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'Expected Points'







'Expected Outcomes' in General

Before I go any further, I'm going to take a step back and explain the concept of 'expected outcomes' in general. Say I can choose one of two routes home from work each day. One route is through the side roads, and the other is via the highway. If I take the side roads my commute always takes 20 minutes.






The EP value of the punt option is relatively straightforward. Based on recent historical data, we know the average net distance for punts from each yard line. The closer a team is to the end zone, the shorter a punt will tend to be due to touchbacks. Since we know the net distance of the punt, we know the expected subsequent field position for the opponent.


Field Goal Attempts

The EP value of a FG attempt is based on the probability of making the kick, which is dependent on kick distance. Just like taking the highway home from work, we can calculate the overall value of a FG attempt. Below is the graph of FG percentage by line of scrimmage.

A successful FG is worth 3 points minus the value of the ensuing kickoff for a total of 2.3 points. A missed FG is worth the EP value of a first down for the opponent at the spot of the kick (or the 20 yd line, whichever is larger).

For example, with the ball on the 20 yard line, the NFL average FG percentage is 82%. The spot of the kick would be the 27, which corresponds to 0.7 EP (that's -0.7 EP for the FG kicking team). Therefore the EP value of a field goal attempt from the 20 would be:

(0.82 * 2.3) + ((1-0.82) * -0.7) = 2.0 EP

Going For It

The value of a successful conversion attempt would be at least the EP value at the 1st down marker. Often, conversion attempts would obviously go further than the marker, but for now let's consider the minimum value of the conversion. The minimum value of an unsuccessful conversion attempt would be the EP value of a 1st down for the opponent at the spot of the attempt.

The probability of a successful conversion is primarily dependent on the distance to go. Field position also affects the chances of success due to the compression of the field in the red zone. With less area to defend, the defense's task is easier. The graph below plots the probability of a successful conversion by distance to go, broken out by areas of the field.

For example, a 4th down and 3 at the 50 yd line could be converted 56% of the time. A successful conversion would (at worst) give the offense a 1st down at the opponent's 47, worth 1.8 EP. And an unsuccessful conversion would give the opponent a first down at the 50, worth 1.9 EP to them and -1.9 EP to the current offense. The value of going for it is therefore:

(0.56 * 1.9) + ((1-0.56) * -1.8) = 0.3 EP

A Sample Situation

Let's say you're the coach of a team facing a 4th down and 3 from the opponent's 37. It's early in the second quarter and the score is tied. Should you call a punt, attempt a FG, or go for it? In reality, coaches have called for the punt 100% of the time in close games early in the second quarter. But is this the best thing to do?

Let's start with a punt. From the 37, we would expect a net punt distance of 23 yards, coming to the 14 yd line on average. The 14 yd line corresponds to -0.2 EP for the opponent, which is +0.2 EP for your team.

A FG attempt would be successful 45% of the time. A made FG would yield 2.3 EP factoring in the kickoff. A missed FG would give the ball to the opponent at his own 44. This is worth 1.1 EP to him and therefore -1.1 EP to us. The total expected point value of a field goal attempt would be:

(0.45 * 2.3) + ((1-0.45) * -1.1) = 0.4 EP

A 4th down and 3 conversion attempt from that part of the field would be successful 56% of the time. A successful conversion would mean a 1st down at at least the opponent's 34, which is worth 3.3 EP. A failed conversion attempt give the opponent a 1st down at his own 37, worth 1.3 EP to him and -1.3 EP to us. The total expected point value of going for it would be:

(0.56 * 3.3) + (1-0.56) * -1.3) = 1.3 EP

So in this example, the best decision is to go for the 1st down. In simple terms, it's worth the risk in the long run. It's not even close.

Putting It All Together

To built a chart of general recommendations where teams should go for it or kick, we can simply repeat this analysis for each yard line and distance to go. We'll start by plotting the EP values for kicks from various yard lines. First, here are the values for punts:

And here are the vales for FGs:







I buy both of those explanations, plus I'll throw in my own take. In addition to the natural conservatism of coaches, I believe much of the reason why coaches don't go for the conversion more often can be explained by Prospect Theory. As I outlined in my Decision Theory article, people tend to fear a loss more than they value an equivalent gain. This is a built-in tendency toward risk aversion means that coaches would be biased toward kicks rather than conversion attempts.


End Notes

The 37 yard line is the boundary between FGs and punts




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