Figuring out the laws of probability

Monday, I wrote a little thing about Oakland's 20-game winning streak last season. A Topps card described the streak as "truly one in a million," but I thought their math was a bit simplistic and I said so. I also went out of my way to dissuade readers from figuring out the true odds, because I know how you like a problem you can get your hands around, and I didn't want to wade through the e-mail that would result from that.

Of course, many of you weren't dissuaded at all, but unfortunately I don't know a lot more now than I knew then, because just about everybody came up with a different answer.

  • Jayadev Athreya says it's one in 500,000.

  • Brian Malcolm says it's one in 200,000.

  • Philip Thai says it's one in 186,283.

  • Brian Cheever says it's one in 185,387.

  • John Toone says it's one in 178,928.

  • Russ Craft says it's one in 13,500.

  • John Kendrick says it's one in 12,089.

  • Jeff Schaefer and Laurence Hart both say it's one in 8,581.

  • Jim Allen says it's one in 8,500.

  • Charles Abell says it's one in 7,330.

  • Mike Fast, Tom Cavileer, and Dennis Bronstein all say it's one in 2,576.

  • John Pastier says it's one in 1,254

  • Div Bhansali says it's one in 955.

    That's 13 different answers to a question that I discouraged people from answering, so you can imagine how many different answers I'd have received if I'd been encouraging. With all that, I think the answer is closer to the lower end of this spectrum. I think if you assume that the A's were really as good as their record, and that their opponents during the winning streak were really as good as their records, then the chance of the A's winning those particular 20 games was somewhere between one in 1,000 and one in 3,000. Which is, I have to admit, not particularly exact.

    But what's a bit more interesting, I think, is this question: Are baseball teams like coins?

    Yes, I know they're not coins in the sense that the wins and losses are just as random as a coin flip. What I mean is that the results of coin flips can be predicted with a high degree of accuracy: if you flip a penny 100 times, it'll come up heads something like 50 percent of the time, within predictable bounds.

    Athletes are like coins in this way. Various baseball hitters and basketball shooters are frequently described as "streaky," but the fact is that hitters and shooters exhibit exactly as many streaks as the laws of probability would predict. Nobody believes this, but it's been tested again and again and again, and I do believe it.

    But has anybody ever tested teams? My guess is that if you looked at the probabilities and then looked at the occurrence of actual streaks by baseball teams, you'd find a pretty close match. Which means that if we could agree on the right way to figure the A's theoretical chances of winning 20 straight against that particular competition, then we'd also have an accurate measure of what their actual chances were.


    Yesterday, Jayson Stark had a nice article about the intentional walk, and whether it's something that should be done away with. And though the subject's now been analyzed from here to Timbuktu since last October, I feel compelled to make a few points.

    1. You can't specifically legislate against the intentional walk. I know that Jayson pointed this out in his piece, but I think it bears repeating because this automatically moots all the easy remedies. If a pitcher wants to walk somebody, all he has to do is throw four straight pitches that are a foot outside rather than three feet outside and two feet high. So you can write any rule you like, but if the rule contains the word "intentional" then it ain't going to work.

    2. The only other "solution" is radical. If you can't use "intentional" -- which is, after all, a judgment call -- then you have to come up with something else, and the only something else that might work is penalizing the defense for any walk that doesn't feature at least one strike. That is, if the pitcher throws four balls and no strikes, the penalty applies even if the poor kid just up from Triple-A was trying his gosh-danged hardest to get the ball over the plate. Essentially, you're adding another penalty for poor control. As it stands now, if you can't throw strikes you give the other team at least one base. If one of your attempts sails to the screen when there's somebody on base, you give the other team at least one base. But now we're talking about giving the other team more bases if you can't throw strikes, even if you were trying to throw strikes.

    And as I see it, that's a big problem. According to my friends at Baseball Info Solutions, last season there were 14,794 non-intentional walks in the major leagues, and 3,013 of those were four balls, no strikes. That's a lot of four-ball walks. And do we really want to give the hitting team extra bases a few thousand extra times? Sure, the pitchers will adjust and try even harder to throw at least one strike, but don't the hitters already have a big enough edge, what with their friendly confines and their Nautilus machines and their joy juice?

    3. I hate the intentional walk. And if there were a practical way to eliminate it, I'd be the first guy standing outside MLB HQ with a noisemaker and a big sign. People want to make this about Barry Bonds, and it's certainly true that we wouldn't be having this discussion if not for Barry Bonds. But Barry Bonds has simply served to bring the issue into the open. True, we don't watch the game to see Barry Bonds get intentionally walked, but neither do we watch the game to see Vladimir Guerrero (32 times last year) intentionally walked or Ichiro (27) intentionally walked or Sammy Sosa (15) intentionally walked. We watch the game to see pitchers make pitches, to see the hitters try to hit those pitches, and to see the fielders try to chase down what the hitters did with the pitches.

    And please, don't tell me about "tradition," because tradition's only a good argument when the tradition makes something better. And thanks to Barry Bonds, my eyes have been opened. Intentional walks -- which, by the way, were never intended by the men who designed the sport -- don't make the game better, they make it worse. Not to be crude or anything, but intentional walks suck.

    It looks like we're stuck with them, though.

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