Pittsburgh Pirates: Player Value, Distribution and Risk

Players are acquired based on what teams expect them to do going forward.  Each player has a projection, but their true talent isn’t known and they’ll fall somewhere within a distribution, which comes with risk.

Neal Huntington has been risk averse in his tenure as the Pittsburgh Pirates general manager.  He’s rarely traded big time prospects, with the move for Chris Archer being uncharacteristic, and he’s not been able to reach the finish line in other big names such as Jon Lester, David Price, or Jose Quintana.  He’s brought in big names such as Francisco Liriano, a former top 10 prospect, and A.J. Burnett, signed a three-year deal worth $28.6 million before 2006 with the Blue Jays and a five-year deal worth $82.5 million before 2009 with the New York Yankees.

Those two names were just names though, as their value was diminished for various reasons.  Liriano never lived up the hype and third place finish in AL Rookie of the Year voting in 2006, posting a 5.09 and 5.43 ERA the two years before joining the Pirates, and he also had Tommy John surgery after the 2006 season.  And after breaking his arm and revising the deal, the south paw received $1 million in 2013 and $6 million in 2014, with the latter being an option.  There was minimal risk, just $1 million, with the Pirates betting on upside.

In Burnett, the Yankees paid down $11.5 million in 2012 and $8.5 million in 2013, with the Pirates paying just $5 million and $8 million in those years.  Burnett pitched to a 5.26 ERA and a 5.15 ERA in his final two years in the Bronx.  Again, there was less value that Burnett needed to provide to make the salary worthwhile given the amount the club was actually paying him, reminiscent to the scene in Moneyball with David Justice where Billy Beane mentions how much the Yankees are paying for him to play against them.

The projection system STEAMER projected a 4.08 ERA for Burnett in 2012 and a 3.88 ERA for Liriano in 2013.  Both pitchers were better than their projection, but given those figures and lesser salary commitments (Burnett also cost little in acquisition cost with respect to prospects), the Pirates were willing to take the risk.

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This is relevant as the Pirates look into acquiring a shortstop.  Risk management is part of the decisions a front office makes when looking at potential upgrades through the free agent or trade markets, both in dollar and player cost, similar to when the Pirates traded for Burnett and signed Liriano.  For the sake of standardization, player value will be with respect to fWAR/600 plate appearances and the four players and their value are totally made up numbers and not real.  Let’s call these four players: KN27, a rookie shortstop, NA13, a trade target, FG13, a free agent, and TT2, an often injured former star who was released and his former team owes him a lot of money over the next two years.

Those four players project at 1.22, 1.15, 0.29, and 2.23, fWAR/600 respectively.  But projections aren’t perfectly accurate, as a player can fall anywhere above and below those figures in a given year through variation, improvement in the offseason changing their talent level, etc.  For ease, assume that the first three players (KN27, NA13, and FG13) talent level is normally distributed, or that the value they are projected for falls 68 percent in one standard deviation, 95 percent in two standard deviations, and 99.7 percent in three standard deviations.  It wouldn’t be too surprising if say KN27 (mean projection of 1.22) produced a 2.0 fWAR/600 season if his standard deviation in projected talent was 0.75.  68 percent of the time KN27 produces a fWAR/600 between 0.47 and 1.97, 95 percent between -0.28 and 2.72, and 99.7 percent -1.03 and 3.47.

KN27 has a standard deviation of 0.75 because of his youth and being a rookie, making him a more risky player than a veteran in terms of projected value.  For this exercise, NA13 and FG13 have standard deviations of 0.5 as both are glove first, bat distant second veterans who are likely to not vary from their projected value.

On the other hand, TT2 is often injured and because of this he presents more risk, but also more upside.  His talent is not normally distributed, rather the log of his talent is distributed normally (log-normal distribution).  This distribution can’t take on negative values, but it’s not normally distributed around the mean.  In this instance, due to the health risks in TT2, the standard deviation is 1.0, as there’s a good chance he won’t be healthy and if he is, the talent is there to over perform the projection.

Running a random number generator for the four players with their respective distributions, mean projections, and standard deviations 5000 times, the values generated approximately are what to expect:

But it’s hard to visually interpret what that looks like, graphing a density plot of the 5000 random values looks something like this.

Looking at the graph, FG13 and NA13 have the most narrow distributions (lowest standard deviations of the four).  TT2 is skewed right (median fWAR/600 of 2.05), and he brings more risk, but he is also the most likely to produce a 3.0+ fWAR/600 season, though getting there hinges on him being healthy which this theoretical player has’t been throughout his career.

Kurtosis measures the distribution, an excess kurtosis of 0.0 is a normal distribution, greater than 0.0 the distribution has more in the tails, and less than 0.0 the distribution has less in the tails.  The values are KN27 0.09, NA13 0.01, FG13 0.11, and TT2 3.05.  The first three players have normal distributions and TT2 has more in the tails, verifying the random number generator worked.

Based on the means and standard deviations, numbers used as illustration purposes, KN27 and NA13 are the safest options, and KN27 doesn’t have an acquisition cost like NA13 does.  It isn’t unreasonable that either player has a 2.0 fWAR/600 season, and the financial cost on both is minimal.

TT2 provides the most upside and also comes at a low financial cost, but he’s often hurt, a part that has been ignored throughout this post.  This is just the beginning of what evaluating what risk looks like, just based on the distributions of projected value over 600 plate.  Projecting the probability of injury and what that does to the value (in TT2’s case, the risk of injury is high, making the player more risky), the costs of depth (especially in TT2’s case), etc are all part of the process the front office must go through when evaluating which players best fit their club based on the 25-man, 40-man, and budget constraints.

Projections are great, but there’s a distribution the players fall on and there’s risk associated with each player as well, and that’s an important concept which too often gets ignored.