The fundamental equations of thermodynamics just start with the DG equation you can do a similar treatment with others so we have seen quantities of interest are essentially ?G correspondingly ?A ?U ?H and so on and minimum value of say G constant T and these are the two quantities of interest in order to do this we need G since this is your work calculation this is your equilibrium calculation you need G as a function of temperature pressure and composition put this in squiggly brackets to indicate in I from I equals 1 to the number of components usually you get these relationships through Maxwell relations that is you find out how it depends on T how it depends on various quantities through the Maxwell relations so you have ?G by ?T is this is –S ?G by ?P is V ?G by ? and ?I but therefore what you need really these quantities you know for example S with if you want to know how S varies again you go back to Maxwell relations you got S with respect to P and so on so all that you can do the only thing you cannot get from here is from Maxwell relations writing getting bad to us if I keep all the variables constant except say N1 and N2 I get equations like this or I and J ?mu I with respect to ?NJ both are equal to of course ?Squad G by ?NI ?NJ normally if you want S with respect to Ni for example what you do is to keep S DT and ?I Ni Dni alone all the others you will keep constant then your Maxwell relation will give you the second partial of G with respect to T and Ni is S with respect to Ni that is equal to you will get the derivative of ?I let me do this first of all let me say this has been reduced to an equation in the chemical potential so we will say need ?I as a function of TP XR-1 so from one I get partial of ?I with respect to T is the same as partial of minus the partial of Si with respect to Ni S with respect to Ni this is ?I with respect to T holding P and all NJ constant is a better way of getting this is not a measurable quantity I told you you stop whenever the right hand side is a measurable quantity so if you differentiate ?I by T with respect to T you get this quantity this is the same as Si bar you said all partial molol quantities are obtained by differentiating an extensive variable with respect to Ni holding T and P constant that is important other molol numbers but T and P are the important variables so if you do this you get minus Si bar of course by T I am differentiating Mu I I get minus Si bar minus Mu I by T square this is the same as 1 by T square minus 1 by T square into T Si bar plus GI bar Mu I is the same as GI bar because G we saw that last class G with respect to Ni holding TP and other molol numbers constant is what you call GI bar and this is minus HI bar by T square so I have one equation that says Mu I by T and keep this equation HI bar is simply in the partial molol property with respect to enthalpy changes in enthalpy are measurable so we will show that this is a measurable quantity so this is equation 2 I will show you how it is actually measured little later we will simply note that this is a measurable quantity you can get a lot of data on HI bar so since I am interested in this equation here the chemical potential as a function of TP etc because my chemical equilibrium is governed in phase equilibrium by Mu I alpha is equal to Mu I beta and if I have Mu I as a function of temperature pressure and composition I can solve the phase equilibrium problem in principle so I have got this I need to know Mu I as a function of P this is very straightforward here Mu I with respect to P will be the second partial of G with respect to Ni and then with respect to P that will give you the first partial of V with respect to Ni this is VI bar this is equation 3 and this is also a measurable quantity volume changes enthalpy changes are measurable and from these changes I can actually calculate HI bar and VI bar now when it comes to composition dependence if I take two of these the third equation is the hardest Mu I with respect to XJ or NJ sorry I should finally differentiate with respect to XJ but right now I will do it as it stands here I take Mu I D Ni and Mu J D NJ all others I hold constant I simply get Mu J with respect to Ni all it says is that the chemical potential of component I depends on the number of moles of J exactly like the chemical potential of J depends on the number of moles of I but since I do not know either I am left in square one this is actually the basic problem of mixed thermodynamics or challenge essentially you do not know the chemical composition dependence of the chemical potential uniquely and there probably no unique solution because the different mixtures behave differently the question is how do we describe this composition dependence in some meaningful form how do we model it you have of course we derived last class you know we integrated this and differentiated it and obtained the Gibbs-Duhem equation subject to I will say 0 is equal to you know we got this that way Ni sum over I Ni D Mu I subject to the Gibbs-Duhem equation so these five equations are the fundamental basis of all mixture thermodynamics although you can play the same game with AU or H you can play the equivalent game with all those equations this is the simplest because T and P appear explicitly here and for chemical engineers T and P are the most natural variables so what I have to do out of all this mess is to derive see first of all let me say this having by writing this equation down I am saying all the chemical potentials together the changes in the chemical potential are constrained by one equation and then I have this equation if between my claim is that between these equations I have essentially one independent chemical potential which I cannot whose composition dependence I cannot describe if I fix that I can solve for all the others so I will show that explicitly what I am going to do is derive a set of partial differential equations for the chemical potential that will give you a method of solving for the chemical potential all chemical potentials except one and one will be completely arbitrary and then you actually call on some philosophical ideas in physics you say you cannot model Mu1 why did you choose one why did you choose component 2 why did you choose component 3 so these questions will arise so we will find a common property which is the free energy change of mixing ?g of mixing what we will do is take the pure components form the mixture in a thought experiment and ask what is the change in free energy and if I will show that if I can model that change I can get all the chemical potential so that is what I am going to do in the next probably half an hour or 45 minutes let me start here all I am going to do is I want to simplify this equation to simplify this equation the aim is to get I will say to solve for Mu I because it is an intensive variable it can only be a function of TPX1 through XR-1 there are only R-1 independent composition variables so I should be able to solve for the chemical potential as a function of these in fact if I give you that rest of thermodynamics is trivial it is because you do not know this that you have to make so many extensive measurements in thermodynamics and go through complicated manoeuvres to predict phase equilibria and reaction equilibria so to do this what I do is to go back here and substitute for D Mu I if Mu I is this D Mu I is going to be partial of Mu I with respect to T DT plus partial of Mu I with respect to P D P plus sum over K Mu I with respect to XK TXK where I have written D Mu I with respect to XK this is actually the partial in this equation TP held constant plus XL any arbitrary composition which is not equal to see I am differentiating here Mu I with respect to XK X1 through XR-1 XK cannot be held constant but since mole fractions are not independent I also have to allow one more to vary which is XR I have written up to XR-1 so here L should not be equal to K or R it is this is change in Mu I with respect to change in XK mole fraction of K holding TP in all mole fractions except XK and XR I would not write this explicitly it is sort of understood in the context all the time come back again and again all I do is put this back in here remember that this is Mu I with respect to T at constant P and all mole fractions that means it is the same as what we got here or Mu I this can be written as right now I would not bother whether it is SI bar or this is the original equation or this I can write it in either form this equation I use Mu I with respect to T is holding all the mole numbers constant and P constant it is equivalent to that in a mixture except you are talking of one mole of the mixture so this term is the same as minus SI it is still minus SI bar DT plus VI bar DP this is also the same plus this as it is now you have to recall and write this in general in general this is what we showed in general for any extensive property DE you can write DE is equal to partial of V with respect to T DT plus partial of V with respect to P DP plus sum over EI bar DNI this is going to be a large amount of manipulation but the final form of the equation is so nice it makes the whole process worthwhile where this is really this is what philosophers call an anthropocentric point of view you are stuck with your notions of equality even if it is not realized in real life you are stuck with your ideal notions of equality impartiality and so on so I cannot model one chemical potential Mu I there will be a hue and gray so I have to model a common property of the mixture and then derive values for Mu I Mu II Mu III etc sort of we are stuck with that mode maybe it is easier to model Mu I and be done with it in each mixture you can choose one component for which you can guess its physical behavior and do it but in when deriving a general theory use these principles all the time so I have this equation you know by integrating what you will get integrating assume this is at constant T and P you will integrate exactly like we did before EI bar is an intensive variable so using the assumption or hypothesis or actually using the fact that EI bar is intensive I told you the big difference is between intensive and extensive properties if it is an intensive property if I change only the mole numbers but keep the composition the same EI bar will not change I will get E is equal to sum over Ni EI bar and then by differentiating this or this is the important result you get a Gibbs-Duhem equation for every property EI bar by differentiating this and comparing with this in particular the most useful Gibbs-Duhem equation is this equation here 5 is a particular case of that result and this is what we use repeatedly and therefore this is generally this is referred to as the Gibbs-Duhem equation but you have a whole series of Gibbs-Duhem equation but this result is important whenever I get Ni times EI bar I simply get E back so if you look at this result here if I substitute this D Mu I here if I put Si bar here I get Ni