According to the latest unscientific polling, 75% of ESPN.com users think that Alex Rodriguez will win at least one World Series before his career is over. My vote was ‘yes’ too, but after running some numbers, I’m not so certain.
Let’s make a few assumptions and see what we come up with:
A-Rod will play until he’s 38. I looked at A-Rod’s top 10 PECOTA comparables and top 10 baseball-reference comparables, excluding contemporary players who have not yet had the chance to retire. The median age of retirement was 38. This seems like a reasonable enough number for A-Rod, considering that he’s made noises about retiring much sooner.
A-Rod’s teams start at a 90-win baseline before A-Rod’s contribution. Basically, I’m assuming that A-Rod’s teams are already going to be potential playoff contenders without Rodriguez on the roster. Certainly this is likely to be the case as long as he stays with the Yankees. But even if he departs, his clubs are going to be pretty well off. It isn’t easy to afford A-Rod, which means that any club that spends on A-Rod is probably going to be spending money in other places. And Rodriguez has some discretion to pick and choose his employer; I think we can be fairly certain that being on a contending club will be one of his priorities.
If A-Rod’s team reaches the playoffs, they have a 1-in-8 chance of winning the World Series. Keep it simple, stupid.
From here, it’s a matter of adding A-Rod’s PECOTA projected WARP to the 90-win baseline. For example, PECOTA projects that A-Rod will be worth 7.0 wins in 2008, which implies that the Yankees (or A-Rod’s surrogate employer) will be a 97-win team.
What are the chances that a 97-win team wins the World Series? Well, if a team actually wins 97 games, it will almost certainly make the playoffs. But we don’t really have a 97-win team; what we have is a team that’s projected to win 97 games, with a fair amount of uncertainty around that estimate. I addressed that ambiguity in this article, and came up with a curve that estimates the probability of a team reaching the playoffs based on its projected win total. A team projected to win 97 games, for example, will reach the playoffs 74% of the time. If it wins the World Series in one out of eight of these instances, its chances of winning it all are about 9.3%.
We can go through this process for each year from now through 2014, A-Rod’s age 38 season:
WARP is A-Rod’s projected Wins Above Replacement total; TeamW is the team’s projected number of wins once we add A-Rod’s total to the 9-win baseline. Play% and WS% are the team’s chances of reaching the playoffs and winning the World Series, respectively. Note that PECOTA only projects A-Rod out through age 35; I’m simply lopping half a win off his WARP from there forward.
If you add up the yearly WS% numbers, you wind up at 64.9%, but that isn’t the answer we’re looking for, because A-Rod could win the World Series two or three or eight times before he hangs up his spikes, and the 64.9% estimate is double (or triple-, etc.) counting those instances. The way around this is to figure out the probability that Rodriguez won’t win the World Series in any given year and multiply those numbers together. I won’t bore you with the math, but this works out to a 49.2% chance that A-Rod will win the World Series, and a 50.8% chance that he won’t.
There are a lot of assumptions that could be critiqued here, including the unmentioned assumption that the probability of A-Rod winning the World Series in any given season is independent from the next one. But, hey, it’s a Tuesday afternoon, a rather dreary one at that, and we’re trying to have some fun here. Will Alex Rodriguez win a World Series? It’s a coin flip; not much better and not much worse.