their powder dry and their weapons ready to use if need be. Flying Cavalry Men make daily border sweeps. They are grounded only when inclement weather limits aerial observation. The main task of watching the enemy side falls on the mobile ground patrols. Their visibility is least impaired by bad weather. Communist border guards scrutinize us with equal intensity. The East Germans seem to make themselves more visible than the Czechs. Note that the fence that runs here is a double one. The East Germans are diligent in keeping them in good repair. Also conducts surveillance from the air. Their helicopters are Russian-made and fast. Their pilots are skilled. Communist watchfulness is meant more for their own people than for us. A trap for would-be escapee uses seen below from one of our helicopters. Long strips of earth are plowed close to the fence. When the earth is soft, it leaves tell-tale footprints of anyone attempting to flee the Communist paradise. The soft, fresh earth holds a deadly menace. It is seated with mines. The warning sign is ours. Concrete bunkers crop up at intervals. They are sighted so as to command a wide field of fire along the fence. The striped border markers bring a slight touch of color relief to the grim scene. Stones painted yellow also serve to mark the boundary line. One of the grotesque results of the division between East and West Germany is this house that straddles the boundary line. Its occupants abandon the part on East German territory and live only on the West German side. There are a few authorized openings in the East German barrier. This is a legal crossing. A customs station through which flows a meager amount of traffic from the two Germanies. The men crossing to check the automobile are West German. One is a Solner, a customs official. The other is a member of the German border troops, the BGS. Good luck. Thank you. Good. I'm Taylor. This is Lieutenant Schoen from the BGS. I'm Taylor from Kolde. The West Germans patrol their border jointly with the U.S. Cavalrymen. They make contact frequently to exchange information. One zero man over two. They're both off and into one zero seven where we present the locates. Good. I have been from here to tables, some new sports, to counters, and into here. An American sergeant is doing the interpreting. I have been from here to tables, some new sports, to counters, and into here. An American sergeant is doing the interpreting. Thank you. We have done this observation so far. Good day. I think we know each other. I'm Bevel Stoeff. Since when have you been here? Good day. I think we know each other. The 14th Armored Cavalry Regiment has been promoting German language classes among its troops with great success. Three weeks of classroom courses teach basic conversational German. It is supplemented by a special vocabulary of military and border watching terms. In the fourth week, Americans and Germans go on joint patrol. To promote speaking proficiency and mutual understanding, German and American Border Patrol units live and eat together. The Americans also attend courses in German on weapons used by the Bundesgrenschutz. This mortar is of West German manufacture. On exchange day, BGS soldiers visit the 14th Cavposts and vice versa. Here, a BGS captain explains to American visitors some features of a German patrol vehicle. But contact with Germans is not all military. Social relationships are the same. The 14th Armored Cavalry Regiment probably has the most outstanding record in German-American relations of all United States forces in West Germany. This sustained effort to cultivate friendship reaches deep into German civilian life. A popular activity is a week on the farm, during which cavalrymen help out in spring planting or fall harvesting. Preference is given to farms in the border vicinity. The cavalrymen also have a highly successful emissary of goodwill in their band. The band travels throughout the 14th Cav Area, giving enormously popular concerts. Participating in holiday celebrations and ceremonial affairs. These acts of friendship are strongly appreciated and reshaped by the German military. The BGS soldiers also have a high level of friendship with the German military. These acts of friendship are strongly appreciated and reciprocated by the local Germans. No city in West Germany is more hospitable to American soldiers than is Fulda, regimental headquarters of the 14th. Fulda is also one of the most attractive. Its municipal castle was once the home of Fulda's great prince bishops. It is considered to be, along with St. Paul's Gate and the Organnerie, among the finest examples of German Baroque architecture. The magnificent St. Boniface Cathedral is an international shrine, since it houses the bones of St. Boniface. In stark contrast is this modernistic church. Parts of Fulda have a decidedly modern look. This is University Square, named after its centuries-old center of higher learning. The charm of Fulda and the friendliness of its citizens, that's the Lord Mayor addressing his people, is cherished by the 14th's cavalrymen. The bond is strengthened by a common awareness that the hostile border lies close by. That is why the 14th is in constant combat training. Like its sister regiment, the 2nd Cav, the 14th has a dual mission in Germany, to patrol the border and to carry out a delaying action should the enemy pour his massive strength across the border. The modern U.S. Cavalry Regiment is formatively equipped for this purpose. This impressive array of tanks and armored vehicles belong to just one line platoon. Each platoon is backed up by the additional firepower of a squadron tank troop and the heavy guns of a self-propelled 155mm howitzer battery. Helicopters add an aerial dimension to its ground reconnaissance capabilities. Training in an armored cavalry regiment is rigorous. Tankmen must pass an annual tank crew qualification course. Their effectiveness in simulated combat situations is carefully judged. The cavalry's foot soldiers must also undergo strenuous tests in what is known as MISPIC, Mechanized Infantry Squad Proficiency Course. Like the tank crew qualification course, MISPIC sets up typical combat situations in which the squad leader and his men must display a high level of skill, teamwork, and aggressiveness. Howitzer batteries and 4.2 mortar crews must also pass annual qualification tests. It is all a far, far cry from the horse and saver days. The cavalry steeds are of iron now and have even taken wing, like Pegasus. The thunder of horses hooves has given way to the clank of treads and the beat of rotor blades. But the spirit of the past still rides with the 2nd and 14th Armored Cavalry Regiment. The cavalryman's traditional dash and boldness, his fierce pride in the battle history of his regiment, burn as strong as ever. The 2nd Cav, which fought vagantly in almost all of America's historic wars. The Mexican, the civil, the Spanish American, World War I and World War II. The 14th Cav, which fought the Philippine morows two generations ago and won imperishable fame in World War II in the breakout at San Loh, the Battle of the Bulge, and the capture of the Ramagan Bridge. Yes, the cavalry traditions of honor, valor, dedication are very much alive today. Here on the West German border, there is no questioning as to why men are prepared to fight. The issue is clear. Freedom is at stake. And these two great cavalry regiments, the border watchers, will, if need be, fight to preserve it.