Si bar sum over Ni Si bar is S Vi bar if I put in here Ni Vi bar is V so I will get back SDT and VDP that cancels with the right hand side so what I have left is this here so let me write it out so we will substitute this is 6 this equation is 6 substitute 6 in 5 sum over the left hand side becomes minus SDT and use let us use this we will call this 7 and use 7 you get minus SDT plus VDP plus the last term there which is sum over K coincidentally this sum over K is not over all mole fractions R is not included because the variables are X1 to XR minus 1 so you must write here K normally this is denoted by a prime on the summation that means one mole fraction does not come in the summation usually the last mole fraction by convention so I will put a sum here prime or I will write explicitly K is equal to 1 to R minus 1 and then I have this summation anyway summation over I equals 1 to R of Ni times doh mu I by doh XK DXK this is equal to minus SDT plus VDP right hand side I am copying as it is the left hand side if I substitute this I get minus SDT if I substitute this and some I get minus plus VDP in the last term gives me a double summation so the result simply says sum over E sum over K equals 1 to R minus 1 sum over I equals 1 to R and pull out a total number of moles XI here that is if I divide this by the total number of moles I will get XI but first the argument here is the DXKs are independent thermodynamics demands that this should be 0 the left hand side should be 0 the left hand side should be 0 under all conditions since DXK are arbitrary I can change these mole fractions because this goes only up to R minus 1 I can change any of the mole fractions exactly as I please and this should still be 0 therefore this implies that sum over I equals 1 to R of XI partial of mu I with respect to XK is equal to 0 and you are pulling out the case so for all K for all K equal to 1 to R minus 1 when you derive a theory it has to be proof against all perversities so if you give me any holes I will choose a mixture where I change the mole fraction of only one component and then if you told me this was not 0 for that component then you will get a contradiction here essentially you will get as contradiction of the two laws because you can trace back all the way and go back to the laws from which you derived these. So this is the Gibbs-Johem equation now it looks a little nicer it looks as if all the chemical potentials are treated equally but even this is not good enough notice that the Gibbs-Johem equations now explicitly appear as R minus 1 equations for every K you can write that equation so it is a set of R minus 1 equations which was not obvious from the original Gibbs-Johem equation right this is actually a set of R minus 1 equations for R unknowns µ1 µ2 through µR so you have R unknowns namely µ1 µ2 etc µR and R minus 1 equations because you have what I it is 8 yeah you have equation 8 for K equals 1 to R minus 1 it has to be valid for every K so you have 1 degree of freedom there is no way you can uniquely solve that set of equations if you assume one of the chemical potentials then you have R minus 1 equations for R minus 1 unknowns and again I am assuming given a set of equations you have solutions to it proves they will goes through a painful proof showing that does in fact but having said this I want to set this in a slightly different context let me go back and look at the process of mixing all this trouble arose because of the process of mixing so if I examine that process I can show you that there is one way of getting everything from a combination of chemical potentials that does not specify any one chemical potential uniquely if I look at the process of mixing and I look at G after mixing and G before mixing like AD and BC after mixing and before mixing so G I am looking at delta G for this process delta G is actually G after mixing minus this definition G before mixing I cannot measure delta G but I can measure delta H of mixing delta V of mixing the change in enthalpy change in volume those are measurable quantities but let me derive this here an expression for this this difference is simply sum over I XI Mu I minus Mu I pure if you look at G before mixing all the components were pure components I take X1 moles of 1 X2 moles of 2 etc so I have XI Mu I pure I sum it up I get the free energy before mixing but because Mu I is a partial model property after mixing it simply XI Mu I you can write this for any extensive property you will have to write EI bar and small EI similarly this is GI bar minus Mu I but GI bar has a nomenclature now we call it Mu I symbol okay so then let me write DG again now let me do this sorry let me write D of delta G partial of delta G with respect to say X1 let me do this for a binary and then we will do this for the more complicated it is very straight forward but if I do it for the binary it will be easier let me first do this for a binary I will show you the results and then we will go on to the mixtures let us take a binary mixture so delta G is simply X1 Mu I minus Mu I pure plus X2 into Mu II minus Mu II pure then I want to ask what is partial of delta G with respect to X1 this is done at constant T and P in the case of a binary mixture I can hold only T and P constant as I have to allow X1 to vary so I cannot hold X2 constant if I differentiate this if I differentiate this I get Mu I minus Mu I pure if I differentiate X2 I get a minus sign then I have to differentiate what is inside plus X1 this is a function of composition this is not so I get delta Mu I by delta X1 plus X2 delta Mu II by delta X1 now notice that this term is identically 0 according to the Gibbs-Johm equation the Gibbs-Johm equation there tells you for a binary in a by in the case of binary K can be only one so you get X1 partial of Mu I with respect to X1 plus Mu II with respect to X1 the denominator variable is the same in the Gibbs-Johm equation so you will get X1 XK the same in the denominator numerator will run through all the indices because this is 0 I can now look at these two and solve for one of these for example Mu I minus Mu I pure if I want to solve for Mu I minus Mu I pure all I do is multiply this equation by X2 and add give these numbers again we will call this 9 this is 10 and this is 11 so Mu I minus Mu I pure I will simply say solving 10 and 11 this is simply equal to delta G plus X2 into delta partial of delta G with respect to X1 if I switch the indices 1 and 2 I get the equation for 2 so what this tells you is that I can get the chemical potentials 1 and 2 from delta G itself you can do this in a mixture in a multi-component mixture clearly because you will get this R minus 1 equations and this one you simply solve for the differences Mu I minus Mu II Mu II Mu I minus Mu I pure or Mu II minus Mu II pure and so on but essentially now solving the Gibbs-Johm equations you cannot solve them uniquely so we will simply say the Gibbs-Johm equations represented by 8 have a unique solution they have one degree of freedom regardless of the number of components in fact if I do this in the general case let me just write this down now I take equation 9 differentiate equation 9 with respect to whenever you make these differentiation you choose index other than the dummy index here so with respect to XK then you will get partial of delta G with respect to XK is equal to sum over I XI delta XI with respect to delta XK you hold doing this holding TP XR is not a variable in the problem you are differentiating with respect to XK so you have to allow XK to change so XK XR are not held constant all others are held constant here so you are doing this differentiation here XI with respect to XK holding again XL not equal to K R times Mu I minus Mu I pure plus sum over XI partial of Mu I with respect to XK because Mu I pure is not a function of composition I differentiate this term first and then I differentiate this term and differentiate that time I get luckily the exact thing that I have in the left hand side of the Gibbs Duhem equation so this term is 0 I will copy this here then I can erase that also okay now XI with respect to XK because all others are held constant when XI is equal I is equal to K you will get 1 when I is equal to R this summation is over all components and I is equal to R you will get R XR is 1 minus X1 X2 etc XK so you will get a minus 1 that is the only difference so partial of delta G with respect to XK has only two terms 1 is Mu I minus Mu I pure no sorry Mu K minus Mu K pure when I is equal to K you will get a contribution and then when I is equal to R you will get a minus contribution Mu R minus Mu R pure it is called this equation 12. So if you look at equation 9 and equation 12 this is actually a set of equations this is R minus 1 equations because you have to write one such equation for each value of K other than R so if K equal to 1 K equal to 2 up to R minus 1 so you have R minus 1 equations and I have one additional equation that I have introduced here so I have R equations for R unknowns so you can solve for say Mu K minus Mu K pure I will simply say Mu K for Mu K minus for all K given delta G as a function of TP and X1 through XR minus 1 I have to give you this function if I tell you what delta G is as a function of composition if I give you this as a function of composition then by solving these equations simultaneously I can get every one of the chemical potentials what thermodynamics tells you is that this is not unique so when you say modeling in thermodynamics it invariably boils down to guessing a function F and you can guess any function F you will produce your own functions every one of you can have a model in thermodynamics except that nobody else will use your model unless the results you derive from that model agree with experimental data for a large class of systems no point having a model for each individual systems that means you are only measuring data or you are describing it but if you have the many classes of systems that you can describe with a one function I can have a model for delta G which describes all ideal mixtures never another model that describes all alcohol water and polar non-polar mixtures and so on. So if you can find a model for a class of systems then you are in business so essentially the task of thermodynamics is to guess a delta G the delta G should have some boundary conditions you cannot get a delta G function that is non-zero when you have only a pure substance that is when I do not have a mixing process it should go to zero so when all the mole fractions go to zero except one which is one then delta G should be zero so there is some boundary conditions you have to satisfy for example for a binary mixture you write delta G as X1 X2 times a function arbitrary function that function cannot be infinite it has to be a bounded function that is all. If you write X1 X2 in front automatically when X1 goes to one or X2 goes to one it will go to zero so you are safe so they use some games and then you can say you