## Irrational Play Calling

As if you need any more evidence of how irrational many coaches can be when facing a 4th down, here’s some more.

In ‘no man’s land,’ the region of the field from the opponent’s 30-35 yd line, punts don’t buy you much and field goals are just above 50/50 propositions. Going for the conversion occurs fairly frequently, particularly on 4th and short. This is the confluence of 4th down decision making where all 3 options are reasonable choices.

But once a coach has decided that going for it is not worth the risk, he can then choose between attempting a FG and punting. Neither of these options is affected in any way by distance to go. Only field position matters. A field goal is just as rewarding and just as risky on 4th and 1 from the 30 as it would be on 4th and 15 from the 30. Same goes for punts. Distance to go should only affect conversion attempts. It would be irrational to base a decision between a FG and punt based on something that only matters when attempting a conversion. But that doesn’t stop NFL coaches from doing exactly that, a fact first noticed by commenter 'Jim A' last season.

On 4th down from identical field positions, coaches tend to attempt FGs more often with shorter distances to go and punt more often with longer distances to go. For example, when kicking on 4th and 1 from the 32, coaches went for the FG 100% of the time. But when kicking on 4th and long (7+ yds) from the 32, coaches went for the FG less often--80% of the time.

Here is the graph for field positions between the 30 and 35:

I excluded all kicks in the last 3 minutes of each half and in overtime so that bias from last-minute hurry-up kicks are not included. For example, a team would always want to try a FG in the last seconds of the 1st half, regardless of distance to go.

I also checked to make sure there is no bias in the data with respect to field position. If the 30 yd line happened to feature more 4th and short situations than the 35 yd line, then that would explain the tendency to attempt FGs more often with short distances to go. But that’s not the case. The average yd line for all distances to go within the 30-35 yd line region is the same—the 32.6 yd line.

It’s as if teams with 4th and short feel like they came so close that they really want to come away from the drive with points. And teams with 4th and long feel more resigned to giving up the hope for points,  preferring to pin the opponent deep in his own territory. Any other theories?

### 45 Responses to “Irrational Play Calling”

1. Anonymous says:

I'd be curious to see which coaches tended to shift towards punting on 4th and long.

2. Anonymous says:

In a mediocre attempt at playing devil's advocate -- could it be that it's easier to get a couple yards on a fake field goal than a fake punt?

3. Anonymous says:

I think some coaches may choose based on a process of elimination in these situations. In a fourth and short situation, the coach first eliminates the third option of punting and then chooses between the field goal and going for it. With longer yardage, going for it is eliminated and then the decision is between punting and kicking. This would explain why punting occurs at significantly lower rates when the yardage shortens. I'm not saying this approach to the decision makes sense, but it does explain the data.

4. Borat says:

My beleve its is that with less than the fivie yards a FG may cause more encrochement penalties thus drawing the offsides of the enemy team and culd result in the Down number First.

5. Vince says:

That's not necessarily irrational. If you trust your kicker (based on your kicker's leg, the weather, and so on) then you kick the FG. If you don't trust your kicker, then if it's 4th and short you go for it but if it's 4th and long then you punt. That oversimplifies things, but it gets the basic idea of why that pattern isn't irrational.

6. Matt M says:

Just stumbled across the site, so forgive a basic question: how much data are we talking? A year's worth? More? Is it possible that you've run across a fluky situation where the teams facing the longer distance just happened to also have better FG kickers? Because if not, there's not much rational explanation for it.

7. Matt M says:

@Borat,

If you're trying to draw a penalty for a first down, wouldn't you line up your offense and try a hard count rather than choose a kicking formation?

8. Brian Burke says:

Data is from all kicks 2000-2008 seasons. I don't know off the top of my head because I did the research back in July, but the total number of cases is easily in the 1000s.

9. Matt M says:

Then I'm going with "no rational explanation." BTW, great blog. Very interesting stuff. I have a feeling I'll be wasting a lot of time digging through your archives over the next few weeks.

10. 81Trucolors says:

What about the fact that teams have the option to fake the field goal and are more likely to be successful on 4th and short?

