I’ll only make one quick comment about the Carlos Pena-Mario Ramos et al deal between the Athletics and the Rangers: I’m getting tired of the Billy Beane hagiography. But that’s because I’m at heart contrarian and impatient. It’s hard not cheering for the little Athletics that could, and the engineer driving the train.
But what I’m responding to is the second half of Rob’s column on Monday, about the comparison between DiMaggio and Ted Williams’ most famous streaks. The story is here: ESPN.com: MLB – DiMaggio’s streak not even one in a million
Here is what I wrote to Neyer, after some time working through the numbers:
Hi Rob,
I enjoyed watching Jose Burilla’s math from my untenured position here in Brooklyn, but I think he missed one pertinent detail: The question being asked is about the odds of someone else breaking the record, not for the odds of the immortal repeating? Right?
While Williams’ consecutive times on base streak would be relatively easy for him to equal, because he’s the all time OBP leader, it would be significantly more difficult for the average player to best.
And while DiMaggio was no slouch in AVG during his career, he ranks 41st all time in that category, I think that means he was more average in AVG than Williams is in OBP.
The odds of a .334 OBP (last year’s AL OBP) hitter to equal Williams mark are about 1 in 42,000,000.
While the odds of a player who gets hits in 23.8% of his AB (last year’s AL average hits per PA) getting a hit in 56 consecutive games is roughly 1 in 220,000,000. While it will clearly be easier for someone else to break the Splinter’s record than the Clipper’s, the difference is about half as large as advertised because of the differing contexts.
I suppose that the proper way to ask this question, however, would be to look at peak values. It only takes one hot run by one player, after all, to break either record. So, last year the top AL OBP was Jason Giambi’s .477, which is quite similar to Williams’ lifetime OBP, but significantly lower than Williams .526 OBP in 1957, the year he set the record.
The times Giambi would match Williams’ record in 1 million games, given his performance last year, is 7 (Williams, at the pace he performed in 1957, would have done it 34 times).
The best hit per plate appearance mark in the AL last year was by Ichiro, of course, who had hits in 33 percent of his plate appearances. Given a million games at that rate Ichiro could be expected to hit in 56 straight games 38 times.
For DiMaggio to repeat his feat would have been much harder than for Williams to repeat his, but that doesn’t mean DiMaggio’s is a harder record to break.
Best,
Peter
Almost immediately after sending that off I realized I’d overlooked something. So I fired off another letter:
It occurred to me after I sent the last email that DiMaggio probably had a better than normal year in 1941, too. So I looked it up.
His H per PA was .307, a far sight lower than Ichiro’s, though better than his career mark.
That translates to him hitting in 56 straight games 7 times out of a million. As Jose pointed out, at his career average level he would have done it once (which he in fact did, of course).
BTW, I’ve fudged the PA per game data. Ichiro would have more than DiMaggio, of course. The average ALer last year had fewer appearances (4.28) per game. I did all the probabilities at DiMaggio’s 1941 rate as calculated by Jose.
Thanks for listening.
Peter
I’m not sure what the lesson here is. What surprises me a little are the huge swings in probability, depending whether you measure from peak value or average value. The bottom line is that the odds are long (one million games represents 6,173 seasons) and a slight difference can improve the odds seven fold, but that doesn’t mean we’re ever likely to see its like again.