Sabermetrics study: measuring $/WAR and projected player salaries

Originally submitted for an Economics class at Lehigh.

Wins above replacement, or WAR, is a statistic in growing popularity among baseball fans and executives. It’s one of the most popular statistics used in sabermetric analysis and is even being used to take into account whether teams should keep, sign, or trade players. In this report, I researched the comparison between players’ WAR values in 2013 to their salary number.

First of all, since the Retrosheet database only went up to 2013, that’s the year I used (instead of 2014), which is still recent enough to be relevant. I also only looked at players in their thirties instead of all players, because otherwise it might skew the data. This is a little bit different from looking at it based on years of experience, but essentially all major league players have played for a few years by the time they get to age 30. I decided to use 30 as the minimum age because it eliminates players on their rookie contract who haven’t hit free agency yet. One obvious player who will be eliminated from this study is Mike Trout, who had a WAR of 8.9 in 2013 while making just $510,000. So obviously, he would be the highest valued player.

So, the study looks at players in their thirties and their salaries to not only see who the best value players were, but comparing them to what they should have made based on the value of the win. According to an article on Beyond the Boxscore, the value of a win is around $7 million, meaning a player who finished a season with two wins above replacement should hypothetically receive $14 million. But, Fangraphs back in 2013 calculated that the average value of a win was about $5 million, and since this number changes with the signing of bigger contracts (which has happened recently), it only makes sense to use the 2013 value. So, the higher a player’s WAR, the higher they should be paid. Some players end up with negative WAR values, and therefore it’s impossible to calculate exactly what they should have made.

Hypothesis: The earlier the batter is into his thirties, the higher chance he’ll be overpaid compared to his value.

After using MySQL and other data analysis, here is what I figured out. First of all, I applied a few qualifications for players so that the list wasn’t too long. I required that the player record at least 50 at bats in the 2013 season because anything lower than that would lead to some inaccurate data. Also, some pitchers are included, but only in relevance to their batting stats. So the only pitchers that are in the data table are ones who have surpassed the 50 at-bat minimum. The WAR reflects that—it’s just their offensive WAR, not their WAR as a pitcher.

The points of data that I needed for each player was name, year of birth, age, salary, and then three numbers that I calculated myself: $/WAR, projected $ and difference between actual and projected salaries. The first of those calculated statistics is just what it sounds like—I found how much money each player cost relative to their WAR value. Some players ended up with extremely high numbers if their WAR value was below 1.0, which is technically the baseline for the $/WAR calculation. So any player with a value of one win above replacement would have a $/WAR value of their exact salary.

I decided to make a second column to put it into perspective for how much a player should have earned based on his WAR. As mentioned before, a win above replacement was valued at $5 million in 2013 according to Fangraphs, so a player with a WAR of 3.0 should hypothetically make $15 million that season. Obviously, it’s impossible to guess a player’s exact value at any point, so teams can only guess for how much they should sign a player. That’s why the projected salary column is interesting, because it shows how underpaid or overpaid a player was. As with $/WAR though, if the player had a negative WAR value, his projected salary will also be negative. So essentially it suggests the player added nothing to the team and actually cost them additional money. Any player in that category is one who the team would want to eliminate. The third category is just to see how much a team underspent or overspent for a player.

After gathering the data, it seems as though the results are inconclusive. It would not be accurate to say that the earlier a batter is into his thirties, the more likely he is to be overpaid. First, here is a table sorting the top 20 qualified players by WAR value.

WAR table #1

As expected, when the data is sorted by WAR value in descending order, it also sorts the projected salary column in the same way. Miguel Cabrera had the highest WAR of this data set, and despite his $21 million salary, he technically should have made $37 million in just that season based on the production he gave the Tigers. David Wright, who had the next highest WAR value at 6.1, actually should have made about triple his $10.2 million salary in 2013 based on his performance.

Now, there are always going to be players who earn huge contracts and still earn less than their projected amount. It would be hard to justify signing a bunch of different guys to $30 million per year contracts because it’s hard for players to maintain a WAR value high enough to warrant that. In fact, all 20 players on this list received a lower salary than their projected salary based on WAR. Joe Mauer was the closest among any player on this list, earning just $3 million less ($23 million) than his projected salary ($26 million). Thinking about it with sabermetrics, he was paid very close to his value.

Now, here are the players with the lowest WAR values and where they stack up:

WAR table #2

Macier Izturis is the worst player on this list based on WAR, having a -2.2 WAR value and a projected salary of -$11 million. Obviously that doesn’t make sense logically, but it shows that he not only should have earned his $3 million salary, but he should have paid his team $11 million for how much he negatively affected the team. That’s never a situation to be in.

The worst contract on this list is that of Vernon Wells, who earned $24.6 million in 2013 despite a WAR of -0.7. That is the definition of a disastrous contract. He really should have paid the Yankees about $28 million for how bad he was. Most of the players with the worst WAR values received a salary of under $10 million, but they really should’ve earned much lower salaries. Based on the “logic” I’ve been using, no player with a negative WAR value should even receive a salary.

Now, the most important part of this study was to see whether people in their earlier thirties are more likely to be overpaid based on their WAR. After looking at the players who were technically underpaid the most, the opposite is actually true. Here’s the table:

WAR table #3

Every player on this list is under the age of 35, and only two of those players are 34. Most of the players fall in the 30-32 age range, meaning the younger in their thirties they are, the more likely they are underpaid compared to their WAR value. One reason for that is because many players are more likely to be in their prime in their thirties, but that means they’ll also have hit free agency at least once and should’ve received a larger contract. Also, not as many players are in the 35-39 age range, meaning there’s less of a chance for players to populate the table above, but there were still 50 players out of the 159 total who were in that age range. And still, none of them were in the table for most underpaid players.

To contrast that table, here are the top 20 most overpaid players among the data set:

WAR table #4

In this table, there is a much higher population of players in the 35-39 age range whose are vastly overpaid. Thirteen of the 20 players have a negative WAR, and eight of the 20 players are in the aforementioned age range. One thing to point out is that there are a few pitchers on this list such as Cliff Lee, A.J. Burnett and Bronson Arroyo, and they really shouldn’t be judged based on their batting abilities. As for the rest of the players, it seems like the older they are, the more likely they are to be overpaid. All eight of the people in the 35-39 age range who are in this table are in the top 10. As mentioned before, Wells has the worst contract of any player I looked at, earning more than $20 million despite a negative WAR. The 38-year-old Alex Rodriguez was the second worst, recording a positive WAR value, but he still should’ve earned about $26.5 million less than he made. It was not a good year for the Yankees, clearly.

In conclusion, it seems that my hypothesis was incorrect because I thought it would be the opposite of what the data actually showed. Players earlier in their thirties were more likely to be undervalued than those in their later thirties. I thought it would be the other way around because I thought players in their later thirties would already be on their third or fourth contract and probably on the decline in their careers, therefore likely earning a lower salary. But it seems like many older players were either still on a huge contract, or they just had such a low WAR that they shouldn’t have earned anything.

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