(Yes, the Worcester Worcesters. Some sources call them the Brown Stockings, but I like calling them the Worcesters because it shows even less ingenuity in naming than the name "Phillies" does.)
There are three facebook groups. (I wonder if there's a myspace group; the link goes to a paper that's been circulating about the class differences between Facebook and Myspace.)
Then I remembered that I have Phillies tickets for their game against the Cardinals on July 13th, the first game after the All-Star break.
I got to thinking -- what are the chances that I'd see the Phillies' ten thousandth loss? They've lost 9,991 games so far; they've got nine more to go.
Surely the 10,000th loss is a historic moment in all of professional sports. No team has lost this many games. (The San Francisco (formerly New York) Giants have won 10,000.)
It's not so hard to compute this. What I needed to know was the probability that the Phillies lose each particular game. This can be found via a method which for some cryptic reason is called the "log5 method", which I learned about from this article from Diamond Mind which computed the probabilities that each of the 2002 playoff teams would win the World Series. The method is as follows: if team A wins pA of its games, and team B wins pB of its games, then the probability that team A wins in any given game against team B is
pA(1-pB) / (pA(1-pB) + pB(1-pA).
The best justification for this formula is that it works when you test it on actual data. (Actual baseball data, that is; I'm not sure if it's good for other sports.) But an intuitive justification for it is as follows: you have two coins, coin A and coin B. Each coin has "win" on one side and "loss" on the other. Coin A comes up "win" with probability pA, and coin B comes up "win" with probability pB. To simulate a game, flip the two coins. If one comes up "win" and one comes up "loss", that gives you the outcome of the game; if they both come up the same, flip again. Notice that the formula passes a couple sanity checks. If pA = 0, then it always gives 0 -- that is, if a team never wins, then its probability of winning against any opponent is zero. If pB = 1/2, then it just gives pA -- so a team which is playing aginst average teams performs how it usually performs.
To adjust for home field advantage, I added 0.02 to the home team's winning percentage and subtracted 0.02 from the visiting team's winning percentage; this is the method used at Baseball Prospectus' postseason odds simulation, which I'll have more to say about later.
So, for example, the Phillies play the Reds tonight, in Philadelphia. The Reds have won 29 games and lost 48, so their winning percentage is .377; we replace this with .357 since the Reds will be playing on the road. The Phillies have won 40 and lost 36, so their winning percentage is .526; we replace this with .546 since they're playing at home. The formula tells us that the Reds' chance of winning tonight is
(.357)(1-.546) / ((.357)(1-.546) + (.546)(1-.357))
which is 0.315. This is the Phillies' chance of losing, which is what I'm interested in.
So after tonight, the Phillies will have eight losses to go with probability 0.315; they'll have nine losses to go with probability 1-0.315, or 0.685.
They'll play the Reds again tomorrow night. After that game, they have seven losses to go with probability (0.315)2 = 0.099; they have eight losses to go with probability (.315)(.685)+(.685)(.315) = .432; they have nine losses to go with probability (0.685)2 = 0.469.
Thus, I set up a spreadsheet which calculates the probability that after each game, they have 9, 8, 7, ..., 1 losses to go. The probability of the Phillies getting their ten-thousandth loss on a certain day is the probability that they have 9,999 losses before that day ("1 loss to go"), times the probability of losing that day.
The results are as follows. The rows in red are home games, following the same color scheme as the sorted schedule. The winning percentages are from mlb.com standings as of June 27.
|Date||Opponent||Chance of 10,000th loss|
|Jun 27||v. Reds||0.000000|
|Jun 28||v. Reds||0.000000|
|Jun 29||v. Mets||0.000000|
|Jun 29||v. Mets||0.000000|
|Jun 30||v. Mets||0.000000|
|Jul 01||v. Mets||0.000000|
|Jul 02||@ Astros||0.000000|
|Jul 03||@ Astros||0.000000|
|Jul 04||@ Astros||0.000467|
|Jul 06||@ Rockies||0.002946|
|Jul 07||@ Rockies||0.009603|
|Jul 08||@ Rockies||0.021746|
|Jul 13||v. Cardinals||0.030071|
|Jul 14||v. Cardinals||0.041621|
|Jul 15||v. Cardinals||0.052571|
|Jul 16||@ Dodgers||0.091757|
|Jul 17||@ Dodgers||0.106722|
|Jul 18||@ Dodgers||0.112506|
|Jul 19||@ Padres||0.108077|
|Jul 20||@ Padres||0.097745|
|Jul 21||@ Padres||0.083264|
|Jul 22||@ Padres||0.067340|
|Jul 24||v. Nationals||0.031618|
|Jul 25||v. Nationals||0.026675|
|Jul 26||v. Nationals||0.022282|
|Jul 27||v. Pirates||0.018717|
|Jul 28||v. Pirates||0.015312|
|Jul 29||v. Pirates||0.012425|
|Jul 30||@ Cubs||0.014016|
|Jul 31||@ Cubs||0.010085|
|Aug 01||@ Cubs||0.007142|
|Aug 02||@ Cubs||0.004984|
|Aug 03||@ Brewers||0.004103|
|Aug 04||@ Brewers||0.002533|
|Aug 05||@ Brewers||0.001533|
|Aug 07||v. Marlins||0.000613|
|Aug 08||v. Marlins||0.000441|
|Aug 09||v. Marlins||0.000317|
|Aug 10||v. Braves||0.000251|
|Aug 11||v. Braves||0.000171|
|Aug 12||v. Braves||0.000115|
|Aug 14||@ Nationals||0.000074|
|Aug 15||@ Nationals||0.000051|
|Aug 16||@ Nationals||0.000034|
|Aug 17||@ Pirates||0.000024|
|Aug 18||@ Pirates||0.000016|
|Aug 19||@ Pirates||0.000011|
|Aug 21||v. Padres||0.000008|
|Aug 22||v. Padres||0.000005|
|Aug 23||v. Padres||0.000003|
|Aug 24||v. Dodgers||0.000002|
|Aug 25||v. Dodgers||0.000001|
|Aug 26||v. Dodgers||0.000001|
|Aug 27||v. Mets||0.000000|
And I've only got a three percent chance of seeing this historic moment on the 13th of July. I hope I don't see it, because that would mean the Phillies would only win four out of their next thirteen.
edit (Friday, 2:39 pm): Frank athot dogs and beer features a similar analysis.
signed to your rss
в конце концов: благодарю.. а82ч
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