An exciting U.S. Open is in the books and we're heading out to the Travelers Championship of this week, which should also be a lot of fun because no John Rom for this week, but a lot of studs in the field and it should be enticing. What? I thought you were going to say it's fun because John Rom is not in the field.  It was unprofessional of me to laugh, but it was fun. No one cares my intros. No one cares about these. You're not here for this. You're here here, Brandon. So there we go. Welcome on in. The Czech Fantasy podcast, powered by Number Fire. That's right here on the FanDual Podcast Network and NumberFire.com. My name is Jim Saunders. I am a senior writer and analyst for NumberFire.com. Joined here in case you didn't know, by Brandon Genula, he is the managing editor for NumberFire.com. Brandon, John Rom, Victorious. How are you doing? Well, speaking of having more fun without John Rom, I would have had a whole heck of a lot more fun. Yeah, your secret quotes were Louis Westhazen and I had Harris English. Yes.  And they were on the list solo, second, solo, third for some long shots, but John Rom making and I ran the numbers. It's really hard with like putts, but he was like under two percent likely to make both of those putts. Yeah. And yeah. I mean, like, yeah, I love John Rom. So I'm not, like, disappointed in any way for him or that he won. He was actually I was talking about the Call of Duty League as well, which kind of helped him get that win, which, you know, Call of Duty League, not my number one priority, not my number one choice. But I love a good love, a good eSports fan. So, you know, I mean, it could it could have been better. But, you know, John Rom got a major. Does this make you have like any sort of like rudge against Rom now? Like I obviously said in the past, you have it. But now because he robbed you of having these two potentially just nails sleeper picks for for golf digest, are you just like going to hold it against him forever now? No, I'm not important enough to factor myself into John Rom's accomplishments. But if you don't account for yourself, who will Brandon? This is just a good philosophical question. Like, if you're not going to think about Brandon and Abdullah, who will that's not a good job of that for me. So she makes she makes sure I don't lose lose track of everything. I think of you constantly take that for what you will. But either way, we're here to break down the Travelers Championship for this week from a PGA DFS perspective. As always, it's not just the heat check talking PGA each and every week. We also have the Q&A show. That's at 3 30 p.m. Easter on the Fandal YouTube, Twitch, Facebook and Twitter pages. You can swing by there and ask Brandon about his win simulations, talks and betting, talks of DFS to get set for the Travelers Championship. That is at 3 30 today. So make sure you're subscribed on the Fandal YouTube, Twitch, Facebook or Twitter page and get your questions in no matter where you are deciding to watch that for today. Also make sure you are subscribed to the Number Fire Daily Fantasy podcast feed wherever you get your podcast. The Travelers Championship is at TPC River Highlands for today. It is 6,841 yards and a par 70. So it's one of the few courses with a salary with a salary with it. I've gotten so used to like changing some some terms in my head to salary, like not saying price and stuff like that. So like, like if I'm at the grocery store and I see like, oh, what's the price of those bananas? I think salary. I've gotten so used to it. I've now changed the yardage to salary. So we're going to go with that. It's six thousand eighty one, six thousand and forty one dollars. Either way, there are 156 golfers in the field. The traditional cut rules are back in play this week. Top 65 plus ties make that at the first two rounds. So finding cut makers will be important once again this week. Brandon, what stands out to you for TPC River Highlands? Well, now that I know this the salary of the yardage, I just got to convert that to meters and then I'm all set to figure out what we need for this week. But yeah, I mean, it's a short course and it's rare over the past like year. So we've had one other course, you know, shorter than seven thousand yards on the PGA tour. So it's super rare to see that number, but I'll dig into that a little bit more in just a second.  Shorter hitters can be relevant here. Last year, we had Kevin Shrillman, McKenzie Hughes, Kevin, Ryan Armour, Zach Johnson, Brendan Todd, Abraham Anser, all in the top 11. But, you know, for the most part, those guys were gaining strokes off the tee, you know, partially because of their fairways hit number, but also not all of them are substantially short, Brendan Todd. Always the one of my favorite anomalies being zero with percentile and distance, but one hundredth in driving accuracy, again, over the past 100 rounds, which you got to love seeing something like that. But if you look at the yardage, like kind of hole by hole, there are really four short holes, two par threes are around 150. There's a, you know, a sub 300 yard par for the 15th. The 16th is a par four that's on the scorecard at 333. So, you know, that's going to affect the cumulative distance, but it's not like every single hole is short. And so therefore driving distance is kind of a disadvantage or doesn't help at all. That's not really what we see. So for sure, I want guys who can gain strokes off the tee one way or the other. Doesn't have to be distance, but gaining strokes off the tee is important. We've got bentgrass greens that are typically fast. I tried to do some research on this because I'm always interested and nobody really ever seems to know fully. I saw some conflicting information, though, where and this all comes from Fantasy National with their speed splits on greens. The Velcro numbers, it's too hard because there's not enough of a sample and then, but like, we know that good putters are better than bad putters on average speed greens. It gets a little bit more pronounced on faster greens, but then on lightning fast, it get the gap gets closer. So like it's not really linear, at least from the data that I pulled. So either way, I want good bentgrass putters for this week. So my key stats after all that are strokes gained approach number one, just because it's always most important. Strokes gained off the tee, bentgrass putting and birdie are better rate. Yeah, looking at the off the tee stuff from past events here at TPC River Highlands last year, they're obviously, like you said, or sorry, going back to 2019, Shaz won. Shaz is not very long off the tee, but you did have some guys who have some distance and aren't the most accurate who fair. Well, walking Neiman was up there, at least at that time, wasn't super accurate. Kevin Tway was a good finisher. Bryson was up there, Jason Day. So to me, I think it does lend itself to just going straight off the tee because I just want guys who can gain whatever way they want. And obviously, like the accuracy does matter, given the the the par threes. So to me, I think just wrapping it all together and going strokes out the tee is going to be the optimal way to go here. I also had birdies are better gained as well, which is on your sheet because golfers can go pretty low here. Like, I think didn't Jim Furrick shoot like a 58 or something absurd like that recently at this course? You don't know you can't throw that at me. And I mean, I don't expect me to know. We just talked last week, too, about how I can't remember anything. Do you remember who won the US Open? Not Louie. OK, OK. Well, yeah, but not the guys you picked for that in there. You're welcome. Yeah, I think that's for me, getting guys who can go low is a key. So I think that the way that I'm thinking about this here is if I had a guess, I'm going to wind up being higher on guys who have some giddy up off the tee just because they grade out well and strokes me off the tee and also birdies are better game. So it's not like an active active search for me to try to find guys who are quote unquote bombers. I just think that's naturally where I wind up going in pursuit of guys who are good overall off the tee and who can generate birdies. There tends to be a lot of overlap there. So my guess, Brandon, this week is that I'll wind up being different from consensus and different from where the most popular plays are, just because I think that I'll probably be on a different archetype than a lot of the people are. Yeah, I think you can probably play this one a lot of different ways. You probably talk yourself into things. Jim Furek did shoot his 58 here. Sorry, Jim. I'll apologize. We have he and I have a back and forth to both. No, to both me and other Jim, because he's he's other Jim here, by the way. He's other Jim. Well, yes, as that only that only makes sense for sure. So sorry, Jim, for not answering your question that I was not prepared to answer. That's on me. Thank you. I'm sure I'll I'll try to grow you throughout the show with some questions. OK, good. I'm looking forward to this. I will know the answer to every single one because I'd never let my co-host Brandon down. We're going to talk more about the travelers and talk about TPC River Highlands, who has done well here in the past in just one second. But first, it's always exciting when a player scores a goal in the Euros. But this year, it's twice as exciting because Fandals paying out double the winnings when you bet on a player to score during a Euro 2020 game. Just signed up for a Fandals sportsbook and pick your goal score for a shot at two times the payout. In tournament featuring some of the best goal scores in the world, you'll have plenty of options to choose from. But no matter who you pick, Fandals will double your payout of two hundred fifty dollars and you'll have your bonus less than seventy two hours. Though there is no better place to bet Euro 2020 than Fandals sportsbook. Must be twenty one plus in present in Colorado, Iowa, Indiana, Michigan, New Jersey, Pennsylvania, Tennessee, Virginia or West Virginia. New users only first real money wager only ten dollar first deposit required. Bonus issued as a non-withdrawable side credit that expired in seven days. Max bonus