11. Guy says:

Brian:
I suspect you are seeing a difference in teams and/or situations, rather than (or in addition to) an effect of yard to 1st down. Only a minority of teams fail to convert with less than 4 yards to go, so this could easily be a non-random group of teams and/or time/score situations. In contrast, I assume that with more than 5 yards to go almost no one converts, so this pool of teams will basically be a random cross-section. Note that most of the FG/punt difference occurs between 1 and 5 yards to go -- after that the lines are pretty flat --supporting this possible explanation.

I think you should look at the 4th/short teams to see if they differ in ways that might lead them to logically choose more FGAs. Such as:
1) better FG kickers from 30-35 yards;
2) difference in score that makes FG more valuable;
3) weaker offense;
4) coaches who prefer FGAs to punts at this distance (I'd guess some teams will be heavily over-represented).
I'm sure there are other possible differences as well.

You could also look at outcomes: do the 4th/short teams make a higher % of their FGAs?

12. Matt says:

Here's a crazy theory... just throwing ideas out there.

If a team has trust that their kicker can hit a "long" field goal and get to 2nd or 3rd and long. Maybe they start to adjust play calling (run more) to get into position to at the least come away with the 3 points. ie. they run twice from 2nd and 10 to get into 4rth and 2 (at say the 33) which for them is FG attemptable.

The Giants would never do this because of a shaky kicking situation. On 2nd and 10 (at the 33) they will pass because 9 yards doesn't help them score, they NEED a first down. If they don't convert they punt. We have definitely seen that coaches (incorrectly) coach to get some points, rather then maximizing scoring opportunity.

There is probably way too much data to be skewn this way, but its possible.

13. Brian Burke says:

Matt-I like that theory, but I did throw out kicks from the last 3 min of each half, which I think would contain most of those "only need a FG here" situations. But, it still could have an effect.

Borat has a good point, but if the cause had to do with the possibility of drawing an offsides, then we'd expect to see a sharp difference between the tendency to punt and tendency to attempt the FG between 4 yds to go and 5 or 6 yds to go. Instead, it's fairly steady from 1 to 9 or 10 yds to go.

Guy, I don't understand what you mean by "only a minority of teams fail to convert with 4 yds to go."

14. Vince says:

Here's a more rigorous explanation of what I was trying to say in my last comment. Let's say that coaches first decide whether they'd prefer to punt or kick the FG, and then decide whether to go for it or use their preferred special teams option. If they're rational about deciding between punts or FGs, then they'll choose whichever one has the higher expected value. The expected value of a FG varies a lot depending on the conditions - it's a lot higher in a dome than it is in Pittsburgh in December - while the value of a punt doesn't vary as much. So when a FG is the better option, it's typically going to be because the FG has a high expected value (maybe 0.8 pts.) and the punt has a decent expected value (maybe 0.1 pts.), and when the punt is the better option, it's typically going to be because the punt has a decent expected value (maybe 0.1 pts.) and the FG has a bad expected value (maybe -0.5 pts.).

So when the FG is the better ST option it has an expected value of ~0.8 points and when the punt is the better ST option it has an expected value of ~0.1 points. When the coach decides whether to go for it or to go with the ST option, a rational coach will be more willing to go for it when the ST option is worse (worth only 0.1 points rather than 0.8 points), so he'll be more likely to go for it when the punt is the better ST option. On 4th and short, coaches are more likely to go for it when the choice is "go for it or run a ST play worth 0.1 points (punting)" than when the choice is "go for it or run a ST play worth 0.8 points (FG attempt)." On 4th and long, going for it isn't an option, so we can see that coaches think that punting is a better option than kicking the FG about 1/3 of the time. But when going for it is an option, on 4th and short, it doesn't eat into the two ST options equally because one of them is more valuable than the other. So, as we see in the data, a higher proportion of ST plays will be FGs on 4th and short.

15. Borat says:

Nice!

Thanks you, Brain.

16. Borat says:

@ Matt.

Under either the reguar offensive formation or under a FG formation if you fail to draws the enemies offside you are more likely to succeeds with a FG than converting the 4th and 4 meters to gane in a regular offensive play. Yes?

If the enemies remains stationary before the snap the FG attempt is not affected. If the enemies remains stationary before the snap on an regularly offensive play it is more riskies to intrude 4 meters. No?