can use Weierstrass's theorem and say what can f of X1 be whatever it is I can approximate it by a polynomial so I will write a polynomial and you can write a whole series of models like that that is called the Wohl's model Wohl introduced this polynomial expansion so you can get several models initially people derived models in different ways the most interesting model though was the very first one which was quite exciting which was derived by Van Laar, Van Laar was a student of Van der Waals it is one of the most beautiful papers in mixture thermodynamics after that people discovered that you could write arbitrary functions from real analysis they said after all what can this function be it can be a polynomial and so on. So there are different forms of this and what I will do is go through and start with Van Laar's incidentally there are two this whole all these theories the thing that I have derived and the delta G expressions that you get are all all come under what are called physical theories of solutions these come under theories of liquid mixtures they assume that if you know the components in any given mixture in 1890s there was another guy called Dolzaleck in this guy said actually you guys are all mistaken first of all I will show you a concept here of an ideal mixture you can show what is the simplest solution to the Gibbs-Johem equation and that is called the ideal mixture he said Dolzaleck said all mixtures are ideal you know you behave non you observe non-ideal behavior because you are a fool and you are looking at the wrong components actually in a mixture of 1 and 2 the real substance say A and B the real substance may be A 22 B 1 or it may be and A 12 B 13 you do not know they may be they associate that way and if you looked at the right components all mixtures are ideal that is if you look at it as a mixture of A 22 B and A 12 B 13 it is an ideal mixture but if you look at it as a mixture of A and B as some foolish human beings too and this is from Dolzaleck but let me first look at I think the simplest thing is to first start with ideal solutions the word ideal is used in this context as the simplest solution to the Gibbs-Johem equation and this is done by inspection I have this Gibbs-Johem this is sum over 1 into R J is 1 to R – 1 this is the Gibbs-Johem equation simplest solution I will write down a solution I will assume that mu I depends only on the composition of I you can treat it as a pure guess or you can go back and apply everything to an ideal gas mixture and derive this result as well it is possible to do it both ways but as far as I am concerned the Gibbs-Johem equations always have 1 degree of freedom and I can make a guess is just you treat this as an intelligent guess and then we look at the thermodynamic consequences I will show you that this corresponds in fact to your exact notion of an ideal mixture an ideal mixture is one in which it consists of molecules that do not have interactions between them so there should be no energy change when you mix things ideally and I will show you that this result actually agrees with that and I will also derive a result for the entropy of mixing which will be the same as what you would get if you went back to an ideal I will show you but we will come back here just substitute this here if you substitute this here you are going to differentiate with respect to xj again holding all mole numbers all mole fractions constant except j and k right j and r because this one the differentiation is j equals 1 to r minus 1 and you are substituting this here you get xi log xi with respect to xj in the only two variables that can change are i equal to j and i equal to r so you will essentially get when you substitute this here to what was this equation this equation is 8 substitute into 8 you get xj partial of log xj with respect to xj plus xr partial of log xr with respect to xj that is all on the left hand side all others are held constant this is equal to this is 1 by xj into xj which is 1 this is 1 by xr into xr into minus 1 because xr is 1 minus x1 minus x2 etc up to xj so 1 minus 1 so this is identically 0 all I am saying is I have got a set here that satisfies that equation you can actually guess the solutions to this equation by hook or crook I do not care how you get the solution as long as you have a solution it is a valid thermodynamic model for as far as I am concerned so valid thermodynamic model for chemical potentials from this you then derive results in phase equilibria you derive results in reaction equilibria and if it does not agree with any experiment your model will be thrown out the test of the model is simply agreement with experiment finally otherwise it is as far as thermodynamics is concerned supremely indifferent anything that satisfies this set of equations is a valid model in fact you may be able to find for every model you write you may be perverse enough to write all kinds of complicated models involving transcendental functions but you will find one system that satisfies that model you can always find a system but that is no meaning at all I mean what you have to do eventually is to give some physical meaning to the model your parameters in the model you have to relate it to something and so on so this equation this is called an ideal mixture let me show you the consequences of this we have mu i by t with respect to t is h i bar by t squared this is thermodynamics take this model if you differentiate mu i by t I mean if you different first divide by t and then differentiate you get mu i pure by t on this side it is mu i by t right from the model I get mu i pure by t by t and then if I next term is 0 because if I divide by t and then differentiate our log x i with respect to t is 0 because I am differentiating with respect to t holding p and all of all mole fractions constant but this is again from thermodynamics this is thermodynamics here hi by t squared small hi is specific enthalpy of pure I so it says hi bar is equal to hi that means there is no enthalpy change for each for any component per mole when you do a mixture this means delta h is equal to 0 because delta h mixing is h after mixing minus h before mixing h after mixing is x i hi bar some and before mixing it is a hi x i times small hi this you know is ideal behavior this is what you understand by ideal behavior that we know interaction energies if there were interaction energies or equal interaction energies between all pairs right this out between between all pairs of molecules this happens for example in homologous series you mix methane and ethane really no intermolecular force difference between a molecule of ethane a molecule of methane so such mixtures often have delta h equal to 0 no energy changes occur in so the word ideal therefore etymologically is acceptable it describes exactly what you would think of in a mixture of substances that had no intermolecular forces stop there it is only 40 seconds what I do is continue next class and complete the ideal mixture in what I will do is to introduce chemical potential you will write mu i is equal to mu i pure plus rtln ? i x i an activity coefficient the reason engineers need an activity coefficient is because you need a default option it will always be systems about which you are ignorant so in your computer program you must be able to say if I tell you nothing ? i equal to 1 whereas for chemical potentials I did not have a default option but here in the you have to say at the worst case I can I guess ? i equal to 1 or if you do an iterative calculation you will start with ? i equal to 1 so in that sense it is better to use a variable that occurs that tells you the departure from ideality then use a variable that is


The fantasy football playoffs are just around the corner. We've actually had a pretty good waiver wire of week number 13. We're gonna break things down, let you know who to add, how do you players going forward and much more answering your questions live on air. This is the waiver wire Q&A right here on the FanDuel YouTube, Twitch, Facebook and Twitter channels. My name is Jim Sonnis. I am a senior writer and analyst for numberfire.com. Joined here as always by JJ Zacharias and the editor-in-chief of numberfire and FanDuel JJ. Happy week 13 to you. How did week 12 go for on your end? I haven't, it was the one week that I have each year where I'm in a ton of leagues and just across my leagues on Monday night, I lost so many games by like a point. It was just very, very depressing. It happens to me at least once or twice a year. You have those weeks. I'm trying to look at it from a process standpoint and feel okay about it but it was very depressing last night. Yeah, I lost my head to head on FanDuel with my coworker Brandon Gadoula by I think like a point eight points. So I feel you there. That one matters more than like the cash leaks because I got to be Brandon and I've not done so, so far this year. The way this will work is same as always where if you got a question about week 13 waivers, send it in YouTube, Twitch, Facebook, Twitter does not matter, send it in. We'll take it here live on air to get you set for your week 13 waivers. Let's start things off here with Elias over on YouTube. He's a recorder back replacement for Jalen Hertz with him potentially being banged up and then having a buy after that. So Taysom Hill is available. There are cards available preference for you for potentially a two week fill in for Jalen Hertz. Taysom Hill will be mine. I mean, I understand the worry about his foot and then the injury that he's been dealing with but I don't think they'd be throwing him under center if they didn't feel confident that he was healthy. And Dallas isn't the best matchup in the world but as in the, I mean, I haven't even looked at the week 14 schedule. So I'm trusting you that this is the matchup that they get the Jets next week. And if that's the case, obviously that's a great matchup for Taysom Hill. So yeah, I mean, Taysom Hill will be my guy, my go-to. I think Derek Carr is absolutely fine, especially this weekend's Washington. He should be totally good. And I think he's probably even a safer option than Taysom Hill just because we haven't seen Taysom Hill under center this season. But I feel pretty good about Taysom being able to get the rushing yardage and to do at least moderately and get moderately close to what he did last season. To me, he's like a diet Jalen Hertz in terms of how we should approach him in fantasy where I don't know if his passing's gonna be as good as Hertz. I know Hertz is coming off this terrible game, but it's not like he's just been this atrociously bad passer all season long. And I think Hertz just generally is a little bit more aggressive on the ground than Taysom Hill is, but the way they generate points, the way they score points very, very similar. So that's sort of how I would view Taysom Hill whereas Hertz is like a high-end QB one, mid-range QB one. Taysom's probably more of a low-end QB one. Yeah, and Sean Payton