Wednesday, December 19, 2007

Tom Brady Redux

Tom Brady now needs five touchdown passes in the final two weeks to break Peyton Manning's record of 49. Will he get there?

The bettors at World Sports Exchange certainly think so; they've made Brady more than a 2-1 favorite to get to 50. But the betting market for obscure props like this one is rarely efficient; the ratio of 'fan money' to sharp bets is unusually high. So we can't trust the market for the answer to this one.

The big unanswered question, of course, is how much action Brady will see in Week 17 if the Patriots are still undefeated at that point. The Giants are heavily favored to clinch a playoff spot this weekend, so they likely won't be trying their hardest to stop the Pats' juggernaut. Will that convince Bill Belichick to coast to a seventeenth win by letting his backups play the second half? Will the Pats play it safe either way and not risk an injury to Brady, the one player they truly can't afford to lose?

I'll operate under these assumptions:

- If the Pats lose to the Dolphins (roughly a 6% chance), Brady sits almost all of Week 17.
- If the Pats are 15-0 and the Giants have clinched a playoff berth (66%), Brady plays with this frequency:

1 quarter: 20%
1st half: 10%
3 quarters: 15%
full game: 55%

- If the Pats are 15-0 and the Giants are still playing to get in (28%), Brady plays with this frequency:

1 quarter: 15%
1st half: 10%
3 quarters: 5%
full game: 70%

As for Brady's true skill level of throwing touchdowns, I'm going to set it at 2.5 per game, or 40 per season. I think this is fair. Yes, he's well over that pace this season, but his previous career high was 28, and only three other QBs in history have thrown 40 over a full season. Regression to the mean is a powerful force.

I'll spare you the boring calculations, but the Poisson distribution tells us that with this set of assumptions, Brady breaks the record 44.2% of the time, a far cry from 2/3.

If Brady is assumed to play all eight quarters of his remaining games, he breaks the record with 56.0% frequency.

Using a true rate of 50 TD/season and the above playing time distribution, Brady breaks the record 62.0% of the time.

If you assume eight quarters of play and a true rate of 50 TD/season, that number increases to 74.7%, but I think that's unreasonable on both counts.

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