Game of Risk

On Friday, Jeff Sackmann wrote a very interesting article on a “new” (untapped might be the better word) market inefficiency in baseball. My baloney detector immediately went off; ever since the publication of Moneyball, every few months somebody reads the tea leaves and declares a new inefficiency in the market. In Michael Lewis’ book it was famously declared that on-base percentage was not valued properly by the market. Soon thereafter, it was pitching and defense. Then guys with bad clubhouse reputations, platoons and international free agents were all the rage.

And in the not-so-distant future, people will declare market inefficiencies based on pitchers who are awesome only on Tuesdays, hitters who perform better against teams with left-handed first basemen…

And so it was with a fair amount of skepticism that I read Jeff’s article, in which he suggested that the acceptance of risk was a way to exploit the market. But I think Jeff is on to something, and his article opens an important dialogue in thinking about risk.

A general manager who suspects that his shortstop won’t be available for half the year could go out and spend big on an iron man like Michael Young, whose value is in large part tied into his ability to stay on the field. Or the same general manager can accept the fact that his shortstop will end up on the DL and have contingencies ready, either by picking up a second basemen who can shift over if necessary or pre-targeting players on other clubs for stopgap trades. It may very well be that in today’s environment, the latter strategy may give you more bang for your buck.

This line of thinking is related to two important sabermetric concepts that are worth mentioning.

Replacement Level

Most of you are probably familiar with the concept of “replacement-level” or “bench-level.” The idea is that a player’s value ought to be measured not against an average player, but against whatever player the team might play in his stead. The typical sabermetric concept of a replacement-level player is “freely available talent,” loosely defined as a Triple-A journeyman or 26th man or whatever you might find hanging around the waiver wire. The concept is naturally tied to defensive position; the replacement-level first baseman is expected to hit a fair bit better than the replacement-level shortstop.

(If you are interested in what kind of player is replacement-level, last year’s Alex Cintron is a pretty decent example. Last year, he had 0 WSAB and 4.6 VORP.)

While the details about what constitutes the replacement-level benchmark is a matter of debate, the concept has given us a framework with which to discuss value. But when we start talking about assessing and managing risk, we might view value through a slightly different lens.

Imagine you had an opening in right field last offseason. Trot Nixon is available, probably cheaply, but for good reason—he is coming off a down year, has a long injury history and can’t hit lefties to save his life. Are you going to take a chance on a guy who may not be very good when he plays, won’t play every day when healthy, and may not be healthy for the duration of the season? Let’s take that bit by bit:

  • Will he be any good when he does play? That’s a matter of projection, and if you’re a smart general manager you have an in-house projection system. If not, you can always check Fangraphs or PECOTA. And any general manager worth his salt probably bought the THT preseason book and saw that he was projected to 2.1 Wins Above Replacement.
  • He can’t hit lefties. This is where you start to assess, manage, and accept risk. Maybe you have a righty who can mash lefties, or perhaps you can acquire one cheaply as a complement to Nixon. Some teams may be able to dip into their reserve of minor leaguers to find a decent outfielder who can hit lefties a little.
  • He can’t stay healthy In a similar way that you manage your platoon risk, you can manage your health risk. You can plan to let his platoon partner play full-time during his DL stints or something similar.

    All of a sudden, that 2.1 WAR doesn’t look so bad. You can put Nixon in a position to succeed, hopefully boosting his rate stats, and have a backup plan that hopefully involves a greater-than-replacement-level performance. If your name is Mark Shapiro, then you notice that you’ve got Casey Blake hanging around and jump all over Nixon. It is here that we see that replacement-level analytics has the drawback of putting players in a vacuum instead of the context in which they will be used. But teams aren’t built in a vacuum, so a guy whose value is brought down by playing-time concerns can still be an important—and successful—part of the team.

    It’s not a new concept, and as Dave Studeman pointed out on the THT internal mailing list, teams have probably been practicing risk management and acceptance in some form for quite some time. David Gassko’s article last year on “chaining” takes advantage of similar thinking—a player’s value depends on the context in which he is used. And by choosing the right context, a general manager can indeed find value for less than the market might suggest.