today didn't confirm that Taysom would start, but based on the reports, it sounds like that's a pretty sure bet. So I think if you are proceeding for today, I would assume that Taysom will be the starter for tomorrow. Let's talk to Jack here on YouTube. He has both Kirk Cousins and Russell Wilson. Is it worth it to drop Russ to add Taysom looking forward to the fantasy playoffs? So, I mean, it sounds crazy, but I think if you have Kirk Cousins, I would be okay doing that because I think Kirk is just the starter, like just the play over Russ from here on out. So you're really looking at that QB two. I mean, I'm assuming this is not a super flex leaguer or two quarterback link too. You're looking at a backup quarterback. You need some upside. I think it's fine. I mean, Russell Wilson looks broken right now. So I'm not really, I know his fantasy total looked fine. He was a top 10 quarterback this past week just because he was able to, I mean, number one quarterback scoring's just been down, but number two, he was able to get that touchdown at the end of the game to be able to, I think he had like two 47 and a couple of touchdowns. But yeah, I mean, I think that Taysum Hill still prevents or provides more upside than Russell Wilson does at this point, even though I don't mind the Seahawks schedule from here on out. I just don't trust this injury that Russell Wilson's been dealing with in the way that he's looked. Especially with you having Kirk Cousins as being a solid guy, it does lower the need to hang around for the upside there. Cause Kirk actually does have some upside too. Let's talk to Demetrius over on YouTube. Would you drop Logan Thomas for Cole, Comet, or Froston Monroe? Now we don't know yet the extent of Darren Waller's knee injury. Not sure if he will miss multiple weeks, maybe even play this week potentially as well. Logan Thomas came back last night, six targets, but the Washington football team seems like they want to be a pretty run centric team right now. So how are you viewing these tight ends here? Yeah, I mean, I was just looking over at my other monitor to make sure I had Logan Thomas' target share from last night. 17.6%, not bad. I think that you're right that they ideally want to be a run centric team. And we've seen that the last couple of times that we've seen them. But I don't know if they'll be able to necessarily do that, you know, just because of game script and game flow. Fortunately yesterday, they had a fairly decent game script for them to be able to do that. And not only that, but Seattle's been pretty easy to run on this year. So I'm not surprised they found success on the ground. So I'd probably still rather have Logan Thomas. It sounds like Darren Waller is more week to week, not like an IR situation. So he could be back next week. I think Foster Monroe is a good streamer this week because the last time we saw him without Darren Waller, he was the top five weekly tight end. But I think I would stick with Logan Thomas here because he's still, you know, 18% target share, sell six targets last night. I think he was fine. And they're facing the Raiders this week and that's one of the better games of the week, honestly, from like a total perspective. So I think that should be a good spot for Thomas to get back on track there. Let's talk to Joseph, picked up Dallas Goddart. He has now Goddart, Logan Thomas and Mike Gasicki has to drop one or two of those guys. So if you've got those three tight ends, what's the ranking of those three for you? Probably Goddart, Gasicki, Thomas. I know Goddart's coming off a really, really bad game, but I think that we can kind of throw out the Eagles offense this past week because they just didn't have it going for him. And then, you know, Logan Thomas we just talked about. I think he's still fine. I think he's fine, but I think he's still iffy. I'd probably go in that order. Goddart, Gasicki, Thomas. And Joseph, with that order being what it is, I would keep two because Goddart does have the buy next week. So you'll probably want someone to hang around for that buy with him. She can make one, four, five. If Jalen Hertz is still questionable by Thursday, do you go with Taysom Hill? So basically, do you take the guy you know will play or do you write it out and potentially put yourself in a thin situation with Jalen Hertz? That's tough. I mean, we only have so much information right now on Tuesday. I'm hoping that we would have a little bit more information. Like if Jalen Hertz practices, you know, today or sorry, tomorrow or on Thursday, then I think that you can feel confident in Jalen Hertz if he doesn't like, let's just pretend that he just doesn't practice all week.   But yeah, I mean, Taysom Hill is still a decent enough play is probably the top streamer this week. Yeah, I think that he'll give you 80% of what Hertz would give you if you're thinking that he might not go. It makes sense to just kind of lock him in there. Okay, Jim City Gridiron is in a good spot at Wide Receiver. Would you drop or shot Bateman for Boston Scott or Amir Abdullah given the injuries in those two respective backfields?  And if you think that Bateman can help another team, you know, I think we're at the point where I don't know if it's really gonna happen for Bateman this year in terms of just being like a reliable fantasy starter. He's probably gonna need an injury to Hollywood Brown or even Mark Andrews just to see better target distribution in his favor and that offense. And you know, we say it every week or at least I say it every week, you know, yes, the Ravens are more pass heavy than they've been in recent years, but they're still one of the most run heavy teams in football that still hasn't changed, right? And a lot of that is Lamar Jackson just running the ball himself. But, you know, I think I would feel okay enough doing something like that if you really, really need the running back help. And if you know that you won't be helping another team dramatically by dropping or shot Bateman. Yeah, I think that that makes a lot of sense. And especially with the Ravens passing offense being a bit dysfunctional right now, that does help things too. So Dr. Jack, once again, now would you be comfortable starting the Eagles defense for all three of their fantasy playoff matchups? They get the Giants twice in there and Washington once. So typically we wanna stream with defenses. The good thing is those are all streamable spots. The question is, is Eagles defense good enough to justify that? So JJ, would you hold them through their buy in order to get access to three okay matchups there? Yeah, I'm just afraid that they're not good enough, that they don't generate enough pressure that they're not gonna generate those sacks and the turnovers that we need. Could they be fine through those three games? Of course, yeah. But I would rather just find defenses during those weeks that have better matchups and play them over just saying like, I gotta stick with this one defense from here on out. If you have limited transactions or if you're not able to make transactions in the playoffs for whatever reason, sure, Philadelphia is a team that you could go after and target. There's better defense out there with better schedules like Buffalo, for instance, or even Tampa Bay. But yeah, I mean, Philadelphia would be fine from that perspective, but I would still much rather stream than just play with one defense from week 15 through 17. Right, I think it's another thing you talk about a lot where this is the time of year where you are okay adding handcuffs or running back. And if you're holding the Eagles defense until week 14 or week 15, I guess in this situation because they're a bi-week 14, you are burning one extra bench spot you could use on a backup somewhere else who may come into relevancy if something were to happen in the backfield. So I think the bench spot to be more valuable in that situation. Let's talk to Jeff. Is Matt Breda or Devin Singletary trustworthy? He has Nick Chubb on by, Miles Sanders, Alex Collins, Jeff Wilson Jr., a buddy, and Latavius Murray, his other options. Singletary did have a good snap rates on Thursday. He got some decent work. We know he has limitations, but I feel like when those are my alternatives, I'd feel a lot better about Devin Singletary suddenly. JJ, what are your thoughts on these guys compared to the other options? Yeah, I mean, I guess, right? Like I guess you would lean Singletary there, but I would rather not have to rely on a Buffalo running back. And who knows what happens with Zack Moss if they want to make him active again and utilize him again. They've been really weird with Zack Moss all season long. We went from him being inactive to him seeing the biggest workload in that backfield to him being an active again. And that was, you know, he did have that injury in there as well. But yeah, I mean, I guess Singletary, it's just a really tough situation to be in altogether. So sorry, Jeff. Yeah, condolences, Jeff and Godspeed. Let's talk to you, Richard here. Who would you pick up? Jordan Howard or Sonya Michelle? So Howard potentially could come back to a good role for the Eagles. Don't know his status this week as of yet. He was not put on IR though, which does matter. Sonya Michelle basically just directly a handcuff to Daryl Henderson at this point. So who do you prefer between those two? Yeah, this is one of those transactions where it just depends on what you need for your team. If you need production, if you need someone who could be a flex, you know, Jim and I were actually talking about this earlier today when talking about Miles Sanders. I mean, realistically, I think you can make the argument that Jordan Howard is the best running back on that team from here on out, as long as he's healthy, just given what he's done when he's played, how he works within that offense, and the fact that Miles Sanders has durability issues or has so far this season and last season as well. So I think you could at least make that argument. And I think that when Jordan Howard's back, we're gonna see him still see a pretty decent workload, you know, like 10 plus carries a game. So, you know, I think that he can work as a flex if you need something like that, if you're in a deeper league. But if you're not in a deeper league, if you're in like a 10 or 12 team league where, you know, you have two or three running backs that are really solid that you can throw in your lineup each week.  So I would rather hold Sonya Michelle in sort of a vacuum, but I can understand if you need to go Jordan Howard instead. My friends have showed us they would use Michelle heavily if Henderson were out. So I think that's a valuable information point to have as well. Let's talk to Larry. Is it time to drop manual standards? And obviously this is always dependent on what you're adding, dependent on what you got, stuff like that. But in a vacuum, JJ, are you okay dropping Manny? I guess, I guess.  