Pete Rose and betting market efficiency
Courtesy of Zubin Jelveh's blog, a link to a short paper analyzing Pete Rose's 1989 bets (from the Dowd Report). It's called "Market Efficiency in the Baseball Betting Market: The Case of Pete Rose," by Douglas Coate.
The paper is only two pages long; it lists Rose's bets, both on the Reds and on other teams, from April 8 to May 12, 1987. Rose placed 190 bets, typically of $2,000 each. He lost $4,200 on the Reds (27 bets), $36,000 on other NL teams (72 bets), and $7,000 on his AL wagers (89 bets), for total losses of $47,200. (My numbers add up to 188 bets instead of 190 because I probably counted them wrong from the table.)
Coate describes Rose's bookie's odds as even money, with a 10% fee payable on losses. This is equivalent to 10:11 odds. He says the losses "include about $20,000 to $25,000 in transaction fees," so even if Rose were able to have gotten even money, he still would have lost.
From this, Coate argues that these results are "consistent with an informational efficient [betting] market," and says that Rose's expertise "was not an advantage."
I'd agree that it's interesting that Rose didn't win, and I do think the betting market is very efficient, but I think that looking at Rose's bets is a very weak way of testing for strong market efficiency.
First, why presume Rose is an expert? It's pretty well established that most professional baseball managers work from their gut, not from science or empirical evidence. Rose may have inside information, but professional gamblers have analyzed the market, and, in some sense, have a lot more information impacting their bets than Rose does.
Second, during the period in question, Rose bet on every Reds game except one. It's not very plausible to assume that he would have had inside information impacting every game, would it? Even if he did, somehow, know that over the entire month, the Reds were better than could be predicted from publicly-available information, that would have become apparent as they started winning games and the odds adjusted.
Third, any advantage you'd gain by having inside information isn't worth that much. For instance, suppose Rose knew that Eric Davis would be out of the lineup. If Davis was 50 runs better than his replacement over a season, that's 0.3 runs over a game. That's 0.03 wins, or one extra win every 33 games. Knowing about Davis's absence is a fairly big piece of insider information, and even if Rose had one of those every game he bet on, he'd only win one extra game out of 33 (perhaps going 17-15 with a rainout instead of 16-16).
Suppose, on average, Rose had this kind of insider information one out of every three games (which still seems like a lot, especially considering he bet on so many different teams). In that case, instead of going 95-95, he'd be expected to go 97-93. Rose's results aren't significantly different from either of those numbers, so if you say there's no evidence that Rose could beat the market, you have to also admit that there's no evidence that he didn't have insider information and *could* beat the market. Rose's bets just aren't a powerful enough test to tell us much about market efficiency.