two hundred fifty dollars restrictions apply. See full terms at sportsbook.fandals.com gambling problem called one hundred gambler in Colorado called one hundred five two two forty seven hundred in Iowa. One hundred bets off in Indiana. One hundred nine with it for confidential help. Michigan one hundred two seven seven one one seven in Tennessee. Call the red line one hundred eight eight nine nine seven eight nine or in West Virginia is a one hundred gambler dot net. Let's dive into who has done well here at the past at TPC River Highlands and Brandon Paul Casey did his typical major thing this past week where he made me sweat a whole lot the first couple of days and then decided to go bonkers over the weekend. So Paul Casey coming in with good form if we just exclude the first two rounds and also has done well at this course in the past. What do you see with Paul Casey here at TPC River Highlands? Yeah, I mean he's your guy so sorry for stealing him here but played here six straight years with five top 20s for top fives. He's gained strokes to the green and all of them at least four point two to be a little more specific there. He's putted pretty well here, which is never a guarantee with Paul Casey. But we are in bentgrass greens and that's Casey's loan positive putting surface in his career. We've seen some some high end finishes from Casey lately as well. Twenty first at the Valspar, fourth at the PGA, sixth at the Porsche European Open, seventh at the US Open as you alluded to. I have him in the 99th percentile and adjusted strokes gained approach over the past year comes from my database, which is just for field strength and recency as well. A 92nd percentile and strokes gained off the tee. Seventy first percentile and bentgrass putting splits. That's just over the past 100 rounds, according to Fantasy National. But you know, pretty much everything points to Paul Casey being a high floor play. But are you seeing any reasons to show caution with your guy, Paul Casey? Kind of just the salary because like I was I was big on Casey last week. That was because he was in the 9000 range this week, despite it being not as tough, but like a tough field still. He checks in at eleven six and that's pretty high for someone. Oh, I know you mentioned that he's been a good putter here before, but like overall, should we view Casey as being a plus on the greens? Probably not. And then you've got guys like Bryson up there, who's good on the greens. Cantley is up there. DJ, there's some po I believe on these greens as well. And DJ, obviously, is lights out there. So I worry a bit about that with Paul Casey, given that I can get the good ball striking elsewhere in this range. So if Casey were like in that second tier of salary, which we'll talk about plenty, I think, later on, I feel like he would be a rock star. But when the opportunity cost is like taking away a DJ, Bryson Brooks, or Cantley, it's a little bit tougher. I don't think that he's like I don't think it's terrible that he's there. I just it's harder for me to prioritize him when there are so many good golfers around him. Are you having a similar issue with Casey or no?  The question really comes in, you know, 11-6 is close to those other stars. But do we have any questions about whatever Bryson gave us at the US Open? Maybe he's got some of that. I can call it like frontal lobe overload or something. Not as smart as Bryson is, but no one is he Bryson's mind. But yeah, I mean, he went from like making a make in a surge, almost having that ace to imploding. Is that going to weigh on him? These are not usually the things that we talk about. But I think it's a fair question to ask so close after, you know, coming close to going back to back at the US Open DJ. I mean, even when I wait for a recency is the most likely winner here because his form is just very good, even if it's not fantastic. So I like DJ, but I don't necessarily feel like I have to play DJ. Brooks, I'm not going to be interested in coming off a major. So like, you know, yeah, maybe cover all that up and just look at the stats. Yeah, Bryson DJ, they're going to be better plays than Paul Casey, but kind of factoring that in, I think Paul Casey is still one of the best plays in the 11,000 range, which is very loaded this week. And so I think the question is, do we feel good enough with the low end values just to play Bryson and Dustin possibly Brooks, however you feel? Or does that like 700 from Bryson go a long way to getting back up toward like 9000 for your sixth golfer? I think it might because it's a pretty quick drop off this week. I think it's a quick drop off, but there's no difference for me between the 95,000 range and the 85,000 range. Like, so that's the difference that I have is like, I have no problem. Like, if if the difference between Bryson and Paul Casey is a guy at 95 versus a guy at 88, I'm actually OK, but taking the 88 because there's no one really in that mid 9000 range who I like. So I think that's the key difference for me is I just don't like that range, which means I am more OK selling out to get to Bryson. We'll talk more about can't lay later on. We'll talk about that that tier in general, too. So but that's kind of where I'm coming from with regards to that. Now, Brandy, you mentioned the intro that distance does help here. It may not be something where you sell out for distance, but distance helps. And good evidence of that is Bubba Watson. He is a two time winner here. He did that back in 2018 and 2015. That's in addition to two other top five. So clearly he's got some upside here. Bubba does have some miscuts on his ledger, too. He actually missed in two of the past four years. Last year's was largely due to putting Bubba lost 3.3 on the green, but gained 3.7 to green across his two rounds. So he's still good. He just didn't pop very well, which could happen. The recent form for Bubba is spotty. He has lost an approach in three straight and seven to the past nine measured events. He's still making cuts and gaining off the tee, but. It's not as clean with the irons as Bubba was last summer. And the distance from that has increased recently. So he's 10-4. Bubba feels like like if you're going to put a guy as being like, oh, course fit, course fit, course fit. Bubba may be the guy we value that more for than others. But it's still 10-4 for a guy with some middling approach play over a decently large sample now. And that's concerns me. So Brandon, where is Bubba Watson at a place he's won at twice before? I'm not particularly there, but it's it's also one of those where and I say this kind of a lot, but I'm not going to talk into an out of playing Bubba Watson at a course where he's won. For me, and you talked about the missed cuts, like he gained strokes. So he probably missed the cut on the number last year. But while losing 3.3 strokes, putting, which he's, you know, generally putted well here, lost 3.7 and his other missed cuts. So as long as he's not completely terrible with the putter, he should make a cut. He's going to gain strokes off the tee, which he's been doing just without fail for pretty much, you know, just a long time. And that's the most predictable stat of the four. So I think it's a fine. Overall, it's it's a fine case to make for Bubba. But I don't think that the salary is quite right, because he's too close. He's just like a little too close to some other golfers. I kind of prefer like, it's probably going to sound really dumb, but I prefer Kevin Strylman for a salary of 200 more. I prefer probably Kim Smith for 400. Siebel Kim for 500 less. What about Charlie Hoffman at 10 three? So Harris English, flushing it again, 10 eight. Lucky Neiman 10 nine. So like, I don't I think that Bubba will probably be a little too popular. Given the the wins here. I agree. And part of that is because I agree with your thoughts and Kevin Strylman, who is next up on our course history list here. And Strylman could have been in either course history or current form, because he's been really good recently. But also specifically good here at TPC River Highlands. Really good last year. What do you see with Strylman here checking in at $10,600? Yeah, he turns into from the Stryl boy to the Stryl man at this course. Been top fit. We've said that before. I can mute you. There's no Cal today. So I have the ability to mute you. That's true. I'm not afraid to use it. Hey, man, that's that's fine. Hey, man, that's that's fine. It saved me. I could just rest my voice for for the afternoon. I can I can impersonate you. Um, go ahead, go do it for Kevin Strylman here. I'm not going to do it. I'm not going to do it. Top 15, three of the past four years, thirty third, the other year that didn't fit. Doesn't account for his 2014 win. He won by gaining seven point eight strokes putting, but has gained two degrees and four straight. He's been lingering lately as well. Eight at the PGA, which is kind of hard to, you know, we're getting into we're getting into we're in major season. So we can kind of look and give a little bit extra weight to the to these results in majors. But eighth at the PGA, 20th at the Charles Schwab, 13th at Memorial, 15th at the U.S. Open. So it's really hard to like argue against Kevin Strylman and the stats point to success as well. Ninety second percent, how in fairways gained over the past 100 rounds, 91st percentile and adjusted to green data over the past year. Eighty fourth percentile in birdie, a better rate over the past 100 rounds. So it's kind of a lot to like with Strylman. He's not without his flaws. I was, you know, I actually picked Kevin Strylman to write up here, assuming he'd be closer to 10,000. Sure. At 10, 6, you start to get into, like, is that too much? I don't think it's quite too much, but it does kind of lessen the appeal a little bit for Strylman, whose win odds are also a lot shorter than I would have initially anticipated. But I think like it makes sense when you look at like his stats, look at the current form, look at the course history, like it's it's aggressive, but that doesn't mean it's like bad. I think it's a way to phrase it. And like when you see someone who's done well at a course, going back to that course and then you just look and see like multiple top 15s, especially at majors, like that's going to cause a reaction. So it's just a little, you know, it's it's a little steep, but he might also be in my head to head lineup against you. Yeah, that's like I feel really good with him, even at that salary. I think it's not a it's a pretty decent tier overall. So like we were talking before about like Bryson, I think a good counterpoint to that would be or Bryson, DJ, et cetera, et cetera, would be like if you go Casey plus Strylman, you're going to be pretty balanced. You can just you can live in the upper 9000 range is better than the low 9000 range. That could be a work and like it's not just Strylman, too. We talked about Hoffman before Bubba could potentially be in there. I like Joaquin Neiman.  