Expected Value in Football

[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]

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

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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.

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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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