Saturday, October 3, 2009

Playing The Odds: Coming Back From Two Touchdowns To Win

Our good friend TheNajdorfDefens (an internet moniker named after some obscure chess strategy that forced a draw in 1927 or something) sent me an article over the course of three emails. I set out to edit it into something cohesive but quickly realized that any editing would eliminate its unique Najness. Here it is, more or less in its entirety. I've added my own comments at the end.


Here is a common NFL [or college] situation. You are losing by 2 TDs in the 4th quarter, say 21-7. Essentially, to win you need to score 2 TDs to tie it up and then win in overtime, while shutting out your opponent.

So, Team A has the ball down 14 with 10 mins or 6 mins or 3 minutes left, drives down the field for the TD, and then the only debate centers on kicking deep versus going for the onsides kick.

Aha, but the mistake has already occurred!

We, for our entire football-watching/coaching careers, implicitly assume that the Team after scoring the TD should kick the XP to cut the margin to 21-14.

But, if you’re trying to win the game [and as Herm Edwards reminds us, ‘You play to Win the Game’] you shouldn’t kick! You should *always* go for 2 here.

I can hear you laughing, so some very simple math will show us the light where ‘common sense’ has failed.

NFL Teams are 60-65% to score from the 1, and 55% to score from the 2-pt conversion market. Let’s be conservative and call it 50%, fair?*

Scenario A: You score 2 TDs, kick XPs and go to Overtime. You are 98% to hit both XPs and 50% to win in overtime, OT famously being a coin-flip. We can call that 49-50% odds of Winning.

Scenario B: You go for 2 after your first TD:

B1) 50% of the time you make it, and are only down 6. With your next TD you kick the XP as normal to win the game.

50% of the time you miss, and are down 8 now:

B2) Down 8, you score another TD and covert the 2 50% of the time. You go to Overtime, where you win 50% of the time. Odds of this = 12.5%.

B3) You miss both 2-pters, and lose the game.

So, you have a 50% chance of winning in Scenario A, and a 62.5% [5/8 for the percentage challenge] in Scenario B. And that’s with using a conservative 50% estimate of converting for 2 on the play.

In addition, in Scenario B1 you have additional winning chances because you no longer need a TD to tie it, you can kick two FGs and take it to overtime if you can?t penetrate the end zone.

So the odds of going for 2 from the start are at least 25% better than trying to get to OT.

In fact, Team A needs to have an incredibly awful <40%>

Bonus : Coaches/players/fans who passionately ‘believe’ in their teams and like playing ‘aggressive’ are rewarded both qualitatively and quantitatively. Win-win!

So why don’t Coaches use this obvious logic and try to win more games?

I think you already know the answer: they’d rather go into OT and win ~50% of the time than have a 63% chance of winning in the 4th Q, because 20-25% of the time they miss both conversions and lose in regulation [as if that’s worse than losing in OT].

Coaches in the NFL would rather keep their jobs than win games. But I remain amazed that the Pats, or Steelers, or Eagles or etc have yet to realize the error of their ways.

The math is so simple I’m sure I’m not the first person to figure this out, but I have not seen this discussed anywhere on the various sites I follow, not even the smart guys at Football Outsiders but it certainly could appear there or at 2p2 or elsewhere.

ps I did just find this paper which shows the math in more detail, but uses a 6% miss XP rate for NFL kicker which is absurd [approx right for NCAA], the the conclusion and analysis is still correct.

Oh, I didn't even mention the 'surprise' factor of doing this - 21-7, you drive down and score with 6 mins left, the Def trots off and the S/T comes on with like 9 lineman and 2 safeties, and your offense lines up either gaining a *huge* advantage or forcing the other team to take a timeout. [You could even be really sneaky and have the Off pretend to walk off, then run back to the LoS and snap the ball, or put the kicker in with like 3 WRs and run a fake, etc, etc.]

*Naj did find some additional research that indicated a 43% success rate for 2 point conversions which would make the winrate 55% instead of 62%. Still considerably better than the 50% winrate that we typically expect for overtime.

Additional Comments

As many of us know there is a growing body of research in football that is discovering that many of the standard strategies are wrong. Teams punt far too often. Teams should run more on third down than they do. Naj gets into something else but I'm not sure I agree with him, or at least not completely. The question comes down to whether to go for the win in regulation rather than the win in overtime. Taking a simpler equation, a game scoring touchdown at the end of regulation, assuming a 99% conversion rate for extra points and a 43% conversion rate for two point conversions the team is still more likely to win by taking the game to overtime.

Naj argues that from a two touchdown deficit the two point conversion should be attempted on the first touchdown, and then if missed the team would (of course) attempt to tie the game with a two pointer on the second touchdown. The net net of this is that the team would outright lose in regulation 33% of the time, would outright win in regulation 43% of the time for an overall 55% winrate when using this strategy (assuming the team in deficit is able to score twice). While I can't argue with the math, it is so specific to this situation: down exactly two touchdowns with <10 minutes, it is easy to see why teams don't pursue the strategy. It simply doesn't come up very often. And for Naj's last question: why don't the "smart" teams realize this and do it, I think the answer is pretty obvious. For one thing, they are down exactly two touchdowns far less often than the dumb teams, and they are in a position where they will win more than 50% if the game goes to overtime, sometimes far more than 50%. Take 2008, teams like Pittsburgh or Baltimore or Tennessee would have been foolish to settle for a 55% winrate in regulation. They could count on their defense to prevent a score on an opening possession 80% of the time (made up number).

Thanks Naj for the contribution.

1 comment:

  1. To be clear, you would pursue this strategy with more than 10 minutes left down 14. You'd do it the entire 4th Q and probably the last few mins of the q3 as well, it's not limited to the final few minutes only.

    I think you'd want to be 60% or more to win in OT to kick twice and take the coin-flip [hard to imagine on the road]. And a team like Pitt or Balt or Tenn is going to score from the 2 more than 43% of the time, if you adjust one side's odds you have to adjust the other side of the equation.

    But I think Pat's comments illustrate a good point, if you are much more likely to win in OT then you can play for OT [with the proviso you may not get the ball] if you are more likely to score from the 2 you should obviously go for 2 more - the 'good' teams are almost by definition better than the 43% NFL average.

    And vice versa for teams that are worse at each, of course.
    Obviously if you can't score twice, it doesn't matter what you do, but the added bonus of going for 2 first means you do NOT need 2 TDs, you can tie it up with FGs which is another advantage.

    The point remains, there are several NFL teams that would benefit from going for 2 after scoring a TD when down 14.


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