Sam Burns hasn't looked great since the injury, but he hasn't been bad enough where I'm crossing him off either, gain pointing out at the U.S. Open in two rounds, gain three and approach the Memorial. Both of those are senses withdrawal. So I actually think that those kind of guys are interesting for this week where, you know, I think that my my default build will not be in this like the low the mid 10,000 range, but I do want to have builds that put me there because there are enough guys like Strylman, specifically who do interest me in this area. Yeah, I think with the course set up just not demanding distance, what that does for me is just injects a ton of variants because you just have more golfers who can contend. And anytime that that's the case where, you know, you don't have to be long, we just have, you know, 150 plus golfers of the of some of the best in the world. Some of these guys are going to catch fire for four rounds.  That's never what I'm saying ever. But it's more to say the win odds for someone like Bryson or Dustin or Brooks, they get lower because you're not cutting out so much of the field for being short. So I think what it comes down to is like you say, do you take a stand and say Bryson, DJ, Brooks or Cantley or one of these guys, they're going to win. You got to build around them and get, you know, it's going to be two of those in the top three or something like that. And so you got to build around the value or do you just say it's not going to be them coming off the US open. So we want to build a more balanced lineup and that's probably where I'm going to lean for a fandal purposes this week. Yeah, I think that that makes sense. I think that I will probably be getting one of those top five in most lineups. And we'll talk about that in the roster construction section with checking out the bookmaker odds, but we can talk about that then. Now you mentioned how the pool of golfers who can contend is larger at a short course than the other courses. And there's good evidence of that by looking at Shaz Ravey who won here. Back in 2019, he's not like a course horse necessarily because that's his only finished better than 25th since 2012. He was 11th back in 2012 too, gained 5.6 in approach. But the approach play has consistently been there for Ravey. He has gained an average of one stroke per round throughout his career at TPC River Highlands. The putting has hurt him and he's not gaining as much as others off the tee. That tracks with what you talked about before where the distance does still matter here despite the length or can help, I should say, can help versus does matter. Ravey ranks 80th off the tee the past 50 rounds but 18th in approach. The problem is is 133rd and birdies are better gained in 92nd and Bencraft plus Poa putting. So it's tough to see him duplicating the upside he showed here back in 2019, which makes it tough for me to get here. So, Chaz Ravey, a past winner here, Brandon, could be a guy who in our minds benefits from making a shorter course but I don't think I'm gonna get there personally. Where do you sit on Chaz for this week? I don't dislike him. I think the salary is right. We're still looking at someone who can be a problem overall with the putter although for what it's worth, Data Golf does have Ravey as the biggest beneficiary of playing it at TPC River Highlands, not from how he's done here but just from a statistical fit, he gets the biggest boost from his baseline or expected boost, I should probably say. So I'm like, I looked into Ravey quite a bit. I'm probably not there myself but he's also one of those golfers where I'm not gonna talk you out of him just like Bubba, I see the case for it. It's just probably not strong enough for me to prefer him to some other golfers in that same salary range this week. I think that's the big hangup I have is that there are guys, the 9,000 range, like right at 9,000 and the upper 8,000 range, I think it's really strong for this week and if I can go there and get guys who actually do make birdies over a larger sample, I'd rather get to them. So it's partly due to concerns around Chaz's putting and stuff like that but it's also because I've got alternatives who aren't gonna get a rosterate bump due to being past winners, which might not happen for Chaz but like, I know it's not gonna happen for them. So I think that that's the round and rather go for this week. Let's transition now to current forum, check out golfers who are coming in on a heater, Scotty Schaeffler, I guess like it's hard to say whether or not he's on a heater but like he's been consistently contending, consistently hovering near the top of the leaderboard. He comes in this week, Brandon Schaeffler, what do you see with this current forum as he is here this week at $11,000 just beneath that top tier? Yeah, been really consistent with some strong finishes and tough fields and that can get overlooked if you're not winning, if you're not entering with like a 36 or 54 whole lead or something like that. But I mean, we know what Schaeffler does and it's just be one of the best T-degree players we have on the PGA Tour. Finished eighth at the PGA Championship, missed the cut at the Charles Schwab despite gaining minimally T-degree, third at Memorial with 11.8 strokes gained T-degree and which was second best that week, seventh at the U.S. Open despite losing strokes off the T which is a little surprising based on his profile but overall over the past year, he's in the 96% tile in this field and adjusted strokes gained T-degree, does have some worrisome bent grass splits. I know you're looking at bent grass plus Poa but I have him in the 24th percentile on bent grass. His Poa splits are probably gonna make that worse for Schaeffler but it's a smaller sample with 61 rounds but I'm not that concerned with Schaeffler because he's gonna put the ball in play off the tee. He's gonna gain strokes off the tee. The Irons are probably gonna help him gain as we see almost every week from him and he can make birdies and go low. So I think Schaeffler is very much in play and it just goes back to like that. I'm probably cool building around Schaeffler or Cantley, maybe even Abraham answer as my top guy which sounds really silly but I'm gonna have a much better chance to hit one of those realistic winners this week because maybe it's someone who's just a long shot but statistically it's gonna be someone who's like 9,000 or above. So let's talk about Cantley because you lopped him in there as well as being someone you might build around. He's confirmed just being over his slump from earlier this spring. He's back in elite four mentoring this week over the past three events. Cantley has finished 23rd, 1st and 15th. He's gotten those finishes by feasting in a couple of different categories. It's not just one thing that's pushing Cantley up. He has gained at least 2.5 off the tee in all three events. He has gained at least 6.1 approach twice and he's gained at least 2.8 around the green in each of the past two events. That means that if one aspect of his game is off he can make up for it elsewhere. That means that Cantley, at least to me, despite having a fairly recent slump probably has a pretty high floor. He ranks second behind Paul Casey in Data Golf's true strokes game query over the past 60 months, or six months, 60 months. Woof, past six months. He's second behind DJ over the past 12 months. The tough part for me is that mental hurdle of using Cantley at 11.8 when I could just spend up a bit more to get to Brooks, DJ, or Bryson. So I think Cantley deserves to be there, similar to Paul Casey, but it is a mental hurdle. So how are you doing Cantley this week? Cause it sounds like you're pretty in on him. Yeah, I just got to convert the months into days and then back to me. 15 months is five years, five years ago. And then back to meters, though. Yeah, correct, obviously. I mean, I like Cantley probably as much or more than those guys. You want to head to head on one of them? Who would it be? Bryson. Can you like spot me anything? No. I would never spot you anything. I'll take it. Why? You don't have to, don't let me bait you into these. Who won last week, by the way? We had three, I think, right? I think you won two of them. Aha! As usual. But, I mean- So Bryson confirmed over Cantley this week? For me, it's just with Cantley, like there's nothing to be concerned about. And you talk about the slump and like, yeah, we have to talk about, you know, four event downswings for golfers because that is, you know, on paper or in theory relevant, but it's really not, we're not really factoring in, well, okay, so he's been 23rd at the PGA, won the memorial because of the wrong withdrawal. 