January 20, 2010

Checking the Numbers

Valuing Volatility

by Eric Seidman

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It's no secret that the throes of the economy have affected baseball and its free agent market, especially when an All-Star player like Orlando Hudson struggles to find a one-year deal at even half of his perceived value, and the thought of Adam LaRoche turning down a two-year, $17 million deal invokes more laughter than Kingpin. Though high-end players have certainly gotten paid this offseason, teams are acting much more conservatively, especially with a higher premium being placed on the analyses of associated risks. Two of the free-agent pitchers yet to sign a deal-Jon Garland and Joel Pineiro-exemplify this risk-analysis process, as both represent examples of consistency in Garland's case versus volatility in Pineiro's. Such archetypes are often deemed opposites when it comes to risk.

Aside from one trend last season, Pineiro and Garland don't seem to have a whole lot in common on the surface. The new similarity was when the former became a ground-ball machine who also refused to strike batters out. Garland might be a formulaic romantic comedy, predictable but by no means bad, while Pineiro is the more original and creative film that could be great in the right hands but, unfortunately, is just as likely to earn a Razzie nomination as it is one from the Academy Awards. Despite the risk associated with Pineiro after last year's breakout and the suspicion he may not repeat it, and despite the common perception that consistency is valuable, in point of fact both pitchers are risky assets. Risk in this scenario covers the ability for teams to reach their goals, and how certain players may prevent the team from getting to where it wants to get. It might be easier to associate risk with Pineiro given his up-and-down performance, but Garland's consistency is equally risky in the sense that paying for his production may not get a team where it wants to go, and might instead not only prevent the team from making the playoffs or winning more games, it could also preclude more beneficial acquisitions later on.

With that in mind, a team considering either or both of these pitchers needs to not only project their performances, it also has to decide what that type of productivity is worth given their specific situation. Matt Swartz showed us last summer that certain teams gain more utility than others from players, given their circumstances. For example, Roy Halladay is worth much more to the Phillies than he is to the Astros. Projecting Garland and Pineiro is not as cookie-cutter as it sounds, though, as their skill sets can cause some concern as being either fluky, unattractive, or a bit of both.

Consistency is one of the more overvalued performance attributes in baseball, as prior studies have shown that flakiness within a given season is inconsistent from year to year, and that it correlates very weakly to bottom-line, win-based metrics. Though consistency carries value in the sense that executives, managers and fans don't need to bite their nails as frequently, it does not actually make a pitcher post better numbers and it is not always a lock to add more value to a team. Prior to last season, Garland was not only more consistent than Pineiro, he was markedly better. Take a look at their WARP3 and SNLVAR figures over the last five seasons:

WARP3          2005 2006 2007 2008 2009
Pineiro        -0.9 -2.3  1.7 -0.3  2.3
Garland         4.2  3.1  3.2  1.4  2.4

SNLVAR         2005 2006 2007 2008 2009
Pineiro        1.41 0.26 1.68 1.60 4.63
Garland        6.02 4.07 4.30 1.96 3.50

It really isn't even a contest, as Garland performed much closer to the level of an all-star than a bargain-bin innings-eater while Pineiro appeared lucky to actually call himself a major-league pitcher. A rendezvous with Dave Duncan in St. Louis cured Pineiro's pitching woes, and suddenly he finds himself not only in the same discussion as Garland, but seemingly in line to receive a much more lucrative contract. The issue here is that few know what to expect from Pineiro, while there's little doubt what Garland can bring to the table.

When it comes to consistency and volatility, a discussion of an expected value comes into play. The expected value is essentially the weighted summary of a variable: a pitcher worth two wins does not have that set in stone, because it's a projection comprised of several potential outcomes with their own respective probabilities of occurring. He may add half of a win 25 percent of the time, and three wins 30 percent of the time, and so on, with the weighted average ending up at two wins. For a more volatile pitcher like Pineiro, the expected value of his performance will include a much wider range, positive and negative.

For example, if we assume that both Garland and Pineiro will be worth 2.1 wins next season, which does not seem out of place given what we know about each, Garland's expected value might break down as 1.8 wins coming 20 percent of the time, 60 percent delivering 2.1 wins, and 20 percent 2.4 wins. In contrast, Pineiro checks in with a spread of 0.5 wins 20 percent of the time, 20 percent yielding 1.3 wins, 20 percent of the scenarios producing 2.1 wins, another 20 percent with 2.9 wins, and finally 20 percent generating 3.7 wins. Though Pineiro has more apparent upside, the distributions represent the range of possible outcomes, as the weighted mean for both comes out to the same 2.1 wins. The difference is that Garland offers a club very little wiggle room, while Pineiro could potentially add up to four wins. In a vacuum, neither is more valuable than the other, or worth more to a team monetarily. Baseball is not played in a vacuum, though, so it's valid to suggest that Pineiro is worth more to certain teams than Garland, just as Garland should be sought after more by other specific suitors.

To get into which actual teams make sense for each, consider the different expectations from the Mets and Cardinals. Given the uncertainties in the health and talent departments for an entire laundry list of Mets players, they could go 76-86 as easily as they could end up 88-74, a broad range of outcomes suggesting that, just like Pineiro, the Amazin's are pretty volatile. I'd argue that a pitcher like Pineiro becomes all the more attractive to this kind of team, due to the upside potential. Whereas inking Garland or other consistency cardholders could improve the range of wins from 76-88 wins to 77-90, bringing Pineiro aboard causes a jump from 76-88 wins to 77-92, the high end getting into territory that almost assures a playoff berth. Essentially, the Mets can only gain utility from a pitcher as volatile as Pineiro, since they have nothing to lose. It would make far less sense for them to sign Garland, as he offers less of a possibility that the higher end of potential outcomes could reap a spot in the playoff picture.

