Expected Value in Football

[southerndog]

I once saw a guy on a football pregame show talking about punting vs. going for it on 4th down. He said it was a better move to go for it in most situations. I didn't see the whole segment and was in a waiting room, but it seemed pretty interesting.

The guy was a Ph.D. economist.


Has anybody else heard of similar research?
I always felt football coaches were too conservative.

[Bozeman]

Yes, but I don't remember where.

Football coaches are way too conservative,
Craig

[Flounder]

You might be thinking of this guy (http://emlab.berkeley.edu/users/dromer/). He wrote a paper (http://emlab.berkeley.edu/users/dromer/papers/nber9024.pdf) on going for it on 4th down. The money paragraph states

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The results are striking. The analysis implies that teams should be quite aggressive. A team facing fourth and goal is better off on average trying for a touchdown as long as it is within 5 yards of the end zone. At midfield, being within 5 yards of a first down makes going for it on average desirable. Even on its 10-yard line -- 90 yards from a score -- a team within 3 yards of a first down is better off on average going for it. In practice, however, teams almost always kick on fourth down early in the game. The only significant exceptions occur in the "dead zone" around the opponent's 35-yard line, where a field-goal attempt is unlikely to succeed and a punt is likely to produce little yardage, and on plays where the team has one yard to go and is near the opponent's goal line. Even in those cases, however, teams are much more conservative than the recommendations of the dynamic-programming analysis.


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I haven't read the whole paper, so I can't say how close his model corresponds with reality.

[southerndog]

This sounds like it. I think I actually heard of a similar study done on baseball and sacrificing.

[bigpooch]

The decision to go for first on 4th down is made by the
coach. Even if the decision is in the long run better,
the coach needs to consider the occupational ramifications
of such a decision and whether management deems that the
decision was correct. Coaches are often second guessed
after a disastrous result and the more "questionable"
decisions made means the less likely to be employed as a
coach! For further research: model an appropriate utility
function for coaches specifically for 4th down.

[Timer]

>>I once saw a guy on a football pregame show talking about punting vs. going for it on 4th down. He said it was a better move to go for it in most situations. I didn't see the whole segment and was in a waiting room, but it seemed pretty interesting.<<

You should ask Sklansky. He has written of this.

[Lawrence Ng]

Not the New England Patriot's coaching staff. They define aggressive football. =)

Lawrence

[ironman007]

Go Pats! However the Patriots also used the 4th down punt last week to pin the dolphins deep which caused them to score their only touchdown. Punting is correct in a game of field position.
While most coaches could be more aggressive, to suggest it's usually better to go for it on 4th down is pure nonsense.

[AnyAce]

Flounder is right, that is the article. I tried to read it (and have a pretty good math background) and it was tough sledding.

While it works in theory, I think it breaks down in reality a little bit. The problem is that the sample is too small with only 16 games per year. So a coach could go for it on 4th down according to the method in the paper and come up short far more often than the paper predicts just because he is "running bad", something we poker players know about. This would probably cost him his job (as someone already noted).

With more games per season (say like 162) you could make these decisions often enough such that it should even out over the course of the season.

[ironman007]

Punting vs going for in on 4th down comes down to a risk vs reward and usually the risk outweighs the reward which is why in most cases teams punt. Teams don't run bad when trying for 4th downs because they're not playing poker on the field.

[southerndog]

But, what if they played like they were going to have four downs, as opposed to only three?

[RydenStoompala]

That's why Phd's teach and don't play the sports. They'd be killed. They also have to teach because their sports betting can never keep them in food. Easy to prove that fourth down conversions are favored over punting for game strategy, but try and get 80+ college players or three dozen pros to buy into that playing at someone else's stadium in a clutch game. Some of the smartest people to ever use a blackboard are football coaches and they know the math. They're just too smart to fall for it.

[SossMan]

[ QUOTE ]
While most coaches could be more aggressive, to suggest it's usually better to go for it on 4th down is pure nonsense.

[/ QUOTE ]

Why is it nonsense? Because nobody has done it before? If you read the paper, he clearly states that game situations dictate proper decisions (example: it's Gillette Stadium, the fans had to bring shovels to find their seats, my defense hasn't given up a touchdown at home since the Carter administration, my quarterback is Ryan Leaf, etc...)

However, his assumptions are that the teams are of close to the mean in terms of skill and that the game is in the 1st quarter. He gives a great example:

Assume a team is has 4th and goal from the 2 yard line. Assume that the team has a perfect kicker. They have a 100% chance of making 3 points. Additionally, assume they have a 3/7ths chance of making a touchdown (and 100% chance of making the extra point).

What should the team do?

Well, you might say that both decisions yield the same expected value of 3 points. However, you must estimate the value of what happens next. If they go for it and don't get the touchdown, the other team gets the ball on it's own 2 yard line. After Mr. Perfect makes the field goal, they have to kickoff and give it to the other team at about the 35.

Therin lies the difference.

He goes on to determine the point value of having the ball at a certain yard line on a certain down and distance.

Of course, a team is probably not indifferent about a 100% shot at 3 points or a 3/7ths shot at 7 points when there is 0:05 seconds to go in the 4th quarter and they are down by 2 points. That is why he assumes it's the 1st quarter and teams maximizing their total points maximizes their chances of winning the game. This isn't necessarily true in 4th quarter or end of the half real game situations.

[SossMan]

Read Billy Bean's book (he's the GM of the A's). It's very interesting.

[ironman007]

I admit I have not read this paper, I'll try to find it but I was commenting on the statement that is usually correct to go for it on 4th down vs punting and this to me is nonsense.
In college football this could be correct for teams that are much better than the oppenents.
The decision comes down to the classic risk/reward. Your the coach of the Patriots it's 4th and 1 at the 50yd line. If you go and make it you get a 1st down and maybe you score on this drive, remember your offence is not that great. If you don't make it, the other team has the ball at midfield and has gained momentem and there chance of scoring against a great defense has gone up. If you punt, you pin the other team which increases your chance of scoring or forcing the other team into mistatakes, so you punt.

[bigpooch]

You are correct that most people do not consider the
consequences of each decision and the resulting decision
trees. The case of having 4th down and goal at the two
yard line in the first quarter under "normal" circumstances
with the score tied should be automatic: don't send the
field goal unit in! Going for it early in a tied game also
is not a crucial decision made in crunch time; besides, it's
also very entertaining to the fans!

On the other hand, how do points scored in a football game
relate with the equity value of winning the game? Isn't
the assumption that maximizing EV of points scored is
directly related to maximizing the value of the game? I
know it's minor nitpicking and one can argue that between
roughly equally matched teams with the score being very
close, a linear approximation is adequate.

[jedi]

4th and 3 at your own 10 yard line and you GO FOR IT?!?!?!? How absurd is that? First of all, 4th and 3 is no sure shot. The penalty for failing is HUGE, since it provides an opponent with essentially 1st and 10 from the 11 or 12. Geez, depending on the game situation, an intentional safety might be a better decision than going for it.

[ QUOTE ]
The money paragraph states

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Even on its 10-yard line -- 90 yards from a score -- a team within 3 yards of a first down is better off on average going for it.

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I haven't read the whole paper, so I can't say how close his model corresponds with reality.

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