The running of the monkeysby Sal Baxamusa
February 12, 2008
Player projections! It's become a rite of spring on par with pitchers and catchers. Over the last several weeks we've been treated to projections from Ron Shandler's Baseball Forecaster, Bill James and Baseball Info Solutions, Sean Smith's CHONE system, Baseball Prospectus' PECOTA and Dan Szymborski's ZiPS. In a few weeks, The Hardball Times will throw its hat into the ring with The Hardball Times Season Preview 2008.
Spring is the natural time to make projections—general managers, both real-life and fantasy, want to know what they can expect from their players next year. But we can make a projection at any time, be it before spring training or before the All-Star break or before the World Series. In fact, a player's "true talent" at any given time is not his seasonal performance or career average or preseason projection. His true talent on any given date is a projection that accounts for all of his performance up to that point. (For the rest of this article, when I say "talent" I mean "projection incorporating all the latest performance data.")
This boils down to a common baseball question: Should we change our expectation of a player if he is riding a hot streak or working through or a slump? The simple answer is yes. A player's most recent accomplishments should affect how we project his talent.
What is misunderstood by many is just how pronounced—in both length and amplitude—a streak must be to noticeably affect a player's projection. In The Book, the authors found that even the most scorching of seven-game hot streaks had little predictive value on a player's future performance.
But sometimes streaks last a very long time—a month, half a season, sometimes even an entire year. And long streaks can appreciably change our perception of a hitter's talent. As a streaking player accumulates plate appearances, our projection of his performance changes dynamically. We can therefore create "running projections" every month, week or day simply by incorporating all the latest performance data into a projection system.
Enter the monkey
Which projection system should we use for these running projections? All the above named systems are complicated and their algorithms are (mostly) proprietary. But there is one publicly available projection system that anybody can use: Marcel the Monkey.
Marcel is the dumbest, most simple-minded projection there is. Tangotiger, the steward of the Marcel projection system, describes it thusly: "It uses three years of MLB data, with the most recent data weighted heavier. It regresses towards the mean. And it has an age factor." Serious attempts at forecasting ought to be more accurate than Marcel because those attempts ought to be more sophisticated than Marcel.
And yet, for all the hard work done by baseball forecasters, Marcel hangs tough with the heavy hitters of the projection world. The clever algorithms of other projection systems only give us incremental improvements in accuracy over the simian Marcel projections. And the Marcel projection—knowing nothing about park factors, minor leagues, injuries or defense—is very easy to do, requiring only knowledge of a player's previous three years worth of performance, the averages of his leaguemates, and his age.
Most projection systems look at previous performance and weight recent events more heavily than events in the past. Marcel is no different: For hitters, it assigns a weight of 5 to performance within the past year, 4 to performance between one and two years ago, 3 to performance between two and three years ago, and zero to performance prior to three years ago. If we want to adapt Marcel to do a day-by-day projection, we have to fiddle with these weights slightly, applying a scheme that assigns weights on a day-to-day basis rather than a year-to-year basis. I'll skip the boring details, but it turns out that a pretty good way to do this is to assign the weights using the equation Weight = 5.62*exp(-6.6x10-4(days ago)).
With that, let's look at two players who have seen large in-season changes to their projections. These center fielders who recently signed free agent deals came to the bargaining table with similar resumes: a bevy of Gold Gloves, average OBPs, good pop. Yes, this will be yet another comparison of Torii Hunter and Andruw Jones. The former signed a big contract (five years/$90 million) after coming off two big seasons. The latter settled for a smaller deal (two years/$36 million) after what might charitably be described as a down year.
Torii Hunter, getting warmer...
Let's start by looking at the trajectory of Torii Hunter's actual performance and true talent over the last three years.
This plot begins on April 1, 2005 and runs through Oct. 1, 2007. Each letter on the horizontal axis represents a month in the baseball calendar: April, May, June, July, August, September, October, and then April again. The blue line at any given date is Hunter's OPS over the prior 365 days. The red line is his Marcel projection, or true talent, on that day. So, on April 1, 2005, Hunter had accumulated an OPS of .800 over the previous year, while his Marcel projection on that day was just south of .800. His projected or "true talent" OPS dropped gradually over the 2005 season down to around .775.
Bucking the conventional aging curve, Hunter has increased his OPS in each of the last two years, his age 30 and age 31 seasons. Should this change our perception of his talent?
For 2006, yes. His 2006 season pulled our estimate of his true talent back up to around .800. Not a huge difference, but we can see the dynamic change in his true talent on a monthly basis. Hunter followed 2006 with an even better 2007 campaign—and yet, his his projection in April 2007 is almost exactly the same as his projection in October 2007!
There are three reasons for that. One, as 2006 wore on, the memory of his subpar 2003 faded from Marcel's memory, while 2007 wiped away the memory of a pretty decent 2004 campaign. Second, he ended 2007 on a down note, which pushed his projection down from .820 to just north of .800. We can't ignore last September (.647 OPS), and since Marcel considers recent events more strongly when making its projection, his slow finish works against him. Finally, given that he's past the generic peak age of 29, his projection gets a final kick in the groin.
According to Marcel, our perception of Hunter's talent is basically the same today as it was last April. Yet, I wonder if Hunter would have received big money had he hit the market after 2006.
Andruw Jones, getting colder...
Andruw Jones picked the worst possible year to go into the tank. About to hit free agency with an all-time-great defensive reputation and having averaged more than 37 homers a year since his age 23 season, Jones had the opportunity to cash in and get... well, Torii Hunter money. Did his poor 2007 significantly affect his future outlook?
As with Hunter, we're looking at the trajectory of Jones' true talent and one-year OPS starting on April 1, 2005.
Jones had a career year in 2005 and kept going strong early in 2006. On May 1, 2006, his OPS over the past year was off the charts—well, off this chart anyway. His generally strong strong performance in 2005 and 2006 kept his true talent OPS in the .850-.875 range from mid-2005 through mid-2007.
But Jones famously stunk up the joint throughout 2007, posting the worst numbers of his career. His cold snap was so pronounced, both in length and amplitude, that the Marcel estimate of his true talent tumbled almost 50 points. He fell from lofty heights, however, and despite the season-long funk, his true talent OPS at the end of 2007 was still .815. Between his awesome 2005 and terrible 2007, his "true talent" OPS fell only 60 points from its zenith to its nadir, while his one year OPS tumbled almost 250 points.
So, according to Marcel, Andruw Jones' hitting talent today (as measured by OPS, which of course has its own issues) is slightly higher than Torii Hunter's. Of course, we're not considering defense, nor are we considering body type, conditioning, comparable players or any of the other things that the sophisticated projection systems take into account.
Both Jones and Hunter have landed in Los Angeles—well, with teams that have "Los Angeles" in their names, anyway. But Jones has a far cheaper and shorter contract. It's a virtual certainty that recent performance and career trajectory factored heavily into their free-agent deals. By using a simple projection system, we can see that Jones probably has not fallen nearly as far as his contract might suggest and vice-versa with Hunter.
Most importantly, we are controlling for career trajectory, because of the weight we place on recent events. That is, Marcel is suggesting that Jones and Hunter have similar hitting talent today even though Jones has seen serious and recent decline and Hunter has seen moderate and long-term improvement.
The moral of this story is that you're never as bad as you look when you're at your worst, and you're never as good as you look when you're at your best. Regression to the mean, baby.
Sal Baxamusa is a graduate student in chemical engineering. He can be reached here.