The opposite can be said of the Cardinals, who will likely be considered locks for the NL Central throne with a smaller distribution, say something in the 87- to 94-win range. Since they are already favored to qualify for the playoffs, their sights should be set on the Garland types, who will serve to stabilize the back end of their rotation. The Cardinals, ironically the former employer of Pineiro, would not gain much from his volatility, as the high end would not provide much benefit, while the low end could actually remove them from contention. Beyond Chris Carpenter and Adam Wainwright, the rotation is already comprised of potentially volatile pitchers like Kyle Lohse and Brad Penny, so the last thing they need is a trifecta of uncertainty beyond their top tandem.

However, all of this presupposes that Garland and Pineiro will be each other's equal next season, which might not be true, since Pineiro broke out last season, and may struggle to sustain solid performances, especially without the aid of pitching coach Dave Duncan. Plus, jumping from -0.3 wins to 2.3 wins seems like a rare occurrence, so an investigation into similarly large jumps could make assumptions of his potential value much more accurate.

Will the Real Slim Pineiro Please Stand Up?

Sleuthing my way through the WARP3 archives, I searched for all situations in which a pitcher made 20 or more starts in four consecutive seasons from 1974 to 2006, where the total number of starts was within plus or minus five of the total from the year before. This way, we can avoid situations in which someone went from 35 to 20 to 35 to 20 starts, skewing his numbers in the process. In total, 595 such four-year spans were returned, belonging to 193 unique pitchers. Of this larger sample, just 91 such spans belonging to 76 unique pitchers increased their WARP3 by at least 2.5 wins from the first to the second season, a jump commensurate with Pineiro's improvement. Of this subset of pitchers, 72 such sets belonging to 63 unique pitchers maintained a WARP3 above 2.0 in the season immediately following their jump, and 50 spans belonging to 47 pitchers accrued two or more wins in that fourth season. Putting all of that together, jumps in performance akin to Pineiro's are rare, but the improvements are largely sustained throughout history.

The table below shows the averages for the respective groups, with the W1-W4 columns representing the WARP3 totals in each of the four years and the headings 2-Year to 4-Year indicating to which group they belonged. For instance, the 3-Year group experienced a 2.5 win jump or more from the first to second years, and remained above two wins in the third year.

Group      W1   W2   W3   W4
2-Year    1.8  5.5  3.6  3.2
3-Year    2.1  5.7  4.4  3.3
4-Year    2.1  5.8  4.6  4.4

The data indicates that pitchers making vast improvements in their performance tend to differ from Pineiro in the aggregate; they went from average to All-Star, while he went from replacement-level to average. Manipulating the sample to feature pitchers worth one or fewer wins in the initial year to more closely mirror Pineiro's uptick, 32 separate spans from 30 different pitchers were returned, but practically all of them made substantial improvements, averaging 0.03 wins in the first season and 4.06 wins in the following year, before falling to 2.64 wins in the third year and remaining steady at 2.63 wins in the fourth and final year. Pineiro didn't make that large of a leap but the sample of pitchers at one or fewer wins who jump to three or fewer wins consists of a whopping five pitchers:

Pitcher      Year1 GS   W1 Year2 GS  W2 Year3 GS  W3 Year4 GS  W4
Randy Johnson 1989 28 -0.8  1990 33 2.7  1991 33 2.6  1992 31 2.8
Hideo Nomo    1998 28 -0.5  1999 28 2.3  2000 31 2.1  2001 33 2.6
Kirk Rueter   1999 33 -1.1  2000 31 2.1  2001 34 1.0  2002 33 2.9
Derek Lowe    2004 33 -1.7  2005 35 2.3  2006 34 4.7  2007 32 2.6
Bob Forsch    1976 32 -0.8  1977 35 2.0  1978 34 1.5  1979 32 1.0

The most comparable pitcher here, both in age and numbers, is Nomo, who largely sustained his uptick over the next two seasons. Johnson also sustained his improvement, boding well for Pineiro. The hope is that Pineiro does not suffer a fate similar to that of Forsch, who made his improvements and then gradually came back to earth.

Wrapping Up

This research indicates that it is certainly conceivable that Pineiro will not project as nicely as Garland, thereby decreasing the value of his high-end potential, in turn lowering the expected value of his production. Under this assumption, the comparison could end up being between a 2.1-win pitcher and one worth 1.6 wins with the possibility of finishing anywhere between 0.5 and 2.8 wins, a much skinnier range of outcomes.

Of course, the discussion of risk, consistency, and volatility suggests that teams should not be comparing these two and deciding which one to sign, given that the answer is contingent upon the projected standings. Different teams will extract different values from the same players, narrowing the field of could-be employees in the process. It is easy to look at the volatility of Pineiro and the consistency of Garland, and decide that one is better than the other, but this form of often-used comparisons only becomes valid under the lens of team context. The purpose of a free-agent signing is to increase the likelihood that a team's goals are reached. While these pitchers may seem like opposites, they are both risky, with an expected level of risk resting purely in the eye of the beholder.

Next week, we'll look at two more archetypical players on the market in a similar scope in an effort to better understand market functions, and what teams look for in signings.

Eric Seidman is an author of Baseball Prospectus. 
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