You know, he started out so hot. He was seeing such good volume, especially deep volume and just hasn't been there, you know, as it was earlier in the season. You know, his like routes, run numbers are fine and he's getting a lot of cardio. There's not targeting anymore. And a lot of that I think has to do with the fact that they finally started to make Stefan Diggs the focal point of that offense again.  And that's her to manual standards just naturally. So yeah, I mean, I think if you're in like a 10 team league, 12 team league, there's reason to drop manual standards. And his target share with Dawson Knox is troubling is what I would say as well. Dawson Knox being back, looking good. That is a negative factor for Manny as well. Let's talk to Shane. He's got three tight ends. He's got Friar Muth, Goddard and Hawkinson. Who would you rank lowest in that group? How do you rank this, Jim? I honestly don't know how to rank this. I am actually- I think the factor for me is that Friar Muth is in concussion protocol. And that to me is a pretty major concern just because, I mean, Goddard is a buy too. So I think that's a factor as well. I don't know. I don't think you can drop Hawkinson because I just feel like the fantasy community and the fantasy world has sort of like looked at Hawkinson as this like bad tight end asset just because of what they spent to get him in the draft and like a lot of people were getting him over Mark Andrews and Mark Andrews is going off. So they're a little bit bitter about that. But Hawkinson's volume is still fine and Jared Goff's back and he still had a decent week last week because of that touchdown. It's tough though. I think all three of them are sort of in the same tier right now. So I don't really have like that strong of an opinion there. If you want to use that concussion as the tiebreaker then go for it. But I still think Pat Friar, I think all three are tight end ones from here on out. Yeah, especially with Eric Ebron and I are he's missing the next three, next two games at least and probably it sounds like more than that as well. So we've seen Friar Muth have a really good role when Ebron's been out. So they're upside there. Maybe he gets in a limited practice Wednesday. That could help things out but deciding right now is pretty tough there Shane for sure. Chris McAfrey, a mysterious needs a fill in for Christian McAfrey. He has Cuba Hubbard already. Would you go a Mural Abdullah or Boston Scott with that in mind?  You might be able to get some usability from Boston Scott this week because Jordan Howard might be out again. Miles Sanders is dealing with an ankle injury. He might not play. And so if that happens then Boston Scott's probably gonna see 15 plus touches in that back field which will make him an honestly an RB two, like a decent play. So yeah, I would say in a great matchup too. So I would say I would go Boston Scott there because you have Chuba Hubbard. I mean, think of it this way, you have Hubbard already. And if you get a mirror Abdullah, how are you going to handle that week in and week out? I don't think there's going to be a situation where like one of those guys captures the backfield very clearly, you know, over the next couple of weeks without CMC. So I'm probably going to go Boston Scott there if you already have Hubbard. And with the Panthers, it's not a good enough offense where you could potentially start both. Like it's not a, you know, sometimes with Tony Pollard and Zeke, you can like justify starting both. We're not going to get that from this Panthers offense right now. It's Dr. Cliff. Rest of season, Russell Wilson to a tongue of Iloa or Taysum Hill, what a wild, wild question if you would ask this a month ago. But here we are. Who you got rest of the way? I'd probably go Taysum. Yeah, just go with the upside with Taysum. I just, I don't know how you can trust Russ right now. I agree. Mainly a cake schedule looking good from that perspective looks good on paper, but he just looks a little bit broken right now. And Tua, you know, Tua has been fine.  You know, he's top 10 in efficiency in corner number five expected points model. He's basically scored 12 or 13 plus fantasy points in every single start that he's had this year that he's finished since week one. He had that bad one against New England. But yeah, I mean, I'd probably go Taysum Hill though and just go for upside. But it depends on, you know, if you don't want to risk it with Taysum, just look at what your waiver wire looks like. And, you know, maybe Russell Wilson's a little bit safer just because we don't know what we're going to get with Taysum and how long he's going to start or if he's going to start at all. Right. So, you know, if you want to go with Russ, I think it's fine. I don't think it's Tua. I would say go for upside though and get Taysum. Other thing the Tua to consider here is he does have his buy still and that is next week, week 14. He has a pretty good match for this week with the Giants then a buy. I think another good match meant for that as well. Yeah, the Jets. Yeah, and week 15. But keep that in mind, he doesn't have a buy coming up as well. Let's talk to Howe on YouTube. Who would you prioritize? We're looking for someone to pick up who they need to start this week. So, that's what keep in mind. Looking at week 13 kind of specifically here for a guy on waivers, between Boston Scott, Naheem Hines and Rex Burkhead in this situation where you probably need to start someone this week, which of those guys would you lean towards there? Yeah, I mean, I think I understand the logic with Naheem Hines because they get Houston this week and maybe you get a nice positive game script and they utilize him a little bit more as a pure runner instead of just a receiving specialist. But I'm gonna go with Boston Scott there for reasons I talked about before. I mean, not only did he have 62 and a half percent of the team's running back rushes this past week with Miles Sanders banged up in the second half, but if Miles Sanders doesn't go, if Jordan Howard doesn't go, Boston Scott's going to see 15 plus touches against the absolute best matchup that you could possibly find. I actually looked at my adjusted fantasy points and allowed numbers today. And if you look at not just like where the rankings are, but the amount of points that they allow above or below expectation, the Jets this season against running backs have allowed 10.6 more points to be scored on them than the team running backs average. So what that means is if a team goes into a game and they average 20 fantasy points per game, then the Jets would allow 30.6 fantasy points to that team. So yeah, it's a great matchup.  I mean, I really think that he'd be a strong RB too. Yeah, that would be pretty fun. The Jets, not great. Let's talk to Phillip here. Again, thinking about things in the short term, it looks like Jamal Williams is on waivers as is Chuba Hubbard. So good waiver options here, JJ. Jamal Williams or Chuba Hubbard, preference for you. So here's the thing. I think it matters if you're looking at this short term versus long term to some degree, because I do think that DeAndre Swift could only miss this week. You might not even miss this week, technically. So yeah, I mean, if you absolutely need someone to plug and play this week, I think it's very clearly Jamal Williams. I'm not very high on Chuba Hubbard in general for what he's gonna cost you, whether it's a waiver spot, whether it's a free agent budget. I just don't think that Chuba Hubbard is that worth it. I mean, we saw him with over 80% of the teams running back rushes without CMC, like a 10% target share per game without CMC, but even still he gave us zero RB1 performances in PPR formats and that was without Amir Abdullah. Now they have, for a lot of it at least, now they have Amir Abdullah and they've been utilizing him as the third downback in the past catching back. Abdullah, even with CMC playing the last few weeks, Abdullah has had a 14% target share per game over his last five. And so I just think that what we're looking at with Chuba Hubbard and Amir Abdullah is Hubbard sees early downwork. Abdullah sees negative game script and past catching work and Caroline is offense and the team isn't playing very well. So we should expect negative game scripts to hit, right? And so if that happens, then Chuba Hubbard just loses a lot of appeal. So I might say just go after Jamal Williams. You can have him this week potentially and then you have a handcuff, right? You have a guy who would step in and be an RB2 easily if Deandre Swift that ends up getting hurt or if this injury lingers more. So I would probably just go with Jamal Williams here over Chuba Hubbard.  Maybe I sound dumb, but I think it's the logical thing to do. I mean, I wouldn't be shocked if Amir Abdullah gets some like early downwork. Not like, I think that Chuba will be the main guy. I think that Abdullah will get some. Like, and I think that's enough to really ding Chuba. Here's the thing. I didn't mind Chuba Hubbard as a prospect. I mean, you know, his final season was a little bit worrisome after what he did the season before that. You know, there were definitely some flags, but he just hasn't been good. I mean, he just has not been good in the NFL. And I think that Carolina realizes that, which is why they went out and got Amir Abdullah in the first place, right?  Like it got worse and worse, you know, as the weeks went on without Christian McCaffrey. So yeah, I mean, I totally agree with you. Like I think in PPR formats, easily the better value in terms of what you have to spend to get them off the waiver wire is Amir Abdullah.  Yeah, I mean, the team has showed us what they think of Chuba Hubbard. And I think we should take that for what it is. I'll talk to Joseph here. Can you guys please rank these defensive options? Three really good ones this week. Got the Eagles against the Jets, Cardinals versus the Bears and the Rams against the Jaguars. So I think all three of these would be above the Bills. He's asked my trade avi is wiping out for the Bills. The Bills get the Patriots.  They don't take a lot of chances, a lot of risks, which is how you get points in fantasy. So to me, I feel like all three of those are above the Bills. You can correct me if I'm wrong on that, but I feel like I'd want those three options at least for this week specifically. Yeah, to be fair, the Bills recommendation was more about the playoffs because they get Carolina, then New England, which again, you probably won't wanna start them against New England in week 16, but then they get Atlanta, who's been the best team to play defenses against this year in week 17, the championship week. So, you know, the Bills were dropped. In this case, I would probably try to hold two defenses. I would actually go after probably the Rams against Jacksonville. You know, the Rams have been losing.  