    If it’s not a new concept, why should we waste (virtual) ink on it? Because my belief is that it is not possible to systematically exploit inefficiencies without quantification. Imagine that we had a vague concept that getting on base was good and that perhaps that skill commanded a lower-than-justified compensation, but we didn’t have access to on-base percentages for position players. Where would we possibly begin?

    In the same vein, if accepting risk is a clever strategy for roster construction, it would behoove teams to begin quantifying risk. And understanding risk, whether for shortstops or securities, involves understanding variation. In baseball, we can think of two types of variation: performance and playing time. We think a lot about the former, but we don’t spend nearly enough time thinking about the latter.

    PECOTA, for example, includes projections for 10th through 90th percentile performance (and I’m not picking on PECOTA; this is just an example). Each of those projections includes playing time projections as well. While playing time can be correlated with rate statistics (“The Jeremy Giambi Effect”), I posit that health has a greater effect on playing time than performance, particularly when free agents or more established players are involved. And it is for this reason that bifurcating performance projection from playing time projection makes a lot sense. (And yes, there are problems with this: notably, not all injuries cause a loss of playing time and yet can drag down performance. It’s something we’d have to learn how to deal with. Stick with me for a few more paragraphs.)

    Case study: Rich Harden, one of my favorite pitchers. His 10th, 50th, and 90th percentile PECOTA projections are 78 IP/6.78 ERA, 114 IP/4.07 ERA, and 140 IP/2.43 ERA. I can tell you that 78 IP from Harden this year is a pretty decent probability, considering his last two injury-plagued seasons. I can also tell you that a 6.78 ERA, while possible, is way down the list of any A’s fans concerns about Rich Harden. More likely than a 78 IP/6.78 ERA is 78 IP/2.43 ERA; a good performance in an injury-shortened season has been on everybody’s mind.

    And yet, when we project variability, we treat performance and playing time together. As Dave Studeman noted on Ballhype, performance variation can be enhance or detract from the value of a player. Playing time variation, or injury risk, can only detract. What I propose, in the most general terms, is that performance projection ought to focus on rate statistics (AVG, OBP, GPA, MLVr – pick your favorite) and that a separate projection be developed to account for playing time. I imagine that such a projection would involve:

    A Hardball Times Update
    Goodbye for now.
  • A baseline distribution based on the occurrence of traumatic injuries to all players.
  • A positional factor to account for the type (e.g., collisions for middle infielders, hamstring pulls for outfielders) and frequency (I’m looking at you, catchers) of injury.
  • A specific factor based on a player’s injury history/proclivities.

    And how would we do this? I have no idea. My first suggestion would be to gather lots and lots of data, and my second suggestion would be to find somebody smarter than me to undertake the task. An exact science? Perhaps not, but as Jeff noted on Friday, the market for baseball-crazed actuaries may be about to go up. And why not – many contracts are insured right now, and you bet that there’s an actuary somewhere setting the premiums.

    Imagine how cool it would be to be able to multiply a performance probability by a playing time probability. A playing time probability would have a particularly interesting shape, I imagine, since it would be far from a normal distribution and playing time is certainly capped. But this type of projection, combined with an idea of the marginal utility of additional wins (a la David Gassko’s pennants added), would be an excellent starting point for understanding risk assessment, management, and finally acceptance at a level where one could begin to play the market intelligently. I’ve already talked about using uncertainty to price options in baseball contracts —we can do so far more intelligently if we only had better information.

    Come Together

    The most interesting part of Jeff Sackmann’s article is that it suggests lots of interesting future work, and this work will require synthesizing the best thinking from all over the sabermetric sphere. We need a good definition of replacement-level, and we need to integrate replacement-level into the context of team construction. We need to gather as much data about injuries as possible and learn how (if?) we can project playing time separately from performance. We need to understand the marginal utility of additional wins. And we need to be able to put it altogether intelligently. And whoever can do that will have an email of thanks from me in their inbox.

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