Risk vs. Uncertainty
by Jeff Sackmann
February 14, 2007
When we try to predict the outcome of a baseball season, whether as fans or pretend-general managers, there's a whole lot of stuff we just don't know. In fact, if you want certainty, we don't know anything: any player in major league baseball could blow out his arm, crash into a teammate, or just plain lose the skills necessary to hit a slider.
Of course, most of those things won't happen. When guessing the outcome of a team's season, it's a safe bet that somebody will get hurt, some players will underperform expectations, and others will overperform. One mark of a good general manager is identifying the situations in which those are most likely to happen, and then providing the best insurance he can.
When it comes to not knowing stuff about the future, it's useful to draw a line between risk and uncertainty. In More Than You Know, a book on investing strategy, Michael Mauboussin offers the following framework:
So how should we think about risk and uncertainty? A logical starting place is Frank Knight's distinction: Risk has an unknown outcome, but we know what the underlying outcome distribution looks like. Uncertainty also implies an unknown outcome, but we don't know what the underlying distribution looks like. So games of chance like roulette or blackjack are risky, while the outcome of a war is uncertain. Knight said that objective probability is the basis for risk, while subjective probability underlies uncertainty.
In a game of Strat-O-Matic, baseball is risky—you could calculate the likelihood of every event before you roll the dice. In real life, baseball is uncertain—no number of dice (or spreadsheet) is going to tell you Chris Snelling's 2007 OPS. However, when it comes to the game on the field, there's a continuum between risk and uncertainty, and that's what I'm interested in.
Degrees of Uncertainty
We don't know the exact probability of any performance-related outcome in baseball. However, projection systems are designed to take much of the guesswork out of it. PECOTA's Beta and Marcel's Reliability scores go even further, estimating how likely it is that a player will perform at his exact projected level.
In general, pitcher projections are less reliable than hitter projections. Young players are tougher to forecast than those in their late 20s and early 30s. Players who have missed substantial time to injury, as well as players who may be at the tail end of their careers, are more difficult to project, as well.
As you might imagine, statheads don't always agree with general managers on some of these points. There are plenty of active executives (though their ranks are slimming) who would consider a 39-year-old pitcher a safe bet, while they would hesitate before giving a 24-year-old first baseman a starting job regardless of his minor league track record. In some cases, that pitcher may in fact be a sure thing (think John Smoltz) and the first baseman may be undeserving (think Graham Koonce, a few years back).
While it may sometimes be rational to lean on veterans or ignore prospects, what prompted me to write this article was the seemingly irrational degree to which general managers love veteran pitching. In particular, it was Terry Ryan's decision to sign Ramon Ortiz to a $3 million deal, essentially locking Ortiz into a rotation spot and making it much more likely that Matt Garza or Kevin Slowey would not have one.
Ortiz vs. Garza/Slowey
I suspect that general managers gift starting jobs to the likes of Ortiz and Steve Trachsel because such a pitcher seems less uncertain than an "untested" youngster. In some cases, the older guy may in fact be safer. In this instance, though, it would be difficult to make that case. Using PECOTA's 10th, 50th, and 90th percentile projections for the three pitchers, here's how they stack up:
Pitcher 10% 50% 90%
Garza 6.43 4.69 3.51
Ortiz 7.57 5.04 3.82
Slowey 5.61 4.16 3.19
The degree of uncertainty implied by Ortiz's projections make him even less predictable than either of his competitors. The main difference is a drastic gap in performance. Even if we assume that PECOTA is a little too confident about players with limited major league track records, it would take a huge adjustment to make Ortiz a safer bet. (I have no idea whether such an adjustment would be fair or necessary; it would, however, start to represent the thinking of some executives.)
The Depth Argument
How the Ortiz signing does decrease uncertainty is by giving the Twins another replacement-level (or better) starter. There's something to be said for that: even if Perkins or Garza doesn't start the season in the rotation, they'll both probably end up making 10 starts at some point.
To set some parameters, let's say that the Twins have seven starters—Johan Santana, Boof Bonser, Carlos Silva, Scott Baker, Garza, Perkins, and Ortiz—who they can expect to be replacement-level or better between April and August. If they want to be seven starters deep (a reasonable number, given the variability in pitcher performance and health), they need to ensure that they have seven such pitchers in their organization.
Furthermore, it's tough to stash starters in your bullpen; while it can be done, a hurler who tosses an inning or two a few times in a week can be hard-pressed to give you five or six innings the next week. Thus, let's stipulate that the two starters who don't crack the rotation will have to go to Triple-A.
Garza and Perkins can do that. Ortiz, however, was going to sign a major-league deal somewhere, and the same can be said of the other pitchers of approximately the same skill level (Trachsel, Tony Armas Jr., etc.). In other words, putting Ortiz in the rotation for a while is a necessary sacrifice in order to have seven decent starters in your organization. The alternative for the Twins would be to use Sidney Ponson (or another lesser pitcher willing to go to Triple-A) as the #7 guy and let Ortiz go elsewhere.
While it's possible that putting Garza and Perkins in the rotation and leaving Ponson in Triple-A would be superior to giving Ortiz $3 million to start every fifth day, the calculus changes as soon as two pitchers get hurt. To work out all of the math implied by this, we'd have to know the likelihood of injury for each of the seven pitchers. But suffice it to say that signing Ortiz as a 5th starter gives the Twins more depth, even if he doesn't make them a better team in April.
By reducing the uncertainty that comes with relying on major league pitchers to give you quality innings and to stay off the disabled list, Minnesota's depth may even translate into a better full-season record. After all, anything that keeps Ponson out of the Metrodome is a step in the right direction.