Bang For The Buck

Recently, friends and I were wondering if there was a possible way to quantify in terms of dollars exactly how big of a bust Julio Lugo has been. The more I thought about it, the more I wanted to work out statistical systems to compare player’s contributions to their compensation. I ran through several drafts of the following spreadsheet and hit many snags, from sample size to unreported salaries to simple excel goofs. I’m going to treat this as open-source, in that if anybody wants to work on my spreadsheet or would simply like to see it I’d be more than happy to send it over to you. Use the comment board for requests. Here’s the chart, which I will explain below:
Bang for the Buck Chart
First off, a discussion of terms: The third column, “Salary,” and fourth column, “Earned,” represent a player’s base 2007 compensation and an 83 game pro-rated figure (these numbers were compiled after the Red Sox’ 83rd game). The next four columns are based on Baseball Prospectus’ Equivalent Run statistic: based on percentages, PRAR (Pitching), BRAR (Batting), and FRAR (Fielding) represent player contribution scaled to numbers which match our understanding of the scale for runs. So a PRAR of 50 represents a pitching contribution of value equivalent to that of 50 runs scored. The RAR part of these three acronyms are “Runs Above Replacement Level,” meaning number of runs produced above that which could be expected from a player whose talents are at the threshold between AAA and major league. The “RAR” column in the chart is simply the sum of each player’s PRAR, BRAR, and FRAR.
The remaining columns are the meat and potatoes of this study. “RPM” stands for Runs Produced per Million Dollars of salary earned. “CPR” stands for Cost Per Run, or what the Red Sox have paid for each run’s worth of value this player has contributed. “R%” shows the percentage of team run value this player has produced, and “S%” shows the percentage of total team salary this player earns. “EXPS” stands for Expected Salary: given this player’s run value contribution as a percentage of total team run value, what salary should they earn that would represent a commensurate percentage of total team salary? “EXPR” is the sister statistic of “EXPS”: given this player’s salary as a percentage of total team salary, what would be their expected run value as a matching percentage of total team run value? The final two columns, “$BONUS” and “RBONUS” attempt to quantify a player’s value to the team. “$BONUS” is essentially how much more (or less) money this player’s contributions have earned than what they are actually receiving from the team. “RBONUS” is the same thing, only stated differently: how much more production this player is responsible for than would be suggested by their compensation. For example, Josh Beckett has contributed at a level (translated for a full season) worth, in the logic of our team salary, $12,044,171. Since he is being paid $6.67M, his $BONUS sits at a pretty $5,377,504. The flip side of this is that a $6.67M player would be expected to contribute, through 83 games, 22.141 runs worth of value. Since Beckett has contributed 40, his RBONUS is 17.859.
I know I just tore through all of that very fast, but I think it will all make sense if you spend a few minutes looking at the chart. As I mentioned above, there were several problems in making this chart: one of them was simply finding the players’ base salaries. I went through the USA Today database as well as the figures reported on ESPN’s team pages and managed to find a believable figure for everyone; midseason call-ups were more difficult as both databases mentioned above only listed the players on the opening day 25 man roster. For those call-ups (Manny Delcarmen, Jacoby Ellsbury, Kason Gabbard, Devern Hansack, and David Murphy) I used the minor-league minimum for players who either a) are on the opening day 40 man roster or b) have played a game at the Major League level, which is $52,600. For J.C. Romero (we hardly knew ye), I used the MLBPA veterans’ minimum of $310,000. Salary is, to be sure, more complicated than this, what with signing bonuses, deferments, escalators, etc., but I think I got as close as Google will get you. The next major problem was figuring out proper ways of measuring the actual dollar equivalent of the players’ contributions. The single biggest wrench in the works here was the three players whose contributions have been below replacement level: Wily Mo Pena, Doug Mirabelli, and Devern Hansack. As you will notice in the CPR column, their negative numbers suggest statistically that with every run they detract from the team’s contribution, money is actually added to John Henry’s considerable coffers. Since this is obviously not the case, I couldn’t regard CPR as the ultimate finding of this study even though I like almost everything else about it.
$BONUS and RBONUS really work for me: take the discouraging case of Wily Mo Pena. His $BONUS is -$2,778,313, which means that his contribution is worth nearly $2.8M less than we are paying him. That the above is true and we are only paying him $1.875M shows just how truly awful he has been.
What does this sheet show us? Above all, that pitching is a worthy investment. Despite his $6.3M price tag, Daisuke Matsuzaka is second only to Kevin Youkilis (with his paltry $424,500 salary) in bang for the buck. Despite Josh Beckett’s great season thusfar, Tim Wakefield at $4M and Hideki Okajima at $1.225M both represent better value than Beckett at $6.67M. The value of young bats at “young” salaries cannot be understated: between Kevin Youkilis and Dustin Pedroia, the Sox are spending $804,500 and getting Red Sox returns of $17,765,152. Other pleasant surprises have been Julian Tavarez, Coco Crisp (whose defense alone rockets him up the list), Alex Cora, and the bullpen triumvirate of Kyle Snyder, Javier Lopez and Brendan Donnelly.
Who brings up the rear of this list? J.D. Drew, who is making $14.4M (more than Big Papi) and has produced, in total, exactly what Alex Cora has produced on defense. It is ridiculous that Matt Clement at $9.5M has been more valuable so far this season than Drew at $14.4M or Manny Ramirez at $17M, but that’s what the numbers show. Julio Lugo is unsurprisingly towards the bottom of the list as well (the answer to the question that begins this article is $7.6M of a bust, for 2007), as is Mike Lowell who has produced well but not $9M well.
The next step in this, which I will attempt should I find myself in prison or some other situation with thousands of hours to spare, would be to chart this for all of MLB and find the exact market value for every player. Since the Red Sox have had looser pursestrings over the past few seasons we will inherently be getting less bang for the buck than will be, say, the Marlins. And if I wanted to go mad scientist on this, I would explore other measures of success than simple on-field performance: media contracts, ticket sales, etc., to explore the true value of every player to his team. Maybe for next weekend.
Kudos to everyone earning their paycheck.