Thanks you, matt.

17. Phil Birnbaum says:

I like anonymous/3's idea, that coaches eliminate one option first, then choose from the other two.

I also like the idea that it might be a significantly different sample of coaches at each data point. Don't know if that's true or not.

BTW, in the first chapter of "Predictably Irrational," Dan Ariely notes a similar anomaly. Give people a choice between A or B, equally desirable, and they choose them equally. But add a third choice one that's slightly worse than A. Call that A'. Now you have A, A', and B. Faced with those choices, most people choose A. Why? Irrationality, but the theory is that A now "beats" A' easily, and is at least as good as B. B, on the other hand, can't be said for sure to be as good as A' or A. So A wins.

I think anon/3 is on to something by his analysis, which sounds similar to Ariely here.

Maybe ask Dan Ariely himself! This is something he'd be interested in for sure.

18. Nate says:

Vince, you've brought up a really interesting point. I'd like to see the rebuttal to it.

Expanding a bit, let's consider consider two hypothetical teams (we'll call them the Raiders and Browns). The Raiders have a great long-distance field goal kicker, while the Browns do not. The teams are identical in all other respects (e.g., punting ability and likelihood of converting on 4th down).

Between the 30 and 35, the Browns' decision is whether to go for it or punt. We'll say the rational thing for them to do is go for it on 4th and 5 but punt on 4th and 6.

The Raiders, on the other hand, are choosing whether to go for it or kick a field goal. Because kicking a field goal has a higher WP than punting, the "going for it" bar is higher than it was for the Browns. We'll say the rational thing is to go for it on 4th and 3 but kick the field goal on 4th and 4.

Now, let's aggregate these decisions. On 4th and 4, all data points come from the Raiders, so in aggregate the teams choose to kick a field goal 100% of the time. On 4th and 6, on the other hand, data points come from both teams, so in aggregate the teams choose to kick a field goal only 50% of the time.

In other words, we end up with a graph that looks pretty much like the one in your post, even though each team acted perfectly rationally.

Thanks,
- Nate

19. Guy says:

"Guy, I don't understand what you mean by "only a minority of teams fail to convert with 4 yds to go.""

Brian, I meant only that most teams will attempt a conversion at 4th and 1/2/3/4 (according to Romer's study, it's about 50% at 4th and 4 at this yardage). So the teams/situations in your sample represent only a minority (maybe 25-30% overall?) of all 4th/short situations. Since these teams have chosen not to go for it, they are in no way a random sample. (While the 4th/long group is, I'd guess, a random sample.)

The question is whether the 4th/short/non-converters differ in some way that might bias the FG/punt decision. Vince suggests one good reason they might, and I mentioned some others. And the nature of the curve, almost plateauing after 5 yards, makes me think this is mainly a function of the prior go/no go for it decision.

20. Anonymous says:

Great point, Guy. At this point, to believe the phenomenon is due to irrationality, I'd need to see a flat FG% (as opposed to FGA%) line added to that graph.

21. Jeff Clarke says:

I agree mainly with Vince and Guy. I think its a selection bias issue. Since some coaches go for it more often than others do, you are removing a definitively non-random subset by looking only at 4th and shorts where they didn't go. I also think the perceived strength of the kicker is a major issue.

With 4th and short, coaches go for it if they think their kicker can't make it. Kick if he can. So you have 50% goes and 50% kicks, but 100% of the non-goes are kicks. With 4th and long, you punt if you think your kicker can't make it. So you have 50% punts and 50% kicks. 50% of non-goes are kicks. This would be perfectly rational if the coach was accurate in his projection of the kicker's ability.

** Obviously, I know that its not 50/50 and the real numbers are more complicated. The above numbers are just to prove a point.

22. JM says:

Couldn't there be an expected points explanation for this behavior? Referring to your past post on fourth downs, I saw that the expected points of a field goal from the 30 is around 1. The expected points for a punt from the 30 is around 0. The expected points for a conversion from the 30 depends, of course, on the distance needed. For a short conversion, the EP is between 1.5 and 2, while for a long conversion (7+ yards) it dips below 1. So might not a coach intuit that by punting on 4th and 1 at the 30, he is essentially trading 2 points for 0, but for 4th and 10 from the 30, he's trading 1 point for 0. In both cases, he's being irrational, but it could be that his appetite for risk (coaches being very conservative) makes a 1 point expected loss acceptable, but a 2 point expected loss just too great to stomach.