15th of the U.S. Open, but that's not as important as like the missed cuts, which I know that's not what you're saying. What I'm getting at is like, right before that he was on a heater as well because he's very good at golf and he's just one of the best golfers on the tour. So those four weeks, that doesn't, it just doesn't matter in the grand scheme of things. We should not be surprised that he bounced back. We should have, if nothing else expected it because, you know, four events is not enough. So I'll take Cantley over Bryson for the sheer fact of course fit for this week. Also, I mean, not that Victor Hoffman was gonna do much, but he had the with. Yeah, but I think it was tough. Yeah. So I, I think Fee now had like seven Fando points just done to have like one. It was pretty abysmal. A wins a win, man. This is, this is just as good as a case key and versus Josh Allen bet. So, you know, I feel, I feel good about it. Although I do wish that Hoffman would have been okay because that's done. I think to me the upsides of getting to those top, top guys are is worth it. So I'll be getting there. And we can talk more about that in the, no, we'll argue later. Don't worry, don't worry. We'll get to it. Don't worry. You can be angry then. Don't worry. Like Kimley has, I know he won the Memorial under some fortunate circumstances for him, but like he wanted the Zozo. He's got multiple top five finishes over the past. Like he has as much upside. And honestly, my model has him more likely to win this than Bryson. Okay. As someone who's built wins Sims, I get where you're coming from, but you know, either way, let's have a dog Redmond here because we're gonna talk more about those top guys in just a bit. Doc, a guy we used a lot earlier in 2021, I think is when we were hot on doc or was that off of, I think it was out the COVID break, I guess. We were super to doc Redmond. I'm not using the bits. Brandon, are you seeing something here that should put us back on doc Redmond now? Well, yeah, I mean, lots of missed cuts to start 2021, but over his past four, ninth of the Byron Nelson, 59th at the Charles Schwab when he did lose 4.2 off the tee, which is not very good. 42nd at Memorial and then second at Congaree when he gained 5.8 strokes from approach. Also 4.9 around the green switches gotta be a record for him. Yeah, according to fantasy national, he had more than 2.7 in any other measured events, but there's a little bit of flukiness there, but you see someone with two top 10s in his past four and someone who also we've talked about for good reason. I think it's relevant. He was really crisp is the word I chose for Redmond at TPC River Highlands was 11th, gained 4.4 strokes off the tee, 5.1 with approach, lost 1.7 strokes putting, but with second tee to green for the week. So crisp, spicy, good stuff for Doc Redmond either way.  Crisp and spicy. No, it'd be like air fried tofu for your boy over here, but Redmond's around the green play is really bad. So we should probably be worried a little bit about the around the green performance at Congaree, but possibly it's a sign that he's starting to figure some things out. That would be nice. But even if the around the green play doesn't matter, look, if it's coming down to Doc Redmond's around the green play for a course where you probably need to go like 15 under, it's not going to be a good week anyway. So what you're playing is like the really good ball striking, hopefully some good putting for a really good salary. So I think Redmond makes sense. What's your read on him? I think he makes sense. I think the the hangup that I have with him is that he's kind of the opposite of can't lay. So we're talking about can't lay before, like where if one thing's not working, he can make up for it elsewhere. With Redmond, if one thing is working, he could also fail elsewhere. And I think that that's kind of the issue that I have here because like he mentioned how the around the green play might be trending up. It's very possible, but also like his approach play has been a bit more spotty over the past couple of months. The off the tee plays been a bit more spotty. So as he's gotten better at the short game, for whatever reason, the ball striking has taken a slight step backwards. Does that mean that once the ball striking gets back to his longer term form, that he'll suddenly become like a monster? Very possible. Yeah, because he's like a young dude. We can expect gains with the short game. But I just think that I have a tough time getting over it where like there have been long stretches of bat off the tee play, decreased approach play. That's where I have the issue. And I think that there are guys who are just beneath him who are more well-rounded, and I feel better about them doing well in the areas of Redmond also performs well. So I think that's kind of the hang up that I have there. Yeah, I mean, he's not my favorite play in that low 9,000 range, but he's definitely in that conversation. And so I think he's worth talking about, if nothing else, is highlighting how he got that runner up, which should probably draw us back a little bit. Not everyone we talk about in current form is someone that we love. So it's a good exercise sometimes to go through and look at some guys who have like, hey, two top 10s, maybe it's a week for him. And I still think that there's a top four at the US Open.  Hypothetically, Guido Miliosi, beasted at the US Open. He finished fourth there, earned him a spot for this week. He was not qualified before that top 10. But he's $8,800 in the field for this week. Guido Miliosi got the fourth place finished despite losing 0.2 strokes on the greens, which is absurd. He gained 1.9 up T, 5.2 on approach, and 4.2 around the green to gain 11.3 strokes T to green in the freaking US Open, which is amazing. His two events before that were a pair of runner ups, both in the Euro tour. If you look at DataGolf's adjusted strokes gain data, he is a positive everywhere, but around the green, but he's not like a standout anywhere. So overall, he ranks between Luke Liston and Zach Johnson. He has two spots behind Garrick Higo over the past six months. So Miliosi, likely to get buzz this week, thanks to the big outing, I'm probably not gonna get there because there are a lot of good golfers in this range, but I don't think it's like totally off the wall. Like we've used Luke Liston and Zach Johnson. So I think he's like an option. I'm just okay avoiding under the assumption that he gets a popularity boost due to the big run last week. What are your thoughts on Miliosi for this week? Yeah, I mean, I think that it's one of those questions where how does he just not bounce back, but how does he continue from what's been thus far? I'm assuming the pinnacle of his career coming off those two runner ups on the European tour and then fourth at the US Open. For what it's worth, DataGolf does have him gaining slightly positively on the greens because they adjust for field strength, which is nice to see. But I would just have to think that it's a pretty tall order to kind of continue that for a second straight week. He was very, very fired up because he's not like now I'm gonna be in the Masters and it's just one of those things where is he really gonna be at his peak for this week? I hope so, because it'll be fun because he's fun to watch, but for me I would just rather take something a little more established. I do think the one thing that's positive here is that we're talking about the US Open and stuff like that and it is like a long flight to go across the country, but like in the past, it hasn't been a negative for golfers to do well slash being contentious to the US Open and then come here because like Ches, when he won the Travelers, he finished third at the US Open the week before that. So I guess maybe I'm not accounting as much for that narrative. Maybe it's less travel and more the... Right, but like that hasn't impacted guys that much in the past. I'd like to be based on like anecdotal data, I guess, but like past winners here have been guys who have been, I mean, last year it doesn't count because it was weird scheduled to do COVID, but like the Revy year, like he literally like had a career run at the US Open and then won at the Travelers the next week. So I guess like I'm not viewing it as much of a negative personally. All right. He's getting a lot of buzz on fan share for what it's worth. Ches or Miliosi? Miliosi, yeah. Tied for fourth. That's kind of the big concern is... Yeah, I agree. I agree with that specifically. I just think the overall mindset of I don't wanna bump people down because they were in contention at the US Open or may have had like the Bryson stuff last week. Like I think that I'm not gonna account for that potentially as much as you may be. All right. All right. Let's talk here about what the bookmakers are saying for this weekend. Let's fight. Gloves off. There were no gloves on to begin with, but let's put them on and then take them off. Bryson DeChambeau, the slight favorite entering this week at Fan Dual Sports Book. He is 12 to one followed by Dustin Johnson at 13 to one. Patrick Cantley is 15 to one and Paul Casey at 16 and Brooks Kepka at 17. Then there is a bit of a teardrop down to Patrick Reed and Scotty Schafer at 23 to one. Brian Harmon is 27 to one with Abraham Ancer at 28 to one. Tony Fino is 30 to one. Kevin Strylman checks in at 32 to one with Bubba Watson and Harris English rounding the top group. They're at 37 and 38 to one respectively. So Brandon, we talk a lot about balance and it sounds like you are doing that way this week. But for this week there actually is a tier of five at the top whose odds are a decent amount ahead of the rest. So is it worth prioritizing for you one guy in that tier above the rest or are you okay ignoring that tier entirely at times? So I mean, here's something that I would struggle with because I run win simulations. So I have my version of win equity but if I'm talking the betting odds, like yeah, it does feel like those guys are massive favorites relative to the field but my simulations don't necessarily see it that way. Especially with that course fit, kind of negating a lot of what Bryson can sort of earn over the field typically. And again, going back to, we kind of have like a double whammy this week for me where you don't have to be long. So again, I already talked about how that brings more players into things but also the lower the scores go and the easier it is like that helps other golfers because this is the example I always use but this might be a bad example. But Bryson's not just gonna start eagling par fours that everyone else is birdying because he's better than these other golfers. Like you kind of start to lose that gap where, if you can birdie a par four that everyone else can only par, that's a huge advantage. If the scores are gonna go typically what we see, that's gonna be a little bit more negated too. So I think it's a little more wide open than the betting odds suggest. So for that reason, I'm okay starting my lineups on Fando with Cantley at 11 eight to save a little bit of salary or bump down even more. That could be stupid, but that's the way that I see it for this week. I think the Cantley argument is better than the argument is skipping over the tier entirely cause I think that like the falloff is to me after Casey who was 11 six. I agree too. I mean, that's fine. Like he's really good at the short game which probably, you know, definitely helps. It's not a situation where you need to be a bomber. I think that helps too. So I think it makes sense. I'm personally not putting them in that top tier though for me. I'll say this much between Bryce and DJ Brooks, Cantley, Reed, Casey being the top guys in salary. One of them is gonna be in all of my lineups but I'm not necessarily saying that it's gonna be, I gotta get two of those guys. No. It's really tough for me to get to two personally. Right. So two is tough, but I think that like what I'm saying is I want one and then dip down for the second golfer. Like maybe get to Strylman as my second golfer or something like that. So it just sounds like you're much higher on Bryson and that's kind of driving the gap between us. Correct. Yes. That's a fair assessment. Which golfer's odds have moved since things opened up yesterday? I know odds open up later than usual yesterday. There's maybe not a ton of movement there. A bit still. Patrick Cantley who Jim hates now.  