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# Figuring out the A's winning streak

We could spend all month talking about winning streaks, but at some point even my interest would wane. So with apologies to everybody who e-mailed me about this and didn't get a response, I'm going to put the A's and their 20-game streak to bed with this final entry ...

Rob,

I came late to the game, but after reading your article on the probability
of the A's 20-game winning streak, my curiosity was aroused. I went to the Diamond Mind web site and dug up some old work from Bill James, in which he expresses the chances of team A winning a game, based only on Team A's and Team B's current winning percentages:

Chance of A's winning = (A - A*B) / (A + B -2*A*B)

where A and B are the respective winning percentages of the teams.

Now, the A's started their streak by losing the night before to the Toronto
Blue Jays (Aug.12) to give them a record of 68-51. The winning percentages of their next 20 opponents (heading into each game) are shown below:

.444, .441, .479, .475, .472,
.443, .439, .435, .432, .386,

.383, .380, .405, .402, .398,
.593, .588, .584, .401, .399

(No, they weren't playing the Angels, Mariners and Yankees every day ... or at all!)

Using Bill James' formula, and updating the A's winning percentage after each
game, they had a 1-in-6,353 chance that they would win all 20 games.

James further goes on to state that, historically, home teams have had a
.540 winning percentage. This would add .040 to each home team's winning percentage. The A's played the first five games at home, went on a 10-game road trip, and finished with five games at home. Applying the .040 boost to the home team for each game produced a 1-in-5,833 chance.

As a check, I rewrote the program to assume a winning percentage of .500 for
both teams for all games. The formula gave the expected result of 1 in 2^20 (1,048,576).

Yours truly,
Eric Wright, Ph.D.

Wow, Eric, you did the work that I was going to do this weekend!

However, I have one caveat, which is that I'd like to see the same numbers run, but using the team's end-of-season winning percentages. Figuring that their true "quality" is best indicated by their complete season records.

Is that something you could easily do? If not, I will.

-r

You got it, Rob.

The A's played two games against Toronto (78-84, .481), three games against the White Sox (81-81, .500), four games against Cleveland (74-88, .457), three games against the Tigers (55-106, .342), three against your beloved Royals (62-100, .383), three against the Central-winning Twins (94-67, .584), and finally two more with the Royals. And given Oakland's final record (103-59, .636) I get:

1-in-2,750 chance ignoring James' home-field advantage factor, and
1-in-2,268 chance including it.

As for their true quality, I somewhat agree and somewhat disagree. Look at Baltimore's season-ending 12-game losing streak. Were they really a 67-95 team, or a 67-83 team that simply gave up?

Yours,
Eric

Well, look at it like this ... What would give you a better read on a team's true quality: its record after the first five days of the season, or its record after the first five months of the season?

The answer to that question is pretty obvious. That said, it's certainly true that the true quality of a team can change over the course of a season. Year after year, the A's are better in the second half than in the first half because talent is cheaper in the second half, so that's when they make their move. And at the other end of the standings, bad teams often get even worse in the second half, as they trade their high-salaried players and young players get their chance.

The A's winning streak came in August, when the Tigers no longer had Jeff Weaver and the Indians no longer had Chuck Finley, and during those 20 games the A's failed to score at least four runs just once (on the 16th, Corey Lidle outdueled Mark Buehrle 1-0). So I suspect that if we could somehow isolate the true quality of each team in each game, the winning streak would become even less unlikely than 1-in-2,268.

Then again, if we're talking about true quality, maybe we should look at the teams' Pythagorean records -- that is, their run differentials -- rather than their actual records.

I don't think anybody's yet bothered with such trivial analysis, but if you just can't get enough of this stuff, I recommend Alan Reifman's Hot Hand in Sports Web page.

Senior writer Rob Neyer, whose Big Book of Baseball Lineups will be published in April by Fireside, appears here regularly during the season and irregularly in the offseason. His e-mail address is rob.neyer@dig.com.