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10.09.2006

Momentum is nonsense 

King Yao notes that before the postseason started, oddsmakers were offering -300 odds on the Yankees beating the Tigers in a 5-game series -- that is, risk $300 to win $100. Effectively this means that the market claims that the Yankees will win with 75% probability.

Assuming that p is the probability of the Yankees beating the Tigers in one game, and that the probabilities for each game are identical and independent, here are the odds of the Yankees winning:

Win in 3: WWW = p^3
Win in 4: LWWW, WLWW, WWLW = 3 p^3 (1-p)
Win in 5: LLWWW, LWLWW, LWWLW, WLLWW, WLWLW, WWLLW = 6 p^3 (1-p)^2

Total = p^3 + (3p^3 - 3p^4) + (6p^3 - 12p^4 + 6p^5) = 6p^5 - 15p^4 + 10p^3.

Numerically solving 6p^5 - 15p^4 + 10p^3 = 0.75, we get p = 0.64 -- for these odds to be correct, one would have to assign the Yankees a 64% chance of winning any particular game against the Tigers. This is an outstanding claim, given that the Yankees won 60% of their games over the regular season against all MLB teams.

I suspect that main reasons the odds on the Yankees were so skewed were because (1) they had improved their team by adding Bobby Abreu and getting Gary Sheffield and Hideki Matsui back from injury (undoubtedly true, but they were far from being "the best lineup ever") and (2) because the Tigers appeared to be primed for a fall after dropping their last 5 games of the regular season (a load of hogwash).

EDIT: An anonymous tipster noted that I had written WLLWW twice above and left out WWLLW; this has been fixed.

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