From Cantley off Cantley apparently, I guess. Yeah, I guess that's true. Whenever Bryson's there, 17 to 15. He's the only one who was one of the favorites whose odds have shortened. I've seen a little bit of lengthening but nothing really to dig into there. Brian Harmon, 31 to 27. Abraham answer, 32 to 28. One of my guys for the week. Cebu Kim, Keegan Bradley from 65 to 47 and 48 respectively. Ricky Fowler, 75 to 65. Could be back, who could really say there. And Francesco Molinari, 80 to 70. Showed some life. Maybe Betters are buying into the Ricky, rested Ricky narrative. Maybe they're on the Brandon train where like, hey, he wasn't at the US Open last week. Therefore, he's the only guy who can win. That is what I said for Betum. I definitely guaranteed whoever wins this week was not in the US Open. That's what I heard. That's exactly what I heard. Do you think Ricky is turning a quarter here or no? I'm still skeptical but like, hey, couple good events in a row, that's not nothing. I think he's gonna be a dad as well. Oh wow, we have that news. Okay. I mean, like, so he doesn't have to be long off the tee. We've seen the irons get a little better and like, at least less horrible. It's just so hard with an older golfer to know like, when he's done working through stuff and it's there to stay. Cause like, we've seen some better iron play like back in January or February from him. Yeah. Then it got cold again. It's just been kind of hit or miss. Like, yeah, if Ricky gains like what? Six or seven strokes from his short game, which he's been doing the past two starts for him, he's gonna be fine so long cause he's not that bad off the tee.  So at 9,800, I'm not quite there. So I think I said for two different golfers I wouldn't talk you out of. I'd probably talk someone out of Ricky right now. Also related to Ricky potentially being a dad. Do we need to extend the window on the new dad narrative as a result of the John Romwin? Like, do we need to make it like a three month gap before we start to scale back on it? Or how does this work? I think we need to recalibrate the model here. Yeah, I think probably at this point, dad's only for at least another, let's say a month. Well, let's finish out father's day, the month of father's day. Father's month, okay. So June, yeah, at least. Okay, all right. Yeah. We'll talk to the team, the narrative team. They've got knobs that they turn and- I thought you were in charge of the narrative team. I have interns. No, no, no, no, no. They're paid interns, by the way, cause we don't, there's no free labor around here. We respect our interns, paid interns, but they are the ones who calibrate the knobs. I'll have input obviously, it's a think tank. So you don't run the narrative department, but you have interns on the narrative department? No, I delegate. I do run it, but I delegate. But I meant like you're in charge, that's what I mean. You took it a little too literally. Yeah, I mean, I delegate those. Like I'm like a figurative head of the narrative department and then I allow them to do what they do. They mean their skill. That's why they got the position to begin with. You know, the interns, they're good. That's why they're paid. I just don't know how I ask you for narrative advice because you're in charge. You say I have interns, but I don't have answers right now. Well, initially when it started off, I was, but like, you know, the narrative department grew because we benefited from the narratives. Kyle Larson on Father's Day, like, you know, what else do you need? That's how we pay the interns, is via wins. So I'm sorry, we've grown beyond your comprehension and just keep cooking, sorry. We'll re-evaluate at some point, but maybe I won't update you now on the recalibration with the narratives either way. Which lower-salary golfers have win odds to stand out to you? Not a whole lot, which is part of the issue of like going too heavy at the top. Doc Redman is 75 to one, who Jim just flat out hates this week. Leigh 75, Cameron Tringale is 80 to one, Stewart Sink, Aaron Wise are 85, and then it drops to Lonto Griffin, Chris Kirk, Harold Varner the third, and Mackenzie Hughes 120 to one, they're all either 9,000 or between 88 and 9,000 there. Patton Kezire, Brant Snedeker, Kevin Kisner are 140, Eric Van Royn is also in that bucket, but it's not a good week if you try to match betting odds on at least on Vandalsport's book. I'm actually finding that a lot. Like even in the upper 9,000 range, it's not a good week for me. Like if I were to do things that way, because I disagree with the odds this week on a couple of guys, Neiman mostly, that I'm having, like I feel like I'm more okay, which is weird because like I'm talking about, oh, gotta get Bryson in both of all, but like, you know, it's a week where I feel like I'll be deviating from what the odds are saying outside of getting Bryson in. So for me, and just speaking as someone who builds out a model and looks for like, who's actually a good, who should actually be kind of considered what their sports book odds say. Anytime we see multiple heavily overvalued golfers at the top, that makes obviously a lot of golfers below them look a lot more appealing, which is what I'm seeing this week, which is why, you know, if I had Bryson as like 12% likely to win, I'd be like, yeah, just play Bryson, but I don't because, you know, of his form adjusted for the expectation here, he's very overvalued at that number on Vandalsport's book. And so I don't view it as such a must this week. Okay, so that is that. We'll find out Bryson, go ahead. Yeah, I mean, we're gonna, yeah, I'll play it more. No, no, like we can fight. Okay, we'll fight later. Weather for this week, it's gonna be a little bit windy over the weekend, but nothing too bad. There will be decreased winds in the morning, both days, but increased winds in the afternoon. So both waves will get the same treatment. So we can pretty much disregard weather for this week. So let's dive into our player picks for the Travelers Championship based on the salaries at fandual.com. Brandon, who are you erroneously putting at the top of your list for this week at the Travelers? I'm gonna go with Patrick Cantlay. Jim's now Arch Nemesis.  I still love my boy Patty. Patty, you know, like we have those big names, specifically the three above Cantlay with Bryson, DJ and Brooks. I just think that you can make an easier case to save a little bit for Cantlay. I think the gap is a lot closer than the name value would imply. I know it's scary when Bryson does what he can do, but it's also scary when Patrick Cantlay does what he can do and that's be the best golfer in any field that he's in. He's in the 99th percentile and adjusted stroke scanty to green over the past year. 97th percentile off the tee, 92nd in approach. He's finished top 15 at the Travelers three straight years. He is the second most likely golfer to win this week. Again, not even behind Bryson for me, but DJ, just because, you know, Bryson is very volatile. He's got super high end upside, but he also doesn't necessarily, like he feels better than he is and the data says that Cantlay is just as good if not better. So I'm going to make you really mad because it might make all the fighting we've done here pretty worthless, but Cantlay would be my number two in this range. I mean, like that, I think that you have to kind of nitpick between these four and it's, I think we're both just out on Brooks, which I'm mostly out on Brooks whenever it's not a major. Right. But yeah, like Bryson would be my, probably my second because as much as the data says DJ, hey, we're not so different, you and I. Hey, what do you know? Yeah, but like, I mean, even in the past 50 rounds, Cantlay's data golf's number one and their true strokes gained above Paul Casey, which is, and DJ's third, like Bryson, like, yeah. So for me with Bryson, he's just overvalued. So here's why Bryson will win despite being overvalued. He was good at TPC River Highlands even before he was like full current Bryson. And I think that he's a good angle to play if you want to exploit what Brandon was talking about where distance helps despite not being something that is necessary for this week. He has been here five total times. Bryson has finished top 50 all five and the past three have all been top tens. A lot of that has been due to good putting, but like Bryson's a good putter, especially on Ben Grass and Poa, his approach play has been a bit on the upswing recently. He's gained in five of the past seven events, now ranks 37th in approach to the past 50 rounds. So my hope here is that he'll go overlooked due to the narrative that distance doesn't matter as much this week due to the downtick at the end of the US Open. I believe he opened at 11 to one in a sense length into 12. So I think that despite the