What Are The Odds That The White Sox Throw A Perfect Game Today Against The Indians? (06/05/2010)

Don Leypoldt over at The Hardball Times wrote an interesting article about the odds of throwing a perfect game. According to his estimates, the chances of three perfectos occurring in one month is approximately 1 in 2,000,000. Leypoldt's article and analysis inspired me to look at the odds of a perfect game occurring today.

On Base Percentage (OBP) is the likelihood of getting on-base. Outs Percentage (OP), calculated as 1-OBP, is the chance that an out is made. I wanted to take this and look at the possibility of the Cubs throwing a perfect game today, but the variability of pitchers hitting (and the double switch) makes lineup prediction for a whole game more volatile in the NL than AL. So, instead, I will look at the White Sox's opponent, the Cleveland Indians, and assume that there are no late-inning defensive replacements which will occur and that the OPs to date represent their true OBP ability (no sample size/random noise issues).

The Sizemore-less Indians lineup (.324 team OBP), in terms of OP, is as follows:
C - Lou Marson = .727
1B - Russell Branyan = .683
2B - Luis Valbuena = .706
SS - Jason Donald = .714
3B - Jhonny Peralta = .671
RF - Shin-Soo Choo = .620
CF - Austin Kearns = .629
LF - Shelly Duncan = .579
DH - Travis Hafner = .639

The product of each Indian's OP cubed yields a neutral context perfect game probability (or improbability) of 0.00001423%.

By contrast, the Yankees have a team OBP of .366 and their starting lineup's OP, as currently situated, looks like this:
C - Frank Cervelli = .625
1B - Mark Teixeira = .664
2B - Robinson Cano = .593
SS - Derek Jeter = .648
3B - Alex Rodriguez = .626
RF - Nick Swisher = .599
CF - Curtis Granderson = .658
LF - Brett Gardner = .622
DH - Jorge Posada = .607

The product of each Yankee's OP cubed yields a neutral context perfect game probability (or extreme improbability) of 0.00000328%. That means that, as currently situated, the Yankees are 4.34 times less likely to have a perfect game thrown against them than the Indians.

And thus explains the Armando Galarraga "perfect" game. Anyone want to calculate the odds of a no-hitter?