23. Anonymous says:

The premise of the article is that a coaches first instinct is whether or not to go for the first down. I believe this assumption is flawed and that the coaches first decision is whether or not to kick the FG. The other two options (Punt/Go) would be weighed 2nd and 3rd based on their probability of success. Basically in short yardage, FG = option 1, Go = option 2, and punt option 3. Since "Go" carries such a lower probability in long yardage, it falls behind "punt" into the option 3 spot.

24. Ian says:

I'm a fan of the go-for-it/quick kick option plays, that always seem to work well.

So, a team gets it's QB practised on chipping a punt to inside the 10 yard line, that way when they get to 4th and short in no man's land they can keep the offense on the field. If the defense drops a play back to feld the punt, the offense goes for it (after all, it's 11 v 10 and the odds were in their favour when it was 11 v 11) - if the defense doesn't drop someone back the QB quick kicks - with the safety of being able to allow the ball to roll as noone is covering the kick.

Pittsburgh used to do this well with Big Ben and I don't see why other QBs can't be taught to make what is a very basic kick.

25. Happy says:

I notice that the function flattens out after five yards. Beyond five yards the probability of a five yard penalty is irrelevant. If coaches had evidence that a field goal attempt had an increased probability of resulting in a five yard penalty, then we could expect to see a step change at five yards to go.

That notwithstanding, every NFL coach should have a statistician on their staff. Compared to what coaches get paid, we're not that expensive, and we could probably provide a lot of insight.

I'm curious about the statistics surrounding final outcome (including the next possession) of fourth and goal from inside the five yard line.

Often times even if the 4th down isn't converted the opposing team does nothing with their next position, so field position is retained. 3/7 is 43%, but with the retained field position an even lower expected conversion rate may justify going for it on fourth down.

26. Anonymous says:

Here is a possible reason.

In the case of a broken play, it may be that a punt formation has a better chance of picking up a first down, than the FG. I.e. a punt formation, with it's blocking, can allow the kicker to run (or pass) for a first down if the snap is bad and he can't kick it.

If a FG goes bad, it is almost impossible to run for a first down, cause it starts with your qb kneeling on the ground, and the blocking is different.

27. Dave says:

The solution has been stated by a couple commenters and I am hoping their wisdom does not go ignored.

I am quite sure that Vince and one of the anonymous commenters are absolutely right and the premise of the article is incorrect. The first decision the coach makes is whether or not to kick the field goal. Are we in field goal range, yes or no? After that, the decision of whether to punt or go for it is determined by the distance, which explains what appears to be odd behavior depicted by the graph.

What would really settle this debate is if the graph showed the third option- going for the first down. By eliminating this element you have created the illusion that coaches are less likely to kick field goals as the distance goes up, when in fact they are just more likely to punt (vs going for it). I believe that if you showed all three options, you would see the percentage of field goals would stay roughly steady, while punting increases with distance and going for it dwindles.

I'm not sure how difficult it would be to go back and incorporate all of the 4th down conversion attempts for the third element but I would be fascinated to see the results.

28. Brian Burke says:

I think there are a lot of good possibilities here, particularly the one Dave points out. However, that does not make it rational. Just because it can be explained does not mean it's logical.

There are 3 options. Rationally, you should pick the one that gives you the best opportunity to win, period.

29. Dave says:

I am still not convinced that the behavior depicted here is irrational. Here is hopefully a more convincing explanation of what appears to be irrational behavior.

The expected value of a field goal is unseen here, and I believe it is highly unpredictable and prone to fluctuation. A number of factors- kicker, playing surface, and weather- all play a huge role in determining the expected value of a kick. From an arbitrary distance of 49 yards, there will be times when this field goal has a very high chance of success, and there will be times when it has a very low chance of success.

During optimal kicking conditions, the expected value of a field goal will be hands down the best option of the three, regardless of distance for a first down. During dreadful conditions, kicking a field goal will be hands down the worst option regardless of distance for a first down. I'm ignoring the gray areas here for simplicity but hopefully my point is clear.