fact he is the highest salary golfer and the odds on favorites, which is always something that correlates well to a high roster rate, I feel like that might not be as true this week as usual with Bryson. So that's why I have number one. I think Cantley is number two in this tier. And I feel like I would like to get one of those two guys and a healthy chunk of my lineups. That's probably a good question to ask is how we think popularity will shake up between those. I'd probably cap it to this top four. Yeah, it's really brook to me. Who else would Casey would be put in there? Yeah, the top four. The top four meant Bryson, DJ, Brooks and Cantley. I feel like Casey would be more popular than Brooks though, right? Yeah, but it was just, yeah. I don't want to skip over Reed to- Right, yeah, no, you're right. So I'd like looking at fan share right now, Bryson is 15th in tags. I feel like it's a pretty good bet that he's not all that popular. He's behind Cantley behind Casey. He's gonna be the most popular golfer. What? He's gonna be the most popular golfer this week. Guaranteed? I would feel pretty good about that. Just based on the trends of the salary and the odds. Yeah, okay. Fair enough, we've talked enough about this. Let's move on to the other guys in the top range. Who else do you like here as a start-on fan duo? Yeah, someone, we've just been too focused on the top, like four, six really, with Casey in there. But Abraham answered 11,000. I think he's like a core part of, you get one of those top six, which I'm including Patrick Reed in there because Reed's always gonna be unpopular. I know it sounds like I like every golfer, but those top six are very good. But Anster's gonna be the kind of guy who I wanna build around as my second golfer without jumping, I'm not getting back up into that top six. I'm not jumping down into like the low 10,000s for my second golfer because Anster has a lot of upside here. 77th percentile bank grass putter, which is his best surface. I finished eighth and 11th at TPC River Highlands the past two years. Missed the cut at the US Open, but wasn't because of the irons. Gained 5.2 strokes from approach. Distance, while it matters to some degree this week, it's not, you don't have to have it, which is good for Anster, who is 20th percentile in distance, gained over the past 100 rounds on tour. But he's just really good off the tee still because he's so accurate. So I think a lot sets up for Anster to kind of come into this without a whole lot of buzz because he's not one of those superstars. See, I'm seeing now he's third on fan share and tags. So there goes that. But I think it just makes sense from a process standpoint to like Abraham Anster this week. Well, part of the reason I think that we'll have an advantage on using guys who gain via distance is that I think the guys like Anster, who are not super long, will get talked up this week due to that narrative. So that's part of my thought process. I think Anster's still a good play. I think he's fine. I've no real issues there, but I actually like Joaquin Ninen, but maybe a little bit more. And I am deviating from what the odds say here because like, if you compare Oz's salary, Ninen looks like he's over salary, but I think that he's a good play. He doesn't grade out well in terms of fairways gain, but like he can get on the fairway when he needs to. And I think that's why I am enticed by him this week. He ranks fourth and strokes me out at the tee of the past 50 rounds. He is also 22nd in approach. The one bugaboo with Ninen is around the green play. But even with that, he still ranks 14th in the field and birdies are better game the past 50 rounds. So he can go low. And I think he's a good fit for the course given that he can put it where he needs to when he wants to. And he vowed in that with a fifth place finish here back in 2019. So I think that Ninen makes a lot of sense to 10-9. I think that if I'm worried about Bryson being popular, one way to deviate from that is by going with Ninen, who is someone who I do think will go overlooked for this week, just because, you know, again, the odds are a bit longer for him. And I think that that might correlate to his being overlooked a bit in terms of roster rate. What are your thoughts on Joaquin Ninen for this week? So my sims like him pretty much at his sportsbook odds, which might make it sound like, as you said, he's a little too high-salard, but that's actually good because most of the top-end golfers are typically, you know, overvalued. So I'm fine with Ninen, especially if distance does give him a leg up. He's got question marks, so it's a little hard to get, you know, excited about him at 10-9. So would you take an answer versus Ninen bet? I was thinking about it, no, because I think that that answer, I know. I think answer does fit really well. He's a good golfer. So I think that the logic of like, because if we're talking head-to-heads, we're talking about median projection, I think the answer is median projection is better than Ninen's, does that make sense? It does, yeah. Yeah, okay. So let's talk about the mid to salary golfers here again. I think this, like the mid, the middle range, I think that like the top-end guys are good. I think the bottom end of the 9,000 range is pretty bad, but what stands out to you in this middle tier? I like Cameron Smith at 10,000, but my number one golfer in this range is actually who you're going to talk about next. So I landed on Emiliano Grillo. I always question myself. Yep, you got it. Over the past 20 rounds, Grillo, according to DataGolf, has gained 1.49, true strokes gained or adjusted strokes gained. So again, 1.49, almost 1.5. Next best in the field is Paul Casey at 1.23. That's a huge gap. And we know that Grillo has some of the best ball striking on tour. He's been a little bit off the radar on the PGA tour, but has mostly dialed in with the irons. His past six starts have led to 7.1 minus 0.6. It's almost zero there. 7.1 again, 7.5, 2.1 strokes gained from approach. Those two where he didn't get to six were missed cuts. So it's probably going to get there eventually. He's on bent grass, which we know is that the surface for Grillo. So at 9,600, you can never feel super confident in Grillo, but boy, if he's going to gain strokes with the ball striking like that and just be okay on bent grass, you're looking at some potential there. For sure. I think that's definitely enticing for Grillo. The guy you alluded to as being your favorite, I think is Seawoo Kim, correct? Yes. Okay, so Seawoo Kim is $9,900. I like him a lot as well. Stats line up well for Kim this week. He ranks 17th and strokes him off the tee, 23rd in approach and 35th and birdies are better gained. That birdie number should get a boost with no Bermuda greens this week, which are easily the worst surface for him. He ranks 42nd if you go bent grass plus PoA putting. Even if the putting isn't entirely there, Kim should be in play this week because he finished 11th last year at this course, despite losing 1.1 of the greens. He gained 8.4 tee to green there. So Seawoo Kim is volatile, but as we talk about a lot, I'm okay with the volatility if it comes with upside and I think it does here. So I'm good taking tournament swipes at Seawoo Kim. What puts you on him this week? 92nd percentile and adjusted tee to green over the past year. Nice sort of quiet finish at the US Open. I was 18th tee to green last week against that field. So just a lot to like with Seawoo Kim from a tee to green standpoint. Okay, so your second mid-salary play as a guy, I was very close to writing up and decided to skip over this tier entirely. But if I were in this tier, the guy turned to his max Homa and he's your second pick. What puts you on Homa? Yeah, speaking of volatility, Homa has that which can be good and bad. Over his past 11 starts, he's been either top 25, which he's done six times, or missed the cut, which he's done the other five times. But those cuts, like you can't just look at missed cuts and be like, oh, it's a missed cut. A missed cut is a missed cut. It's not necessarily that cut and dried. Some of those missed cuts were the three majors, the players and the Wells Fargo. So it's hard to fault him for missing cuts at those events. We've seen good data from him in the most recent events, aside from those big events. It's kind of, Homa's just struggled in majors, but in weaker or just less elite fields. We've seen super high in finishes, including a win. So I like Homa at 9,400. He might be, despite all that volatility, he might be in my bobble hat against you. That's fair. I would consider him as well. Because again, I might wind up in that range. So if I do, I think that Homa would make a lot of sense. The reason I was there is that the data golf numbers line up pretty well for any more of the past six months. If you adjust for field strength, you know, again, he's struggling the majors, but like you expect a lot of guys to struggle in majors. And birdie maker ranks fourth and birdies are better gained the past 50 rounds. So I think that Homa does make a lot of sense. My choice instead was dipped down to actually $9,000 for my second mid-range play. Technically, we would deem that a value usually, but I want to talk about three guys down here because I thought that they were guys that just liked more relative to salary. That one who's most of me is Cameron Trangale. He is $9,000. I like him pretty decent here. The off the tee play has been, I could say bad I guess recently. He's lost multiple strokes off the tee in three straight events, but he's another guy who has a bit of distance and good accuracy, not great in either. The off the tee play hasn't impacted him too much elsewhere. Like he's struggling there, but it's not bleeding over into the rest of his game. He's still 19th in approach and 11th and birdies are better gained the past 50 rounds. Trangale is 38th in Bencraft plus Poa Putting, and those are his two best services. Trangale is risky due to the poor driving recently. My hope is that it won't matter as much this week and allow him to come through here at $9,000. So that's what put me on Cameron Trangale.  