Player Value, Part 1: General Principles

This is the first part of a multi-part series on how to estimate player value. I've been doing an awful lot of reading, thinking, and discussing these issues over the past several weeks, which is part of the reason that it's been relatively quiet around here. Because writing things out is the best way that I know to master a complicated topic like this, my hope is that this series will help me crystallize my thinking on player valuation and get up to speed on the most significant research to date. It will also serve as a nice set of papers to which I can refer to justify my methods moving forward...and who knows, maybe it'll be useful to others who are working through similar issues as well.

To be clear, little of the big ideas that follow are based on my own work, though I may supplement them with a small study here and there. Because this is a supposed to be Reds blog, I will often use the Reds in case studies. In general, though, you can think of this as a popular science review article ... or maybe a college term paper, given that I'm still new to much of this info. :)

General Principles of Player Valuation

Wins vs. Runs

What do we mean by value? The answer can be fairly nuanced, as evidenced by essays like this or this. I'm going to be a bit generic about it, however: I want to know how much players did to help their team win.

Based on that definition, the ultimate goal would be to have statistics that quantify player value in terms of wins. There have been several efforts on that front, including Win Shares, WARP, and WPA. At this point, however, I'm not satisfied with how any of those stats handle fielding (among other things), so I'm not ready to make the leap to those stats.

The alternative, then, is to use stats that give their units in runs, for which we have many "good" stats that can quantify hitting, pitching, and fielding. How much are we losing by going with runs instead of wins? To get some handle on this, I ran a quick regression of all teams from 1996-2004 with data pulled from the Lahman database and looked at one variable models that predict wins:

Predictor of Wins	R-Square	MSE
Run Differential	0.90	14.78
Runs Allowed	0.43	86.32
Runs Scored	0.35	97.92

R-Square, in this case, indicates the proportion of variation in wins explained by the different predictors. Therefore, this quick 'n dirty analysis indicates that we can explain 90% of variation in the number of team wins by just knowing a team's run differential (the difference between a team's runs scored and its runs allowed). The remaining 10% is presumably due to the timing of when those runs are scored, or variation in run environments (e.g. a run in Coors' field is worth less in terms of wins than a run in PETCO Park, simply because more runs are scored in Coors' than in PETCO, so each one contributes less to wins).

Research to date indicates that most, though not all, of timing-based events tend to be associated with events that involve very little unique player skill -- clutch hitting and pitching, for example, have very low repeatability in and of themselves, meaning that clutch performances are best predicted by a player's overall stats. Others "timing" events, like those having to do with baserunning (SB's and CS's happen more often in close games than in blowouts), tend to result in relatively few net runs per year. Finally, we can make adjustments for variation in the run environment of games via park factors and other techniques. Therefore, I'm ok with using runs instead of wins, at least for the time being, because of the gains in precision that we get from using the available runs-based statistics.

Offense vs. Defensive Contributions

You'll note that in the table above, runs allowed alone predicts wins better than runs scored alone. This is interesting: it indicates that winning teams are slightly more likely to have good run prevention than good run scoring. This could mean two things: a) runs prevented are more important than runs scored, or b) it's "easier" to build an offense-oriented team than a defense-oriented team.

One way to get at this is question to use a two variable model that includes both runs scored and runs allowed by teams, instead of just run differential alone. Doing so on this same dataset results in a model that predicts wins just as well as the run differential model (model R2 = 0.90), and assigns coefficients that tell you roughly how many wins you get from a run scored vs. run earned. It turns out that these coefficients are are virtually identical: +0.099 wins per run scored, and -0.101 wins per run allowed (model R2 = 0.90), indicating that the reason for the result in the table is mostly likely attributable to the "easier to build good offensive team" hypothesis. Furthermore, this means that preventing a run from scoring on defense is worth just as much as scoring a run on offense.

What does this mean for how we evaluate players? Well, clearly, we need to consider both aspects of a players' performance: offense and defense. For position players, this means that we need to know both how many runs they generated on offense, as well as how many runs they saved on defense, both relative to some baseline. If you only consider offense--and let's face it, that's what just about everyone does...at best, defense is used as a tiebreaker--you're likely to severely overvalue players that are offensive standouts but defensive disasters.

With pitchers, at least in the National League, we probably should consider offense and defense as well. However, the offensive contributions of pitchers these days are generally so meager, and involve such a small number of plate appearances, that I tend to just ignore them. However, I recognize that for pitchers like Micah Owings in '07, this might miss a substantial amount of value. Consider it something to look at in the future.

In future articles, we'll go over more specifically how to go about evaluating players.

To view the complete series, click on the player value label on any of these posts.