In the sweep of human history, major-league baseball is, shall we say, a recent innovation. It’s not surprising, then, that we have a poor sense of the proper time scale for evaluating baseball talent. Only since a bunch of men met in La Rotisserie Française to draft mock baseball teams did what happened three years ago become more important to our survival than what happened yesterday.
Take hitters. Tom Tango’s Marcel system says that a hitter’s expected performance in one year is a function of his (and his league’s) numbers in the prior three years. One element of the algorithm is a weighting of 3/12 for the hitter’s performance in the earliest of those three years. There is no way that fantasy leaguers credit 25% of a hitter’s expected performance in 2010 to his numbers in 2007. (In truth, the full weighting is less than 25% since Marcel also calls for 1,200 PA of league-average stats. However, 3/12 is the fraction of the hitter’s portion contributed by that early year.)
Likewise, Marcel asserts that the latest of the hitter’s last three seasons contributes 5/12 (out of all the hitter’s numbers) to the next year. Propose to your leaguemates that less than 50% of a hitter’s expected performance in 2010 hinges on his play in 2009 and you’ll be laughed out of the room.
But those are the ratios per Marcel (and I’m sticking with Marcel here, granting that it is simple, because “simple” can still mean “smarter than us”). The past is prologue, but the immediate past is not the whole story. The point is not that just-closed history is immaterial but that only slightly mustier history fades too fast. I don’t know about you, but six months ago feels like three years ago to me.
What we would be really useful, for fantasy games, is a way to identify players for whom we have exaggerated perceptions—those are the rich buying and selling opportunities. One route would be to examine ownership levels in online leagues or aggregate rankings in mock drafts. However, simpler would be a programmatic approach.
To that end, we’ve created Near-Sighted Marcels (NSM’s). NSM’s are simply Marcels with a more, ahem, human-like ratio of memories. In Near-Sighted Marcels, the remote past still counts, but the recent past counts much, much more.
What ratio of the past three seasons should we use? After careful (in human terms!) deliberation, we went with 80/15/5—that is, our internal projections for players are composed roughly of 80% of this year’s numbers, 15% of last year’s, & a sprinkling of the year before’s. That seems a fair (if humbling) allotment. (In the Comments, feel free to discuss the ratio that you would choose.)
Here is a comparison of the coefficients for both standard and near-sighted Marcel (ratios adjusted to 100):
By this light, humans judge the immediate past to be twice as relevant as does Marcel, but the prior year only 1/2 as much, and the outlying year only 1/5 so.
We generated both Marcels and NSM’s for 2010 for the current crop of hitters. We pro-rated the YTD numbers to a full season by multiplying by 4/3. We also expressed the ratio for NSM’s as 9.6/1.8/0.6 so that the total magnitude (12) would be the same as with Marcels (5/4/3) and mesh with the injection of league-average PA.
Let’s stick to OPS. We’ll define “Sentiment” as a batter’s NSM OPS minus his Marcel OPS (so a Sentiment above 0 indicates a player who is regarded more favorably by humans than by Marcel).
The leader in Sentiment this year is Tampa Bay shortstop Jason Bartlett:
If you give this season a weighting of 80%, you anticipate an OPS for Bartlett of over 850. Now, Bartlett is having a stellar season, but Sentiment advises us not to get carried away by a guy who had a career 699 OPS in 1,700 PA entering this season, and who has hit as many home runs this season as he did for his entire career before 2009.
Among players with at least 300 PA, here are the leaders in Sentiment:
Say what you will about their maturation (and you will say it), these guys should be regarded with a dash of skepticism and off-loaded (for top dollar) with only seeming reluctance. Every thing that can go their way, has.
It’s harder to find laggards in Sentiment with more than 300 PA—depressed play usually means depressed playing time. Still, you could probably guess the big names: Giles, Ortiz, Cedeno, Ordonez, Renteria, Matsui, Upton (B.J.), Burrell, Atkins, Navarro. Guys who (as anyone is happy to tell you) are down to their last swings. If I had a rebuilding team, I would be scooping up these guys like souvenir cups (and at comparable prices).
It’s good to take stock of our limits. It’s even better if we can characterize those limits and play against them. As you plan your keepers for next season, remember those ancient eras when the year ended in an “8” or “7.”
(Here is a link to a spreadsheet with both regular and near-sighted Marcels for all hitters with at-bats in each of the last three years.)