When a field goal is the best option, obviously you kick it. When a field goal is more of a dicy proposition, you have a choice to make. Punt or go for it? Obviously this part of the equation is highly dependent on distance to go for a first down, which explains the nature of the graph.

I know this argument is a slight simplification. But if you agree that the value of a field goal is highly dependent on external factors more so than the other two options, which leads to the field goal *often* being either the best option or the worst option regardless of distance, then the behavior depicted by the graph is rational.

30. Brian Burke says:

I agree. Yes, FG values are subject to lots of things. But those factors would need to be shown to be systematically connected to to-go distances enough to explain what we observe.

31. Guy says:

"Yes, FG values are subject to lots of things. But those factors would need to be shown to be systematically connected to to-go distances enough to explain what we observe."

That's not quite right. The concern being raised is not that FGs are somehow more valuable in short go-to distances. The concern is that, in short go-to distances, the value of the FG has a larger effect on whether the team goes for it, and therefore whether the play makes it into your sample. This will be much less true on long go-to plays, simply because teams so rarely go for it. In other words, the relative value of the FGA has more impact on the go/no-go decision with short yardage than with long yardage.

I think you can largely settle this if you can report the expected WP for FGAs and punts in the 1- and 2-yard situations (when teams don't go for it), vs. the 7, 8, 9-yard situations (again, when teams don't go for it). My guess is you'll find that the WP ratio of FGA:punt is higher in the short yardage situations. There are still other possible explanations -- kicker's ability, different pools of coaches -- but the value of the FGA seems like the most plausible (other than your theory of irrationality).

32. Dave says:

No no no! Field goal values have NOTHING to do with to-go distances! By removing "going for it" you have created an illusion.

Since we are missing the "going for it" aspect of the graph, I'll make up some fake data. NOTE: if you were to take out the "Going for it" part of the data and only show the field goal vs punt, this data would match the actual graph above (roughly).

F = Field Goal, G = Going for it, P = Punt, (F v P)= implied percentage of field goals vs punts, ignoring going for it, as in the graph above. Note that this last piece is a RESULT of the first three.

4th and 1: F= 60%, G= 30%, P= 10%, (F v P = 86% v 14%)
4th and 2: F= 60%, G= 25%, P= 15%, (F v P = 80% v 20%)
4th and 3: F= 60%, G= 20%, P= 20%, (F v P = 75% v 25%)
...
4th and 10: F= 60%, G= 5%, P= 35%, (F v P = 63% v 37%)

Even though the field goal rates have stayed exactly the same (at 60%), the increased number of punts has created the illusion that coaches are less likely to kick the field goal as the to-go distance increases when in fact this is not the case.

33. Brian Burke says:

Dave- I think I understand what you're saying. According to your model, a coach's decision tree would have to be:

1. FG or other?
2. If other, go for it or punt?

Going for it and punts would be in the same family of "non-field goals." But how is that still rational? (genuine question, not being argumentative)

Your model would also suggest that coaches are ignoring to-go distance in their initial decision. A FG rate would be fixed at 60% (or whatever) regardless of to-go distance.

What about an alternate decision tree: What if going for it and FGs are in the same family of "needing points?" And if coaches need points, they should first choose between trying for points and punting. If they don't punt, they then decide whether to kick or go for it.

But that would make the ratio of FGs:punts lower at shorter to-go distances, the opposite of what we see.

Ultimately the only truly rational method is to evaluate the value of all three options in a single stage and choose the one with the highest value.

Instead, there seems to be a single-elimination tournament going on in coaches' heads, as if they can't weigh more than two options simultaneously. They only consider 2 options at once, and eliminate one at each stage yielding the choice. And if I understand Dave right, it suggests coaches are ignoring to-go distance at the first stage.

(This all assumes no large systematic connection between to go distances and the values of kicks.)

34. Anonymous says:

I think Dave and Vince have demonstrated quite well how a coach's mind works. These explanations do not follow a logical decision making process, and that is probably exactly what the NFL coaches are doing. I still think there is some room for selection bias. First, the dumber coach's are less likely go for it on 4th and short, and are therefore more likely to make irrational decisions, so maybe this pattern doesn't hold across the board.