And, you know, they're just a better defense than Philadelphia, who has just as good of a matchup. So I might go with the Rams there. And then the Bills being dropped, I'd pick up the Bills too for what you'll get in week 15 against Carolina and then week 17 against Atlanta. Yeah, I think that this is a spot we're holding to does make a lot of sense. Let's talk to Jim City, Gridiron. Thoughts on the Dallas defense this week. It's Taysom Hill's first start in a while. Would you roll the dice on someone else? Now, I think what's worth noting here, it's not just Taysom Hill's first start, but the tackles are still hurt for New Orleans. I think Terran Armstead plays. Ryan Ramcheck seems a bit more doubtful right now. So how have you in the Dallas defense week versus likely Taysom Hill? Yeah, I mean, this is something that you talk about a lot, Jim, is that you don't necessarily want to use a defense against a run-heavy offense, which is what we're gonna get with New Orleans. Not only have they been run-heavy so far this season, but with Taysom Hill, we're gonna expect like a 0.75 pass-to-rush attempt ratio. I mean, it's gonna be very, very low. And the reason why we say that is because you want drop backs because drop backs generate sacks.  And so from that perspective, Dallas isn't as attractive, but I do think Dallas is still a decent enough play.  Yeah, they're pretty heavy favorites, like five and a half point or something like that. Yeah, four and a half now, yep. Okay, four and a half. So, you know, they're decent favorites this week, you know, from a process standpoint, they still make sense. Yeah, and I think that they're fine. If you have options like Joseph had, where it's like, you've got the Eagles, got the Cardinals, got the Rams, I'd be okay passing on Dallas and just getting one of those options instead in the situation. Now this one is, it sounds like it starts it, but let's kind of address this in terms of how you're feeling Alexander Madison with Dalvin Cook being banged up. It seems like it'll be two games for Dalvin, because they play Sunday and then play Thursday. Quick turnaround, most likely scenario is he sets two games. Are you just putting Alexander Madison back in the role he had earlier on this year?  Unlike last season where that Atlanta game is the one that everyone remembers when he was chalking DFS and, you know, the game script got out of hand for Minnesota. So they didn't, they didn't utilize, I think they actually utilized a mirror bullet last year, right? Instead of- They did this year, but it wasn't just that of you. Oh yeah, yeah, yeah, yeah, yeah, okay. I think it was Mike Boone? Was it Mike Boone? Maybe, yeah, regardless.  But what we've seen in the two games without Dalvin Cook is that Madison had a 21%, a 23% target share in those two. That's better than Dalvin Cook usage in those two games. But it's a small sample. So take that with a grain of salt. But, you know, I really think that they're just gonna utilize Madison as Dalvin Cook. So he should be rostered. He is your number one priority if he's out there. Get him at all costs. If you have a number one waiver priority, burn it on Alexander Madison. I would use most of my free agent budget on Alexander Madison because there's a lot of, you know, what we know right now and what we think is gonna happen right now is that Dalvin Cook will be back in two games or three games. You know, he'll miss two games, he'll be back on the third game. But things can happen. You know, the injury might linger more. Minnesota might just be out of it, right? Like Minnesota might just not be competitive enough. And so they don't wanna risk it with Dalvin Cook. So there's a lot of reason to just go all in on Madison. At the very least, you'll get two weeks out of them as an RB one. And then you'll get a good handcuff whenever Dalvin Cook comes back. And it's worth noting too. This is not the first injury to Dalvin Cook's left shoulder. That is also worth noting in terms of this. One thing I would say is that I think that Kenny Wangu will probably get more work than Amir Abdullah did earlier on this year.  Like it's not gonna like, you can downgrade Madison for where he was, but a downgraded Madison, 80%, 90% of what he was is still a lot better than Boston Scott.  He is amazing. And would love to see it, not expecting it to downgrade Madison too much though. Let's talk to Shane. Well, don't worry about next job. After this past week where the Browns had to air it out because the Ravens dictated that they did so. So Creamhunt is back. Browns are on a buy. What is your only for Nick Chubb after the Browns buy week? Yeah, I'm gonna pull up his numbers really quick just so that I'm citing it properly. I mean, he had a 12% target share this past week. That's better than most weeks for him. So that was good. I mean, a lot of that has to do with the fact that they have no alternatives in that offense to throw to. Not a strong running back rush share though this week with only seeing 53% of the teams running back rushes. I wouldn't necessarily expect that, especially because against Detroit, it was 73%. I think Chubb is gonna be mostly fine. My bigger worry is the environment and the fact that Cleveland's just not moving the ball at all down the field. They're just not effective. And obviously that stems all the way to Baker Mayfield and his injury and what he's been dealing with, et cetera. So I think that's the bigger concern, but I would still say that he's like a low end RB1 from here on out. And the Browns offense probably isn't gonna get a ton better after the buy because Baker's knee and stuff will get better but the left shoulder is not gonna heal over the buy. That's an all season thing. So that's not the buy won't heal everything from that Browns offense. Joseph, little word on Matthew Stafford, is the concern for you at Matthew Stafford enough where you would use the guy like Taysom Hill over him or do you ride Stafford at home against the Jags? In these situations, I think it's okay if you're able to roster two quarterbacks. Like if you're able to play by matchup, see how it goes with Taysom, like I would just feel a lot more comfortable having Stafford on my roster, playing him against Jacksonville, right? Having Stafford on my roster, playing him against Jacksonville, and then just see how things go and you can then play by matchup with Taysom Hill because what if Taysom Hill comes out and sucks, right? Or what if Taysom Hill comes out and he's awesome? You just don't know. There's a wide range of outcomes here. So in this case, I would much rather, so would you prioritize Taysom Hill as a pickup? Depends what's out there. I think it's fine though if you wanna add Taysom Hill with Matthew Stafford on your roster. And I think what I would do is I would play Stafford this week, keep Hill around in case things get worth for Stafford, but I think I'd rather have Stafford for this week specifically, but worthwhile to have Taysom Hill on your roster as well. Larry David, doubted it's him. Thoughts on Brandon Iucanilla and Mitchell going forward with Debo expected to miss one to two weeks. The very rare situation where a wide receiver injury impacts the running back rush share or the rush share of a running back. So how does it impact things for you with Debo likely missing a couple of games here? Yeah, so let's look at Elijah Mitchell. I think that it obviously will help Mitchell just see his typical floor in terms of volume. But the other thing with Elijah Mitchell that I feel like is going overlooked is that your Michael Hacy's been out and that's a huge reason why Mitchell wasn't seeing a big target share earlier this season. This past week, he hit a 23% target share which was amazing and by far his biggest and highest target share of the season. So Eli Mitchell without Hacy and Debo is an RB one. Brandon Iuc I think is a good play too without Debo. I mean, we've basically seen that going on because Debo hasn't been playing as much wide receiver and seeing as much volume through the air as wide receiver but Iuc's been good. So yeah, I mean, I think that Iuc is fine. They were both good already. And I think they both get upgraded with no Debo because they will like, we talk a lot about how good players being in roof and offense can ding everyone because the offense becomes less effective like Calvin Redley with Atlanta but because they've got depth because their offensive line is good because Kyle Shanahan is pretty smart and they can still feel good and upgrade those guys due to volume despite Debo being gone. One final one here similar to the manual Sanders question can we pull the plug on Cortland Sutton? Denver refuses to give anyone outside of Jerry Judy more than four targets in a game. So where are we at with Cortland Sutton right now? Yeah, I mean, the other point about, so okay, so Cortland Sutton is averaging 4.2 fantasy points per game with Jerry Judy a 10.9% target share with Jerry Judy. It is, it's atrocious. I mean, you can find that with like, not only waiver wire guys, but like bad waiver wire players. Like you can, you can, yeah, like you can easily replace that production. Not only that, but the one thing that I'm a little bit worried about and this extends to Jerry Judy as well. Rest of season, the best running back schedule in fantasy football and in football, Denver has it. And so I could see them leaning on the ground just as much as they've been and that really obviously benefits Melvin Gordon and Javante Williams. So I'm worried about both wide receivers hold, hold Jerry Judy because he's still seeing a decent enough target share. I didn't this past week, but it was a tough matchup. Still seeing a decent enough target share with Courtney Sutton and a lot of leagues like 12 team leagues, you can probably drop them. And it does put Noah Fant more in the streamer conversation versus like a locked in type tight end situation cause he's also getting like, again, four targets per game. All right, that is all the time that we have here for today on this waiver wire Q&A, but we have plenty of shows coming on later this week. Tom Vecchio will be on Tomorrow Talks and NBA DFS. We of course have the Thursday night preview of the brand of Ghadjula coming up on Thursday and the snake draft will be on Friday of this week. So make sure you are subscribed to the Fando YouTube, Twitch, Facebook or Twitter page wherever you prefer to watch, hit subscribe there, watch on YouTube, hit the like button because it does help us out a bunch. Find JJ's podcast, the late round podcast wherever you get your podcasts and find 15 transactions over at numberfire.com. JJ, appreciate the time and good luck with waivers for you tonight. Thanks, Jamie, too. You can also find JJ on Twitter at late round QB. I am at Jim Sonnis, J-I-M-S-A-N-N-E-S. Big thank you to Joy Affleck, our video producer for running the video side of things here today. Thank you, Joy, as always. And thank you to everyone for tuning in. Good luck to you with waivers. Good luck to you in potentially the fun week of the regular season. We'll talk to you once again next week. This has been the Waiver Wire Q&A.


