Since WAR has become a popular way of evaluating baseball players, there has been debate on how to value Wins Above Replacement (WAR) in a player’s salary.
At first glance, it seems easy to put a value on the price tag of WAR: total league salary divided by total WAR. The numbers to gather data for WAR and Salary were collected from the Player Value charts on baseball-reference.com.
This results in a $/WAR value of $3.39M for batters with at least 50 PA, $2.85M for starters with 100+ IP, and $4.29M for relievers over 30 IP. These numbers are brought down considerably by rookies who make the league minimum or not much above. Disregarding the rookies, the $/WAR values are brought up to $5.07M for positional players, $4.63M for starters, and $7.26M for relief pitchers.
However, these numbers don’t tell the whole story. Many experts and analysts continue to state that the price tag of WAR isn’t linear, but no one seems to have an answer of what it really is.
From the calculations above, we can observe a clear trend that WAR is valued differently for each of the three groups of players; therefore, the calculations for this exercise were split between starters, relievers, and fielders. Also, to consider both superstar and developing rookies, any Rookie/Arbitration contracts below $1M was disregarded from the calculations.
Below is a plot depicting every position player with at least 50 PA in 2018 for WAR against the players salary. A total of 215 MLB players met these criteria in the 2018 season.
Using these data points, and given the sheer number of outliers, the best fitting equation is:
While these valuations can be used for position players, pitchers typically have a higher value to organizations. Below is the plot of all starting pitchers that contributed 100+ IP in 2018.
The plot results in the following equations to assign value to starters:
Finally, the following plot represents all relief pitchers with 30+ IP in 2018.
WAR for relief pitchers is a fickle thing. Due to the limited outings in a season, one bad outing can significantly damage a reliever’s production for the year. Because of this, the valuation for relievers remain slow even for relievers that just had a strong season.
These large, fancy equations look nice, and give an easy way to calculate exactly what a player’s estimated value should be just by using his bWAR. But what does it really mean?
Taking the numbers from the chart at baseball-reference.com, and applying them into a spreadsheet, the work is already done. Equations are automatically calculated by using a “line of best fit” which basically means to a computer “given these parameters, what equation will give me the most accurate assessment?”
While there are a couple of different types of equations that could be used, a large polynomial (like the equations above with variables raised to an exponent) fit most accurately compared to an exponential ( the number “e” to the power of “x”) or a lower degree polynomial (i.e. the largest exponent is smaller than a six). The best way to assess which equation to use is to simply plug in a set of possible values and find what makes the most sense.
Using the three equations above, we can calculate the Estimated Value of players relative to the rest of the league. How do we use these values to look at players? Who is performing above and below their pay grade?
Arbitration Players: This valuation of arbitration eligible players can be used during their upcoming arbitration hearings this off-season.
| Player | 2018 bWAR | 2018 Salary | Estimated Value |
| Aaron Hicks | 4.6 | $2,825,000 | $9,155,000 |
| JT Realmuto | 4.3 | $2,900,000 | $9,134,000 |
| Nick Ahmed | 3.2 | $1,275,000 | $9,385,000 |
| Miguel Rojas | 2.4 | $1,180,000 | $9,359,000 |
| Luis Severino | 4.8 | $604,975 | $12,760,000 |
| Sean Manaea | 2.8 | $555,000 | $12,313,000 |
| Matthew Boyd | 2.1 | $562,000 | $10,610,000 |
| Scott Oberg | 2.4 | $555,000 | $5,830,000 |
Free Agents: Teams that are money-conscientious should use a similar algorithm to determine exactly what kind of offers they should put forth to free agents in the off-season. Note: Bryce Harper was left off this list because he only played part of the season and did not accumulate WAR at his typical rate.
| Player | 2018 bWAR | 2018 Salary | Estimated Value |
| Manny Machado | 5.7 | $16,000,000 | $10,000,000 |
| Patrick Corbin | 4.6 | $7,500,000 | $12,920,000 |
| Michael Brantley | 3.6 | $11,500,000 | $9,289,000 |
| Craig Kimbrel | 2.3 | $13,000,000 | $5,878,000 |
| Dallas Kuechel | 2.6 | $13,200,000 | $11,890,000 |
| Nathan Eovaldi | 1.5 | $2,000,000 | $8,969,000 |
| Wilson Ramos | 2.7 | $8,500,000 | $3,148,000 |
| Yasmani Grandal | 3.3 | $7,900,000 | $2,394,000 |
Bargain Superstars: These are the players that are giving teams the best value with a salary over $10M.
| Player | 2018 bWAR | 2018 Salary | $/WAR | Estimated Value |
| Mookie Betts | 10.9 | $10,500,000 | $963,302 | $15,938,000 |
| Andrelton Simmons | 6.2 | $11,000,000 | $1,774,194 | $11,000,000 |
| Chris Sale | 6.9 | $12,500,000 | $1,811,594 | $15,416,000 |
| Corey Kluber | 5.9 | $10,700,000 | $1,813,559 | $12,652,000 |
| Lorenzo Cain | 6.9 | $14,000,000 | $2,028,986 | $13,172,000 |
There are obvious errors in using methods like this to try and evaluate the true dollar value of WAR. For example, players with negative WAR and starters at the top of the league break these equations – Chris Davis (-2.3 bWAR) was worked out to be the most valuable player in the MLB, while Aaron Nola (10.5 bWAR) was such an outlier that he was valued at -$56M.
The truth in looking at the current MLB contracts (many of which were signed before advanced metrics took over the sport) is that the bad contracts will bring up the value of players with low production, and that rookie sensations cannot be compensated for what they do on the field. Three of the top seven players in bWAR in 2018 were still on rookie contracts (each below $550,000) while seven of the 23 players finishing the season at or below -1.2 bWAR in 2018 were making upwards of $5M.
Surely, as advanced metrics such as WAR continue to grow in the minds of executives when they sign players in the coming years, a clearer pattern will start to develop as to how MLB organizations truly value WAR. For now, however, we are left speculating exactly how much money one more win is worth to General Managers.
Featured Photo: Wikimedia Commons
