Beyond the Pythagorean win/loss method of calculating what a team’s record should be based on a number of factors, even advanced statistics provides few tools for truly explaining team performance. In fact, there currently exists no really useful or practical mathematical model that helps explain team performance while also including factors such as age, payroll, individual player production, and time lost to injury. You could probably find a rocket surgeon / baseball fanatic who could sit down and code a program to attempt to account for every ridiculous variable possible. Unfortunately, that would take months, and the end result would be something containing Eigenvalues and a substantial portion of the Greek alphabet.
Worse yet, none of this could possibly be accomplished by the time I want something useful, and I’m not exactly a patient person when it comes to riding the cutting edge of the statistical geekery wave. To paraphrase the ad agency for J.G. Wentworth, “It’s my data, and I need it now.” So, instead of coercing a rocket surgeon into compiling a bunch of nonsensical code, I went about crafting something truly unimpressive and as crude as one might imagine. In fact, I accomplished all of this using a simple spreadsheet.
By multiplying a player’s salary by the percentage of possible games played, I created a value which represents the amount of salary the player projects to truly earn solely based on showing up and participating. The Cardinals have played in 103 games, so I probably waited about 3 games too long to embark on this numerical crusade for truth. For starting pitchers, the number of possible games = 103/5. For relievers, the theoretical number of possible games = 103/3, based on a rough average of total appearances made by relief pitchers. For greater precision, I suggest you find someone with more time on their hands and a site that hides really good stuff like this behind a pay wall.
The ratio of games played to possible games played provides a decimal which is simply multiplied by the player’s 2012 base salary. The resulting value is then divided by the player’s total WAR to this point in the season, and this determines a player’s useful efficiency as a function of both availability, production and pay. Naturally, this method skews results in favor of the lower pay tiers, but the micro-trend information provides a compelling view of expected return for big contract players versus other big contract players.
The way to explain this method using an analogy would involve pressing the gas pedal on a car. The player’s base salary for the year takes the place of the engine. The greater the horsepower, the greater the top end speed (in theory). WAR represents the actual transfer of the engine’s power to the rest of the car’s systems that allow it to travel forward. The final efficiency value represents how the power translates to actual speed while taking into account downtown. The final result is total distance traveled, and the metadata for this value tells us about how much it cost to travel a specific distance using a specific engine. If we wanted to engage in even more geek stuff, we could basically calculate fuel efficiency which would require some significant adjustments to the current calculation method.
In keeping with the analogy, the total fleet of cars cost approximately $114,121,000 give or take a Mujica here and a bonus there. Sadly for the garage/fleet owner, the injuries to Chris Carpenter and Scott Linebrink alone cost the owner $11.35M in deadweight for the season. Additionally, the buyouts for Rafael Furcal and Octavio Dotel add on an additional $2.05M. That brings the total to $13.4M which basically means a lot of available horsepower never even left the garage. Of the ones that did make it out the door, several have broken down at various times and cost the owner another $9.4M already this year. That means that the maximum amount of dollars (horsepower) available through the entire year drops to $91.321M.
Sounds bad, right? Well, the team has combined for a total of 28.1 WAR to date which works out to about $3.25M per 1.0 WAR. In the grand scheme of things, the Cardinals are getting a lot out of the horsepower available to the team. The translation from horsepower to wins likely means that the team has worked hard enough to have a better record. After all, that $3.25M figure seems an awfully low price for buying WAR. The discounted price translates to a lot of players outperforming their contracts when healthy. When you look at the individual breakdown, this becomes even more apparent.
- David Freese has produced 3.1 WAR this season for a price of $508K, and he has done so while playing in 93 games.
- Allen Craig production/cost efficiency number (EffWAR) sits at 233188.81 seems rather impressive for a guy who has only appeared in 62 games so far.
- Lance Lynn‘s breakout year means that his EffWAR value of 233863.65 ranks as the best for any member of the pitching staff.
- Event he much-maligned Matt Holliday has produced an EffWAR value of 3750250.94 which means that despite his $17M salary this year, he’s been worth every penny.
- Since EffWAR accounts for time lost to injury, guys like Lance Berkman and Jaime Garcia hold down the back end of the EffWAR wagon.
Because WAR calculations for pitchers tend to get skewed by statistical outliers (ie really bad starts), one might consider adding a multiplier or correction factor in attempting to improve EffWAR. I am not that man. I started this mathematical expedition in search of a valuation for the efficiency with which an entire team produces WAR in spite of all the baseball things that happen to a team over the course of the season. The result? Interesting to say the least, but it certainly was worth the time to do, if only to share it with our 3 loyal readers.
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TIDBIT: If you look closely at the EffWAR graph, you’ll notice 2 things. First, I had an opportunity to divide by zero, and I instead adjusted all values by a nearly insignificant value to avoid this issue. Second, some pitchers have made enough appearances to make their “salary earned” value actually go above their base salaries. I decided to leave this “glitch” in the machine, because it was interesting to show the value added by this, and the year end calculation will obviously align the values much more closely.