I also wonder how much taking out 3 minutes helps the problem of teams needing FGs being able to rush into 4th and short position. For example, if the game is expected to be low scoring, say 3-6, a team might just try to force there way into fg range from the start. Perhaps in low scoring games there are very few 4th and longs from in this range.

35. Dave says:

Interesting stuff Brian. I believe you do understand me correctly. I understand the point you are making with the alternate decision tree and why that would lead to the opposite effect which we do not observe. I completely agree that coaches should weigh all three options at once. Easier said than done.

Also if I had to guess, I would say that the real coaching decision tree is probably a little more complicated than I said at first. On fourth and short situations, the coach weighs the FG vs going for it (with punting a distant third option). On fourth and long, the coach weighs the FG vs punting (with going for it a distant third option). This seems reasonable. The FG is always a viable option while punting slowly replaces going for it as a second viable option.

And I do think that the percentage of field goal attempts is not quite steady but it probably goes down a bit as you get down to 4th and 2 and 4th and 1. It is replaced not by punting but by going for the first down. It does not make sense, nor do I believe that it is the case, that the percentage of FG attempts drops as the to-go distance increases. It's just that punting increases.

Here's what I think an interesting next step would be. Do coaches have a chart for this? Could you make a chart? What does WPA say? It would be cool to have a little chart of opponent's yard line vs to-go distance, in this 30-40 yard area, with the three options presented in order of value.

Another wrinkle would be to suppose that we had some extra information about the field goal kicking game. If we think our kicker can hit 75% of the time from 49 yards we will play it a lot differently than if he can only hit 30%. Ultimately, if you aggregated all of the situations, playing rationally and optimally at each step of the way, I think you would observe results that roughly mimic the effect seen in graph at the top.

36. Guy says:

Brian: you mention above that field position is identical (32.6) for all yards-to-go. And that makes sense for all 4th down plays. But it can't be true for your sample of kick plays (I don't think), since teams go for it much less frequently from the 30 than from the 34 or 35. Your sample (punt or kick) should have an average field position well below 32.6, probably 32 or less. So I'm thinking you perhaps looked at all 4th downs, not just the kick plays?

If so, you should check to see if distance to goal is in fact shorter at 4th-and-short than it is at 4th-and-long. It seems possible that length of prospective FG plays a bigger role in determining whether the team goes for it when yardage to first is short. For example, a team might choose FGA at 4th-and-2 from the 30, go for it at 4th-and 2 from 35, and yet choose to kick at either distance on 4th-and-8. That would result in shorter FG distances for your 4th-and-short plays.

37. Vince says:

I thought my 2nd comment explained why this is rational: FGs (in good FG conditions) are more valuable than punts (in bad FG conditions where punting is a better option than a FG), so coaches should be more willing to go for it in bad FG conditions where going for it has a lower threshold to cross in order to be the best option. When going for it is an option (when the to-go distance is not too long), going for it should replace punts more readily than it replaces field goals, so a higher proportion of kicks should be FGs.

Or we can do it with numbers. Let's say that you have a completely rational coach who makes decisions by estimating the expected value of each option (Punt, FG, Go For It) and choosing the option with the highest EV (no restrictive decision tree for him). To simplify the numbers, we'll say that the expected value of a punt is always 0. The expected value of a FG varies a lot depending on conditions, but to keep it simple we'll say that 2/3 of the time (when conditions are good) it equals 1 and 1/3 of the time (when conditions are bad) it equals -1. I won't give numbers for the expected value of going for it, but what's important is that the EV varies with to-go distance (it's smaller for longer distances) and it also varies for other reasons like the quality of the offense & defense (so at each distance you can think of it as having a distribution rather than equaling a single number).

