Tuesday, November 17, 2009

In defense of the devil himself

Last night's Colts-Patriots football game had it all: a good football game, a Patriots loss, a Peyton Manning win and the meeting of football and statistics. If you haven't heard about it yet, up 34-28 at their own 28 with two minutes left, the Patriots went for it and failed. The Colts promptly scored in four slow plays that took left 13 seconds on the clock, winning 35-34.

Most people on TV, including the announcers, roundly bashed Bill Belichick for the call, but was it really that bad? This New York Times blog argues that going for it on fourth down gave the Patriots a marginally higher chance of winning. Most conventionalists argue that the Patriots should have punted because it's what teams do. The conversion, however, would have ensured victory. A failed conversion, which is not as likely because the Patriots averaged close to 7 yards on every play, still left the Colts with 30 yards to go.

A punt offered none of the chances of ensuring victory, but offered the same problem as a failed conversion, that of stopping the Colts. I think Burke's numbers at the New York Times blog are off because they really prove that if the Patriots had about 100 chances to run that play, they would have won 56 times. Belichick is paid, however, for situational judgment. The probability of winning by going for it on fourth down last night has to do with the players involved on both teams and how they match up against each other.

Peter King at Sports Illustrated, who I enjoy reading even though he usually abstains from the sort of higher-level thinking that shows going for it on foruth down is usually a good idea, had a better analysis, which shows why turning sports over to statheads isn't a good idea.

Let's place the odds of Brady getting two yards at 60, 65 percent. The odds of Manning going 72 yards to score a touchdown in less than two minutes ... that's maybe 35 percent.

You might say Manning's chance of taking his team 72 yards are better than 35 percent. Not sure I would. On his previous seven possessions, covering about 30 minutes of game time, Manning had done the following:

· Six plays, 79 yards, touchdown.

· One play, zero yards, interception.

· Five plays, 79 yards, touchdown.

· Six plays, 16 yards, punt.

· Four plays, 24 yards, interception.

· Five plays, 16 yards, punt.

· Three plays, no yards, punt.

Three punts, two interceptions, two touchdowns. Now, maybe Belichick thought his defense was tired. Maybe he feared Manning. Maybe he trusted Brady. Whatever, the faulty logic here is that Manning was a sure thing to ram it down the Patriots' throats. Yes, he'd just done that, but on the series previous to that one he'd thrown a interception, his second of the night. So if the theory was Manning was going to score for sure, I don't buy it.

It's still hard to argue with Burke's numbers. There was a 60 percent chance that going for it would have won the game, and a 50 percent chance that a failure would not have resulted in a touchdown.

(0.60 * 1) + (0.40 * (1-0.53)) = 0.79 WP (WP stands for win probability)

Personally, I'd give Manning an 80 percent chance of scoring from the Patriots' 30. That gives us:

(0.60 * 1) + (0.40 * (1-0.80)) = 0.68

The Colts had a 30-35% chance of scoring from their own 30, so a punt has a 65-70% chance of leading to victory, making it roughly the same as going for it and failing even if you believe that the Colts had an 80% of chance of scoring. The obvious point to be made is that there was a 60% of a certain victory by going for it, which is what Belichick was going for. I do have to admit that I don't understand the significance of a 2 or 10% increase in win probability, which I can't understand in football terms (eg is 2% like an 8-yard pass or a 28-yard pass?).

When people say things like "you should make the Colts go the length of the field", the unexpressed idea is that you should be beaten by someone else, not yourself. If the odds are equal, which they more or less were, and Peyton Manning beats you, you can say that Peyton Manning beat you and not feel bad. If, given the same odds, you lose because of your own mistake, somehow it seems worse. This mentality of failure by distance probably explains why university students never try as hard as they could. If they did, they might find out that they're not very good. It's better for the minds of many to keep failures obscured by various outside factors and events.

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