## Tuesday, December 11, 2007

### When Odds make no Sense

Betting markets usually are good at prediction, but this morning I read that the betting action has made the Patriots odds-on favorites to have a perfect season.

Two things make me skeptical--Tom Brady's touchdown-to-interception ratio, and the number of games left on the Patriot's schedule.

Tom Brady has a 9-1 touchdown to interception ratio this year. This is astonishing, and surely reflects luck. Over his career before this season, his ratio has been an excellent 2-1 (stat comes from TMQ). A ratio that improved to 3-1 or 4-1 could reflect fundamentals (better line play, better play calling, Randy Moss, etc), but 9-1 must reflect a lucky draw.

If Brady returns to normal, it would be reasonable to expect New England's probability of winning to drop to .9 against most teams, and .6 against the Colts at home. They have five games remaining before they (presumably) play the Colts for the Super Bowl. So the chance of the Colts winning the last 6 is .9^5*.6, or .354.

This is still a ridiculously high probability for going undefeated, but it makes it a 2-1 fair bet, rather than less than 1-1.

Anonymous said...

If you are going to go that route, shouldn't you have to figure the probability that the Colts will make it to the AFC championship? That certainly is not guaranteed. That makes the calculation more complicated but likely increases the probability the Pats go undefeated (if maintaining a 90% probability of winning against other teams)

Richard K. Green said...

OK, fair point. But if the Patriots have a .9 probability of winning every game, they probability of going undefeated is .9^6 = .53, so let's call that an upper bound probability, and the .35 is a lower bound probability. It is hard to make a case for an odds-on bet.

Jonathan Weinstein said...

I would say the touchdowns are unequivocally a change in fundamentals, the interceptions mostly luck.

One back-of-the envelope estimate I like is that in 12 non-Colts games, 10 were no contest and two were coin flips. That would be 11/12 or 93%.

I think the best estimates would look at distributions of points for them and their opponents on each drive, etc.

.6 sounds rightish for the Colts, so agreed the final answer can't be .5--esp. this is football, anyone can get hurt anytime.

Anonymous said...

"I would say the touchdowns are unequivocally a change in fundamentals, the interceptions mostly luck."

I would point out that Brady has been sacked about 30-40% less this season than previous seasons (depending if you look at per game or per pass attempt). With less pressure, Brady throws fewer interceptions. Now add those jump balls to Randy Moss, which would have been intercepted if it had been anyone else. Finally, the Patriots have not been as many close games as previous season (except Baltimore, Indy, and Philly), which allows Brady to be more conservative in his throws and not force any. All those together and I would expect a decline in interceptions.