So what would we see for this coach if we graphed kick type by distance to go? Starting at the far right of the graph, on 4th and very long, Go For It will always have negative EV so the coach will never go for it: 2/3 of the time he'll choose FG and 1/3 he'll choose Punt. As to-go distance gets shorter, he'll start to run into some cases where the EV of going for it is greater than 0 (but still less than 1) so Go For It will sometimes replace Punt as the chosen option when FG conditions are bad, but Field Goal will always be the option when FG conditions are good. That means that FGs will be more than 2/3 of the kicks, since they're 2/3 of all plays and punts are less than 1/3 of all plays. As to-go distance gets shorter, the EV of going for it increases and is greater than 0 more and more often and occasionally even greater than 1, so Go For It replaces more and more punts and even starts to replace some FGs. With many fewer punts and a few less FGs, FGs will be an even larger proportion of kicks (even though they're less than 2/3 of all plays). At some point, as to-go distance gets even closer, Go For It might start replacing FG as quickly as it replaces Punt, so the proportion of kicks that are FGs could stabilize. But as long as teams are sometimes kicking, FG should be more than 2/3 of the kicks because the EV of Go For It will be less than 1 more often than it is less than 0.

In other words, the graph for the rational coach would look a lot like the graph for actual coaches. We know from other data that coaches aren't perfectly rational (they don't go for it often enough), but I don't see any reason to think that they're being irrational about choosing between FGs and Punts because this interaction with to-go distance is exactly what you'd expect if they were rational.

38. Brian Burke says:

Vince-I understand. That easy enough to check. I'll see whether there is the same tendency in dome games.

39. Vince says:

Why dome games? By "good FG conditions" I just mean circumstances where the team has a relatively high probability of making the field goal, which depends on how good your kicker is and the line of scrimmage, as well as weather/stadium issues. I'd expect to see the same pattern in dome games, probably with a higher overall percentage of field goals.

40. Brian Burke says:

Ok. Ran a few graphs. No conclusions here-I'll just throw out what I found.

Only dome games: Same trend, not as pronounced. Punt:FG ratio goes from about 5:95 at 1 yd to go to about 15:85 at 10 yds to go.

Only 1st half, >3 min left--same result as all 4 qtrs.

There are small correlations between to-go dist and yd line. For dome-only games, it is 0.05 and for all venues it's 0.08. In other words, to go distances tend to very slightly increase with yd line within the 30-35 range.

Graphing all 3 options, it is clear that FGs and going for it "rob from each other." Their plots appear to be mirror images. What would that suggest the decision tree looks like?

41. Brian Burke says:

Vince-We know the conditions in the dome games are equal. Plus, we know there can't be a correlation between kicker ability and to-go distance.

42. Vince says:

There doesn't need to be a correlation between kicker ability and to-go distance (or between to-go distance and weather or between to-go distance and anything besides the expected value of going for it). Let x be the average expected value of kicking a FG in the cases where a FG has a higher EV than a punt, and let y be the average expected value of a punt in the cases where a punt has a higher EV than a FG. All we need is for x to be greater than y, and we should get the pattern found in the data where going for it replaces punts more readily than it replaces FGs.

43. Guy says:

I would expect a low correlation between to-go distance and yd line, because the vast majority of your sample is 4+ yards to go (at shorter yardage, most teams run or pass, so they aren't in your sample). Can you tell us the average yd line for 4th-1, 4th-2, 4th-3, and 4+ yards to go?
I don't think yard line explains all of this, but some of it.

"we know there can't be a correlation between kicker ability and to-go distance."

Why not? If two teams both face 4-and-3 at the 33, doesn't the correct choice depend in part on the likelihood of making a FGA? So teams with good kickers should choose the FG more than teams with bad kickers. And the weak kicker team then drops out of your sample.

Brian, you keep going back to talking about all 4th down plays. But what matters is the subset you are looking at -- the kicks. That's totally different -- at 4th and 1, you're only looking at about 20% of the plays. You can only assume these smaller samples are all similar if they are independent from the values of the FG and the punt -- but they are not.

44. Tomb says:

What if there is simply a negative correlation between FG% and 4th-down-conversion rate? What if, for reasons of salary cap or other, teams with good kickers tend to have poor short games or offenses generally? What if punting ability varies relatively little, either inherently or because of punters' relative non-impact on others' salaries?

45. Brian Burke says:

I gotcha. Your theory is that teams with better kickers will forgo going for it more often on 4th and short, when other teams typically would attempt the conversion. This would have the effect of increasing the FG:punt ratio at short to-go distances.