Through Bill Simmons’ latest column, I found this awesome math & probability article on ESPN detailing Bill Belichick’s controversial 4th-and-2 play call last week. I thought I’d touch on it with some thoughts from a business/decision making/organizational-supply-chain-management perspective.
Context: Patriots’ ball on their own 29-yard line, winning by 6 points, just over two minutes to go.
Objective: Maximize Patriots’ probability of winning the football agme.
Decision Tree:
Thought I’d dust off Microsoft Paint for a change
How to read this: Belichick has to decide whether he wants to go for it on 4th-and-2. Each circle represents a point of action that’s out of his control (it’s in Tom Brady’s), and each square represents a point where the ball changes hands (it’s in Peyton Manning’s). If Belichick decides to Punt, he gives Manning control – and if the Colts score, the Patriots lose. If Belichick decides to Play, he gives Brady control. If Brady converts (and further, if they hold the ball), the Patriots win. If Brady doesn’t convert, Manning takes control, and if the Colts score, the Patriots lose.
How to interpret this: As per the article, if the Patriots punt and give the Colts the ball deep in their own territory, the Patriots’ probability of winning is 79%. Or in other words, there’s only a 21% likelihood that Manning can take the ball all the way downfield in around two minutes and score a touchdown. (Though, given how Manning has been playing this season, you could argue this is a lowball estimate.)
But if they play, we know the probability of converting based on empirical data is 55.7%. And assuming the Pats are able to convert the 4th down (putting us at the top-most circle in the diagram), there’s a 92% chance that they’ll be able to hold the ball for the win. If not, the Colts have a 34% likelihood that they’ll drive for the touchdown – giving the Patriots 66% odds of winning in that situation.
Working backwards: Putting the ball in Brady’s hands gives the Patriots a 55.7% chance of winning 92% of the time, and a 44.3% chance of winning 66% of the time. Their overall odds of winning the game by giving Brady the ball, therefore, are 80.5% (92*.557+66*.443). Which is better (sliiigghtly) than letting the punter do his thing.
But the science of management and organizational behavior deals with way more than just numbers. There are an infinite number of intangibles. On the one hand, this basic calculation doesn’t consider dozens of other minute possibilities (consider that the Pats convert the 4th down but then can’t hold the ball – we’d still need to figure out the odds of the Colts driving to score). Or maybe Belichick had a feeling that his punter wouldn’t be able to kick effectively (I’m envisioning the second-to-last play from the movie The Replacements – skip to around 7:30), and that therefore, the win probability from punting the ball was strikingly lower than it seemed at the surface. Who knows.
But most importantly, it’s awfully tough to justify at what was probably the most critical point in the Pats’ game – if not, their entire season. Belichick wagered big – and lost big. There’s already been a ton of fallout from fans, press, and I can only imagine, from the players too. A good manager should know that sometimes the highest-percentage play isn’t always the smartest – sort of like how you probably wouldn’t bet $100 for a 1-in-1000 chance to win 100,001. You win overall (by a dollar!) if you make the bet every time, but maybe you’re better off taking the safe route and pocketing the $100. Or, in Belichick’s case, saving face and letting Manning win the game instead of losing it for himself (@2:00 in).