This is single factor ANOVA done using Excel. Single factor refers to just a single variable. This is a typical problem. The data table shows the energy consumed in millions of BTU in one year for a random sample of households from four regions in the United States. At alpha equal 0.05, can you conclude that the main energy consumption of at least one region is different from the others? Perform a one-way ANOVA test, and we assume the population variances are equal, and the populations are normally distributed. For the ANOVA, our null is always that the means are equal. Mean one equal mean two equal mean three equal mean four. And the alternative is always that at least one mean is different. The ANOVA will not directly tell us which mean is different if it's significant. We'll have to do a post-talk, a subsequent test to find out that. Excel, with the data analysis tool pack, does give you a tool for conducting the single factor ANOVA. But it stops short of running the post-talk, the second part of the test, to tell us which groups are different if indeed the ANOVA is significant. Remember in the ANOVA, if the ANOVA is significant, that means we reject the null that all of the means are equal, and that at least one mean is different. In your assignment package, you will find a spreadsheet that looks a little like this. What you will need to do will be to find your data and enter it in this part of the table. And then you need to run the ANOVA and this red cell becomes very important. Let me show you how to run the data analysis ANOVA. Click on data, data analysis, bring up the dialogue, and find the ANOVA single factor. Click on that, click okay. And we bring up this part of the dialogue and we clear out what we have there. We want to put the input range in this window for the ANOVA, you need to have all of your regions in this case adjacent. You can't have any gaps between your data. So here I'm going to select that range, it's grouped by columns it is, and then the labels are in the first row, which it is, my alpha is .05, and here's where that red cell comes in. You want to make sure that's cleaned out, put your cursor in there, and then click on the red cell so that the ANOVA is printed out in exactly the right spot so that the rest of the test works. I'm going to click okay, and you can see we get the ANOVA output here. We get the summary of the data, the counts, the averages, the variance. This is the ANOVA itself. You can see that we've got a p-value that is less than .05, which means we reject the null, and that tells us at least one of these means up here is statistically different. And the reason you can't just look at them and tell which one's different is because of the large variances. Once we've done that, the rest of the table, the second part of the test, it's called a Tukey Kramer, is completed for you except for this one blue cell, which is the Q-statistic, and I'll show you how you get that now. In this other data section of the Tukey Kramer, you see that we have our alpha there, .04, we've got a cell that's labeled numerator degrees of freedom, which is four, denominator degrees of freedom, 16. We use that information, those three pieces, and we'll go into a Q-statistic table, which is provided for you. This one is for the .05 alpha, and the columns are labeled number of groups, which is number of treatments. In our case, that's the number of regions, so we've got four. And from the table, we can see the denominator of degrees of freedom is 16. So we go down here for 16, look over in the four column, and we see 4046 would be our Q factor. You take that information, and I'm going to type it in there, .046, hit enter, and this part of the table updates. You can see that the calculations show in the results here that group one and two are not different, group three and four are not different, but one and three, one and four, two and three, and two and four are all different. So we had more than just one being different. We had quite a few differences there. So that's how you're going to do your ANOVA problem. You'll have different data, but you'll have a screen similar to that, a worksheet similar to this, I should say. And just be very careful to make sure you put it in that red cell when you say where on the worksheet you want your ANOVA to print out.


What's going on everyone? Sam here with late in sports cards. We are ripping Where is this one box of 22 Donner's football hobby for Brandon L. So good luck here at Brandon. Let's do it buddy wait, what's T T which TT are you talking about? You see Triple threads. I think forest ripped that yesterday like last night. I don't see a triple threads in here I'll check your orders again, but unless maybe you ordered it ship it sealed accidentally, but I could take a look Do you have an order number for it? Okay, perfect. All right. Yeah, I can do that. That's no big deal Gotcha There's press proof there in Waller 49 of 50 gotcha gotcha gotcha gotcha gotcha No worries Make boats that's Walker rookie Five it six two six gotcha. I gotcha. No worries on that one. You see Chidobi Woozie a that is for our canvas. Excuse me canvas Leet series rookie Chris Olava in my homes and Logan Thomas Serendip's price decax support was a Cody Rhodes and an undertaker It read Darian Mathis the commanders. That's funny I Drive all the way to my complex like my The realty office for this new place that I have to drop off a money order CJ Mosley to 100 night. No, no not tomorrow And then I have to go get another money order And then drop it off for the first months like for the security deposit, but I have to like get like do the holding fee and That counts is like my first month and then I also have to give the security deposit because they can't release like they can't release the lease Rock party until they have the holding fee Nice, that's awesome. It was a perfect break. Awesome. That's what I like to hear Skymore classical verse Wanda Robinson red press proof. I was gonna say I again That's the first time I've seen the McAfee that I was gonna say it has to be one of the best canvases you can get For sure. That's awesome. Want thornhill. That was really cool, dude Really cool. There's missing nameplate of Isaiah likely. Nope, Tyler Beatty Just kidding. There's an orange Tony Gonzalez again. There's foils damage to 88. We'll send the empty box and wrapper. Sorry about that They're Brandon my apologies sir Sam Howell rookie Hamilton the rookies autograph redemption for the Ravens nice one there Brandon. Congrats, buddy Very nice. God's court with Sutton TJ walk Tom Brady grid iron Kings Jerome bettis Want thornhill couple packs left for you here, Brandon. That was a dominators Tom Brady Malik Willis campus and Ramon Drey Stevenson and last It's like this does have our Jersey card. Very nice That is gonna be leather Kings Isaiah Spiller a nice one there for the Chargers to 399 Leather Kings Desmond Ritter Cup and LaVisca Chinult. That'll do it for your break there Brandon. Thanks again for your support buddy. We'll get them right out to you


It's been a crazy start to the morning so far. The guys haven't had a single chance to rest It's what we all hope for when we head out for a day fishing with any luck. They'll keep this winning streak going Let's you do your thing Don't let him worry out now rich you be telling stories about you. I know I Got color Ah Could be a snapper Jack look like a snapper Nice Nice work All right. Nice. There we go. That's pretty one. Yeah, that's a hammer My favorite fish. So we just put our first red snapper on the boat today These fish are always welcome, but unfortunately we just missed the snapper season by a few weeks So we've got to put this guy back in the water. Our season here on the East Coast is extremely short We only get a few days every year and it always seems to be rough But the populations are huge this spot holds a ton of fish ton of big ones little ones So we're always happy to catch them, but unfortunately they've got to go back You got him?  I may have to get the gaff on this one Come on get him up There he is Red snapper red looks like it. Yeah pretty red. Look at that. You catch the last one too. No, Ricky red. That's a hammer Yep Man, I was hoping this was a big old grouper Unfortunately, we got to turn those some back in We'll go back down there make some more babies


Not good So money geeks must be here. Welcome to another video guys. So in this one, we are going to talk about a firm Which is a company that we cover here on the channel when they went public And I told you guys what I thought about the company If I was gonna be investing in the company or not. So that was a while back I think that was last year we talked about it I covered the IPO here on the channel and so there's been some major news on the company And I want us to talk about that But before we get to the guys if you're new to the channel We took about how to earn money and the save money how to invest and build wealth So that's something that interests you go ahead and hit that subscribe button and your notification bell to don't miss out on new Content so again a firm is a company that is actually involved in the financial space for by now Pay later so they when they went public, you know They kind of introduce themselves as the leader in that space and I did the video here told you guys my perspective on The buy now pay later, which I said If you guys watch that video or I can hook it up here on the YouTube card to you guys Go check it out. I said I'm not a big fan of borrowing So if I have to unless it's an emergency When and I would have to get into debt for that Well, otherwise, I'm not gonna borrow to buy a couch to buy a TV to buy a phone To buy any sort of our technology unless it's an emergency So I'm not gonna I'm not a big fan of the model. So I said I wasn't gonna invest in the stock So I'm not sure if any of you guys did invest it in the company and if you did good for you But recently I just got these news that just came out of that Affirm shares you see here falls on report Apple is working with Goldman Sachs to offer buy now pay later service So this is huge because Apple is already like slowly but steadily getting into the financial space As you know, you have Apple pay the Apple credit card They have all different financial tools that they're building into their platforms or they want you to use their services to pay for their services Which is kind of I mean awesome in the sense of the keeping everything in-house. You don't want to outsource everything I like the whole prospect of that for somebody that loved the Apple ecosystem if you want to be in that space Good for you. The only reason I don't like the whole approach is that you have pretty much everything Being run by one company even though behind the scenes like in this case They're using Goldman Sachs But if Apple goes down you have an issue with a lot of your services Which I don't like to bundle everything I'm putting on the one company But nevertheless, it was still a business a good business model when a firm came out