How Unlikely Was the "Moneyball" Win Streak?

So it was another typical Friday for me, surfing the baseball sections of the web. I was flipping through FanGraphs articles and came across a story on Melvin Mora (who just retired). That happened to lead me to a 2003 article written by then-ESPN now-SBN writer Rob Neyer on a Topps baseball card pack. One of the snippets from that article was this:

If one flipped a coin 20 times, the odds of it coming up heads on each flip are 1-in-1,048,576. Thus, Oakland's 20-game winning streak from August 13 to September 4, 2002, was truly one in a million. The A's won games 18 and 19 on Miguel Tejada (homer and single) in the bottom of the ninth. Then, after blowing an 11-0 lead, Oakland won its 20th straight on a Scott Hatteberg homer -- again in the bottom of the ninth. The Athletics' final triumph broke the AL record for consecutive victories.

But it wasn't quite one in a million, was it? Because the A's were an excellent team last year -- remember, they won 103 games -- and their competition during that 20-game winning streak was something less than excellent. The A's beat the Royals (62-100) five times, the Tigers (55-106) three times, and the Indians (74-88) four times. They also beat the Blue Jays (78-84) twice, the White Sox (81-81) three times, and the Twins (94-67) three times. So that's 20 games and 20 wins, with only three against a team that finished 2002 with a winning record.

I don't want to figure the actual odds (and I don't want to encourage any of you), but I have to think it was something less than one in a million.

Well, undettered by Mr. Neyer, I went ahead and did calculate the odds to see how much less than one in a million the streak was. If you've had any sort of statistics class it's really not that hard to calculate. For a 50/50 coin flip to land heads every time, that odds are 1/2 times 1/2 times 1/2 twenty times (that's 0.5^20). Since the teams the A's played were mostly awful, you can replace the 0.500 odds with the higher odds of winning that more truly represent the chance of beating each team. For a quick and dirty thought experiment, let's use win percentage (actually, we'll use the inverse of win percentage, which represents the chance that the A's win) and see what comes up. The chance of the A's beating each team using this method become this:

 Team Record Chance to Beat Times Played Royals 62-100 0.617284 5 Tigers 55-106 0.658385 3 Indians 74-88 0.54321 4 Jays 78-84 0.518519 2 White Sox 81-81 0.5 3 Twins 94-67 0.416149 3

So you take chance to beat, multiplied by times played, and then multiply those numbers together and you've got your answer. Replacing the coin flips using the above percentages, the odds drop from Neyer's original 1 in 1,048,576 to a much lower 1 in 185,387. Still darn impressive, but it turns out the achievement may have been closer to one in a thousand than one in a million. Still amazing. Still very cool that it turned into a great movie this year. Still one of the best A's memories we'll all ever have.

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