Conservative decision costs Belichick

on Nov 16 in Decision Making tagged by Trevor Hicks

If you don’t follow American football or know the rules, just skip this post.  As someone who likes to read and think about cognitive bias and decision making processes, I’m fascinated by the reaction today to Bill Belichick’s decision to go for it last night on fourth and two from his own 28 yard line with 2 minutes to go and a 6 point lead.  The conventional wisdom in this case is to punt.  Here’s a very typical quote from former coach, now analyst Tony Dungy:

On NBC, former Indy head coach-turned studio analystTony Dungysecond-guessed his onetime rival, saying “You have to punt the ball in that situation. As much as you respect Peyton Manning and his ability, and as much as you may doubt your defense, you’ve got to play the percentages and punt the ball.”

Read more:http://sportsillustrated.cnn.com/2009/writers/don_banks/11/16/colts.pats.insider/index.html#ixzz0X4BmydR5
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What’s really ironic about that quote is that Belichick probably was playing the percentages by going for it in that situation.  The Fifth Down blog at the New York Times has the math.  Some computer guys have a simulator that figured a better chance of winning the game all things considered by going for it rather than by making the conventional decision.

Most of the media seems happy to pile on the decision, calling it arrogant or whatever.  Now, I’m happy to concede that the above referenced computer simulation can not be considered the final word, but I think it shows that at worst the decision was 50-50 with respect to maximizing his team’s chance to win.  In that case, the decision comes down to believing your offense can get those two yards and that your defense can stop the Colts if they don’t.  The fact that there was a negative outcome after this decision should absolutely not taint your assessment of it.  When you are making decisions under uncertainty, the outcome is only relevant regarding how it may motivate you to reassess the information that went in to the decision.  Good decisions can have adverse outcomes and bad decisions sometimes work out just fine.  If your financial advisor was showing positive returns for your portfolio by gambling the money in Vegas, you might be happy with the outcome but you probably wouldn’t think much of the decision-making process.

If you really think that Belichick screwed up, then I challenge you to work out the math honestly yourself and do the Bayesian analysis.  I’ll even help you out here.  First, you need to consider the scenarios and assign probabilities to various outcomes.

A: Probability of a first down when going for it.  In this case, we can assume a 100% chance of victory, it’s probably only slightly less, but will simplify the math.

B: Probability Colts a score touchdown from the New England 30.

C: Probability Colts score a touchdown after a New England punt.

Bear in mind there are all sorts of possible outcomes, there can be fumbles, interceptions, long runbacks, whatever.  But you just have to figure the probability that the Colts get that winning touchdown to assess the New England decision.

What did you get for your answers?  I’ll say A is 60%, B is 60% and C is 40%.  YMMV.  Here’s the math, the probability of a New England victory when they go for it is:

60% * 1 that is, they win if they make the first down + 40% * 40% that is, they still win 40% of the time even turning the ball over on downs. This works out to .6 + .16 = 76% chance of winning the game if they go for it.  Now, what are the chances of winning if they punt?  Well, I assumed they had a 60% chance of winning by punting (40% chance Indy drives down and scores).  So under my assumptions New England raised its chances of winning from 60% to 76% by going for it.  It didn’t work out for them, even if there were some strategy that could have given them a 99% chance of winning it still might not have worked out for them.  But plug your own numbers in, I promise you that you have to put in what I would consider to be some pretty crazy numbers to make this an “obviously” bad decision just looking at the percentages.  Bear in mind that real decision making also includes an intuitive assessment of the situation on the ground that really is not amenable to quantification.  Figuring probabilities like this is an aid to decision making, not a replacement for it.

The main points are to accept that good decisions sometimes don’t pan out.  Don’t shoot the decision maker in that case!  If you manage managers like I do please bear this in mind when running your performance evaluations at the end of the year.  Next, note that following the conventional wisdom is generally the safest route personally, but might not be in the best interest of your team.