## TMQ Ignores the Percentages

In today’s article, TMQ talks about the fake field goal that Michigan State converted to beat Notre Dame in overtime.  He writes, “The fake might have failed, but if it succeeded, victory was certain.”  Well, yes.  TMQ likes the play, but doesn’t think it’s a “bold gamble”, because “More coaches should play to win rather than to avoid losing!”.  That would also be nice.  But it’s obvious that the touchdown would win the game, while kicking a field goal would tie the game and send it to another overtime.  TMQ seems to be saying that you should try to win every time, but should you?  Let’s say that instead of being 4th and 14 at the 29, it was 4th and 20 at the 20.  Now there’s no chance of a first down if the runner is tackled before the end zone; it’s kick a field goal to extend the game or score a touchdown to win.  I think the call to go for it there would be much more bold.  But to decide what’s best to do, you have to look at the likelihood of each outcome.

TMQ says that the 46 yard field goal facing MSU is a 50/50 proposition.  That means that 50% of the time they miss and lose, and 50% of the time they make it and go to another overtime.  I’ll assume he’s right.  In the second overtime he says that MSU’s victory is another 50/50 proposition; this is actually somewhat untrue because they would have had the ball first, which puts them at a disadvantage because Notre Dame would have known if they needed a field goal or a touchdown to win and could play accordingly.  If TMQ is right, MSU only has a 25% chance of winning by kicking the field goal (50% of the time they make the field goal, and 50% of those times they win in OT 2).  The number is probably less than 25% because MSU would’ve been closer to 40 or 45% to win in OT 2.  The critical question then is, could MSU do better than the 20-25% chance of winning granted by attempting a field goal?

Punting is obviously not an option; they have a 0% chance of winning by punting after Notre Dame has scored.  So the only other option is to go for it, whether by fake field goal or a more standard play.  And, as TMQ so eloquently put it, “if it succeeded, victory was certain”.  So Michigan State must have assumed that they had a better than 25% chance of converting at least a first down, if not a touchdown.  To put it in terms of expected value, let’s say that there is a T probability of getting the touchdown, failing that a F probability of getting a first down, and a S probability of scoring after getting a first down (I’m ignoring the ‘value’ part of the equation because a win has value 1, and I can skip over multiplying things by 1).  MSU needed T+(1-T)*F*S>.25 to be true to make going for it worthwhile.  That is, they needed to score on that play or at least convert a first down and score later (a touchdown or a field goal) to be better than trying a field goal right there.  We can leave out terms where they don’t score the immediate touchdown or convert a first down, or where they convert the first down but don’t score later, because they lead to losses and have an EV of 0.

Using Advanced NFL Stats’ NFL numbers, there’s about a 10% chance of scoring a touchdown on 4th down from the 29 (I increased the number a bit because scoring is a bit easier in college, and to give MSU the benefit of the doubt in going for it).  There’s only a 2% chance of getting a first down; let’s give MSU the benefit of the doubt and make it 5%.  Then we have .1 + (.9)* .05*S>.25, which simplifies to S > 3.33.  Since S is a probability and can’t be greater than 1, that means this equation can’t be satisfied with T=.1 and F=.05; with an S of 1 the left side is only .145.  That is to say, if MSU was guaranteed to score after converting the first down (or scoring on the 4th down play), they would only win 14.5% of the time because the touchdown or first down are so unlikely.  In contrast, with S=1, going for it would be justified if T=.2 and F=.1, for example. A converted first down gives MSU 1st and 10 at the 15, and converting a field goal (especially after three other plays) becomes much more likely, so maybe we can stomach S=.9; T=.2 and F=.1 would still work out.

Summing up, we could say that MSU would have to think that they had at least a 20% chance of scoring right there, and at least a 10% chance of picking up the 14 yards when they don’t score, to justify going for it.  However, in the NFL at least those estimates seem far too high; at more reasonable numbers, the decision to go for it is unjustified, and kicking was actually the best choice.  But, the NFL numbers are based on what NFL coaches do in the 4th quarter (since you can’t be losing in overtime); it’s possible that the probabilities are in fact higher because college coaches expect other coaches to extend the game, and thus don’t have their defenses properly set for a fake play.  In any event, it looks like a tight decision to me.  You have to double the NFL conversion rates just to make it a reasonable probability play.  On top of this, you have all the scorn and second-guessing that would have occurred if the fake had failed.  So I think the fake field goal call was definitely a ‘bold gamble’, even if it was the right play in that situation.

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### 2 Responses to TMQ Ignores the Percentages

1. Ben says:

you KNOW i have to comment on this ;).

really good analysis – I really can’t honestly think why anyone would have an inkling of an intuition that the fake FG was the technically correct thing to do. Well, maybe if you’ve got some kind of selection bias with a slogan like, “Coaches should play to win” (which reminded me a lot of that herm edwards coors light commercial – “you play to win the game!”) I mean, I can understand going for it on 4th down more often than coaches do, but you’re right, that decision was probably irrational & emotional.

It was also awesome.

• Alex says:

I was thinking, Ben probably has feelings on this :-)

It is possible that the fake was the right thing to do. Maybe MSU’s kicker is crummy (I have no idea), maybe they had a 70% chance of converting that pass; there are lots of things that could affect the decision. But mostly, without knowing the numbers, you can’t really evaluate the decision. And with the numbers I could think to look up, it looks like a bad decision. But the numbers could be wrong, or the decision could be close – That Pats/Colts game where the Pats went for it on 4th and 2 was a close call by the numbers, and everyone was riled up about that. And if the numbers are close, I think the factors specific to the game, or the coach’s instinct, has to be respected.

It was fairly awesome overall. Given my rooting interests, I’m just happy that one team lost in heartbreaking fashion and the other team’s coach had a heart attack ;-)