No, he's actually my model's best value if you combine stats and long-term adjusted form relative to his salary. So he would be my number one in that 9,000 or below range. He's historically struggled at this course, but is in much better form now than he was typically entering, which is a large part of the puzzle of course history. So Trangale would be my number one value play actually. Okay, I like it. So let's move down to the actual value plays and actually stick in the same salary. You're talking Lonto Griffin. We like Lonto in general. What puts you on him this week specifically? Well, the same stuff as always with Griffin. He's one of the easiest golfers to write up because he just is balanced. And you just say, you know, that can help him, that can help carry him. But he's a pretty good putter, which, you know, it's kind of one of his standouts. That's 80th percentile on bent grass. The second best golfer at this salary behind Trangale, although Trangale's comfortably ahead, but, you know, you look at Griffin missing cuts, but if you look at the data, he's driving it well, has good iron. So it's less concerning, you know, that the ball striking is generally good. So Griffin definitely not safe, but still a really good play. I agree. I think the Griffin makes sense down here too. And it's, I think there are a good amount of plays down here. So me not having you written him up is not because I don't like him. I just like other guys a little bit more, including Chris Kirk. Chris Kirk is older, he's 36. So he's not one of the guys who put in like the, oh, he's young, so you should buy into their gains bucket, but his putting has been less bad recently and it's been making it more palatable for DFS. We look here specifically from January 1st on, he has been to 13 events. He has gained strokes putting nine times. He has gained two plus strokes three times and he's still had some bad weeks in there too. So it's not just good. It's been some bad as well, but that's actually saved him recently because the approach play for Kirk hasn't been quite as hot as it was back at the early part of this calendar year. But if we look at the larger sample, Kirk still ranks 33rd off the tee, 40th in approach, 26th and birdies are better gain the past 50 rounds. And I willing to trust that data and hope that the putting has gotten better, which makes him appear under salary at $8,900. Brandon, what are your thoughts on Chris Kirk for this week? I didn't really even look at him because there's just been so many other names. And yeah, I mean, we were, I think, both in on him pretty heavily to start the year, starting to cool down now, which is kind of what you see from just any sort of hot streaks. And I think it's probably just kind of the end of what was a really good run, the 26th coming with really, at the Memorial coming with really good short game. So I'm probably out just because I prefer other golfers in this range. Who are the other golfers you like here? I'm gonna go down with, I mean, I already named one for Griffin, unless I'm mistaken. Who else? Okay, sorry. I just wanted to make sure I wasn't screwing stuff up because typical Brandon. Typical Brandon. Doug Gimm, 8,300, he's the one or one of the few I would be okay jumping down to, if I really want to get more access to those studs, he's 8,300, should fit the course well as someone who can gain strokes off the tee, 65th percentile there in my adjusted stats. Really good iron play as well, 91st percentile when adjusted for field strength, just a really bad putter overall, but it's kind of neutral on bank grass. So I think he fits from a value play standpoint. I am 31st in my player ranks, despite that salary. So not gonna say like play him in a cash game, but I'll have Doug Gimm exposure in tournaments. Yeah, I think that makes sense. Gimm is a guy we've been turning to a lot because of the approach play, and if he's going to penalize less off the tee than usual, I think that's a benefit as well. My second low sour guy is Taylor Gooch. Again, like Tringale, not great off the tee, Gooch actually just lost 4.2 there at the memorial, which is not what you want to see, but the hope is that it may matter less this week and that Gooch can make up for it elsewhere, which is what happened at the memorial. So he lost 4.2 off the tee there, but he actually finished 18th because he gained 4.8 on approach and 4.1 around the green. Gooch ranks 15th in approach and 35th in stroke scheme of bank grass plus PoA putting. And that's helping him rank 27th and birdies are better gained despite the bad off the tee play. So Gooch is $8,900. I can deal with some deficiencies off the tee at that salary, but Brandon, what are your thoughts on Taylor Gooch for this week? Yeah, was one of my others to consider in this range for my article on number fire, just such a consistent golfer where I should say balanced golfer, but that does lead to consistency. Just one missed cut in since February, two missed cuts since mid January. So like making cuts, you know, might get you a 40th, which isn't going to do the whole lot, but it can also get you a top 20 in a field like this. So Gooch, one of my favorite plays down here as well. Okay. So that wraps up our tier by tier breakdown. Let's finish up here with our picks to win for the Travelers Championship based on the current odds over at FanDuel Sportsbook. Brandon, I know one of my picks will be Joaquin Neiman. He is currently 44 to one. I think that number is too long. Given the overall play he has shown recently, who are you picking for this week? Patrick Cantley at 15 to one and Abraham answer at 28 to one. Okay. So you've got Cantley and answer. I have Neiman and for my second golfer, I'm going to be Bryson. Sure, I know. Let's go Bryson. 12 to one is too short. So I'm just kidding. I'm not going to pick him. It's, sorry. Did you write it right down? My bad. I can let you bait me into this. Actually, I fear we're going to go back to Bryson. I am going to go back to Bryson. Give me Bryson and Neiman. Bryson at 12 to one, Neiman at 44 to one. You guys actually distance on that. Yeah. I mean, why not? Let's, let's, let's lean into it. And despite the fact that it's a short course, let's see what happens with both those guys. Good overall off the tee. So I feel fair about them entering into this week. You have Cantley and answer versus my Bryson and Neiman. That is all that we have for this week, at least in the heat check side of things, but don't forget we are back here once again, 3 30 p.m. Eastern, the Fando YouTube, Twitch, Facebook and Twitter pages. Brandon is taking your questions about both the FS and betting to get you set for the Travelers Championship coming up this week. Brandon, where can people find your stuff and where can people find you on Twitter? I don't know why they find your stuff. I don't know. I wasn't prepared for that. Numberfire.com. What's that? It's a website. Oh, okay, cool. And I'm sometimes rarely on Twitter. At Cadillac13, G-D-E-L-A-1-3. And I'm at Jinsanus, J-I-M-S-A-N-N-E-S. You can also follow the Fando podcast and network at Fando podcast. Do not forget to subscribe to the podcast wherever you get your podcasts. We are now podcast Spotify, Stitcher, Google podcast radio.com. Wherever you get your podcasts, you can find us there. Big thank you to everyone for tuning in. Good luck to you with your PGA DFS lineups for the Travelers Championship. We'll talk to you once again next week. This has been the Heat Check Fantasy podcast powered by Numberfire.


Let's move on to the hip. This is a six-year-old boy with right hip pain. Here's a radiograph, frontal projection. Let's look at what we can see. First, I look at the congruity of one hip joint versus the other. I look at the density. I look at soft tissues, and I look to see if there is a joint effusion. What immediately grabs my attention is the density on one side versus the other. You notice this is quite a bit brighter than on the contralateral side. In addition, there is a linear thin lucency just under the contral surface on the right, as you see over here. On the left, there's no similar lucency. Now, let's take a look at some of the soft tissues around this joint and compare it to this joint. I'm going to draw a line for you. This is the obturator-internus muscle. This here is the obturator-internus muscle. Okay? The distance, if we will, from here to here is bigger than the distance from here to here. So that tells me there is some elevation or displacement of that soft tissue structure. Also, the distance between here and here is going to be larger than the distance between here and here. Let's go ahead and measure that. That's about 1.1, and here it's about 0.73. So all that tells me is that there is a joint effusion on the right side, the increased sclerosis, and the lucency tells me that there's a little bit of collapse happening, and these are the classic findings of leg cavae perthes, or a form of avascular necrosis, if you will. Some people call it an osteocondrosis. Some people call it avascular necrosis. You know, there's no great answer, but it's an area where there's not enough perfusion happening to that femoral head. In the next vignette, we're going to show you what this looks like on MR imaging.


Hey, what's up everybody? This is Jeff and we are here with 4th. I'm doing a personal for Kenneth Kenneth. Good luck We got top scrum black 2023 super excited happens to be my favorite products, and it's my first personal rip. So Hopefully hits you nice bang. That's a lot friend Jeff said he's pulling an angel Hopefully a trout or no, Tony Good you know, I just like to casually rip it nice and slow I can make almost I can make my shots. No peeking. That's the luck first pack. Let's get it Not a bad start a little Adley Ryan Mountcastle the 150 and we got a tow bar Too shabby friend and They hit for you Kenneth. That's the luck. It's a Yankee Anthony Volpe. Not a bad start dude. Congrats. I'll go to you friend I'll bet start for my first trip. I would say gold Glover Anthony We can keep sleeps next time Alright Kenneth that'll do it


Biosyramic-based root canal sealers have been shown to be biocompatible and comparable to other commercially available sealers. However, their clinical outcomes remain unclear. This article was authored by F.A.L. Haddad and Z.H.A.A.B Aziz.