and went public And they were looking pretty good But now this is not good that Apple is trying to get into the space So I'm looking forward to seeing how this is gonna really play out because we've seen Other reports that Apple was working to get an electric vehicle and that never really panned out so Anticipate that a lot of this report are going to be coming out here, but until we see it I think this one makes the most sense in my personal opinion because Apple is already Working in that space. They already have a credit card So it's easy for them to say hey use our credit card and buy whatever and then pay later So it's easy for them to kind of went to just go that route and start Providing their service again a couple of the fact that they have what they call the Apple wallet Which gives them again additional services that people would want to because it's easy you log into your your Apple account All your services are right there at your fingertip. You don't have to be connecting a bunch of third-party You know services to get you going so I can I can see why this makes the most sense But again, just be careful that We're getting a lot of these news out there Remember when I did a video here on tele-docs that the stock actually really tumble because there was a report that Amazon was working on a Service to kind of counter what tele-docs was doing right telemedicine So Amazon has a service in-house and I said this is not looking good Because if Amazon makes this thing and go public would see some some issues here So I wasn't a big a proponent of that say yeah I was gonna get out of tele-doc and go invest my money and something else and a lot of people People that don't even know me Which I mean you gotta go check the comments on that video people would just like oh, you don't even know what you're doing Oh, tell it dogs is the best like dude like that's okay. This is that's my take I am not forcing you to go sell your Tele-doc shares and ever since that happened where's tele-docs today tele-docs it went from over $200 is not sitting at about 155 it again like I said, that's didn't there's no news right now that Apple is Amazon is gonna do something if they go ahead and do what tele-docs is gonna tumble even some so That's just was just my take on it. So again, if you are invested in a firm guys These news should be very critical. So let me show you guys what happened to the stock after this happened So look at the stock was actually trading up here as you can see here today High was about $66 almost 67 as soon as the news came out if they dropped from 66 or 65 down to about 55 so that's almost like a $10 drop if you can see that today It went down 10% which is insane before kind of squeezing back up again and in currency 58 now, but this is not good news because if this really happens Affirm might actually see a chunk of their business because if they have any customer That is an Apple user that uses the Apple wallet Guess what those people are gone because it's so easy for them to just work within the act the Apple Ecosphere and get your business and take care of your services and pay their bills on time. So I mean I'm not invested in this talk just a transparency I don't plan on investing in it if anything I'm gonna day trade it I'm on a short the stock if I continue to see bad news coming out Because if if Apple comes out tomorrow and actually confirm this and say we're moving forward This is what we're doing. You can see another maybe 10 15% drop Before you can find some support and balance back so that would be a shorting opportunity So that's what I wanted to cover in this video guys again Just a quick recap here affirm one of the buy now pay later services.  So as you can see here the stock actually took massive bidding ticket symbol for our firm is AF RM So if you want to go check it out everything would check it out. Yeah, I said affirm all they do is just gonna buy now pay later service That's it. So let me know what you think about is do you think this is just nothing? We have these big companies that will come out and make this news But nothing really materialized or you think that this is not good for a firm like I'm thinking So again, let me know in the comment section if you're new to the channel We talk about how to earn money at the save money how to invest and build wealth So that's something that interests you go ahead and hit that subscribe button and the notification bell So you don't miss out on new content also guys if you're looking to get set up with investing We both has their promotion where if you sign up and deposit a hundred dollars You get some free stocks links in the description in as always guys.


There were a couple of big mindset shifts that have made all the difference in my life and one of them in particular has been a lot less fun to realize than others. Now in this video, I thought I would share one of the single biggest psychological shifts that I have made and why it has changed my life and how you can use it yourself. What's up guys, Alex Hein over at Modern Health Monk. Before we jump in, check out the first link below this video which is for a free goal setting worksheet. So use this worksheet. You're also gonna get a seven day self growth challenge which means you'll get one email a day with a little video showing you how to improve your life. So check it out, link right below this video. There's a great quote attributed to Benjamin Franklin that most men are dead at 25 but are just buried at 75. Now in 2009, I was sitting at my desk of my very first job working as a teaching assistant in a high school in Rye, New York. Now I liked the job, I enjoyed teaching. It was nice interacting with students in that way in a helpful, supportive way. But really at the end of that first year of my very first desk job working full-time, all I could think was, is this it? Like, this is the grand purpose of my life. I'm gonna sit at this exact same desk for 40 years and I'm never gonna do anything different. And there's not gonna be growth or change or variety. I'm literally just gonna sit here. I'm never gonna take a month off to go travel somewhere cool or go walk the Camino de Santiago or just go do a pilgrimage in Southern France and just drink wine and write. Like, I'm 22 and this is what it's gonna be forever.  And I realize so many of us get stuck because we get this first job and we start getting a little bit of a salary.  And then when you get married, you probably wanna have some shared housing space or a house if you can afford it. That increases your expenses. So then you wanna try to get a raise and you wanna keep that job or try to get more of a raise or a better job or a different job. Then you have a kid. And this is like a pet that's permanent, right? It doesn't go away, right? It's not just like a little hobby where like you're done with it and it's kind of annoying and it wakes you up and it pees on you, then you can return it to the stork. It doesn't really work, right? The second you have a kid, it's there forever. It's a irreversible decision, theoretically, unless you donate them which is kind of messed up. But realistically, if you're a good person, a kid is a permanent decision.  You're now a mom or a dad and you have a lot on your plate. And those dreams that you once had become dim, right? You always wanted to go live in France or go live in Spain or be in au pair or go shoot videos for National Geographic or just go to India and photograph the last remaining wild tigers. You had some dream, some that pie in the sky, parents wouldn't approve of, but would be awesome and would make you feel alive. But now you have a kid and you have a house and you have responsibilities. And the gravity of your life suddenly hits you and you realize, I for sure have this for 20 years. And if not a lot longer because if I have another kid and another kid, then it's really 30 years of being an active parent. And we're not traveling long-term. We're not doing a sabbatical in France. We're not doing the natural, you know, photography of tigers in India anymore. We're in the nine to five life. And that gravity of that sensation of feeling stuck and feeling like you've been cheated out of life that you thought some grand amazing life would happen to you and it didn't is a very difficult feeling to experience. And I think this is why people have midlife crises around 45 because you are now somewhere in between being a youth in their 20s and a middle-aged person in their 50s. And you think, have I done what I felt like I was on earth to do? Did I do the things that I really wanted to do? And if that answer does not come back in the affirmative, people freak out. Comfort is a very slow grave. What often keeps people the same is the lack of growth but the lack of growth due to a few psychological reasons. The biggest one being they don't want to be uncomfortable or inconvenienced. It is an inconvenience if you didn't sleep well going to the gym. It is uncomfortable having to work an extra two hours a night because that's what will get you a promotion to make your material life better. It is uncomfortable to have a new baby that wakes you up all night. It is uncomfortable to not go out every Friday night because you don't make enough money to either, you can either save or you can go out and get drinks with your buddies. All of that is uncomfortable. And a lot of what we opt for is doing what is easy and what is comfortable. And I don't want to be the guy that says life is all about discipline because I don't believe that to be true. But what I do know to be true is that life is extremely uncomfortable. If you stay comfortable all the time because inevitably what will happen is that over three or six or nine months or 12 months what will happen is that that thing you wanted to do write the book, start the gym routine, upload a video on YouTube, take a trip quit the job that you have job you talked about six years ago quitting inevitably what's going to happen is that time has passed. John Lennon said life is what happens when you're busy making other plans.  I've seen that in my own life there was never a good time to write a book. There was never a good time to start a business. There was never a good time to shoot these videos. There was never a good time to work on something that can improve my life. Sometimes a smaller percentage of the time I wanted to but most of the time I didn't and most of my own change in life was motivated by pain. So it's easy to change in life when it's something you want to do but very often there are going to be things that will upgrade your life dramatically that you don't want to do that are uncomfortable. So if I can leave you with one thing here it is yes always follow your passion and what excites you but always be moving towards doing things that are uncomfortable that you know will improve your life because one thing I know for sure is that comfort will keep you exactly where you are now and if that scares the shit out of you that you don't want to be here in five years then make the right decision.