By Steven DiMaria – Syracuse University ’21
Abstract
The goal of my research is to project an estimated contract extension value for Aaron Judge. Judge is going into his second season of arbitration eligibility, so he has two more years of team control before going into free agency. He is eligible for arbitration in both of those seasons, so he will see his salary rise in each of the next two seasons. There are various factors that go into projecting an extension including estimating his performance for the rest of his career, his salaries for the next two seasons, his value on the open market, and looking at the Yankees organizational depth chart and financial picture now and in the future. Work has previously been done on existing projection systems, principal component analysis, modeling, converting WAR to dollar value, the shortened 2020 season, roster construction, comparable contracts, and injury risk. It is most important to project Judge’s WAR for future seasons in order to gain an understanding of what his overall value will be moving forward. Other statistics such as home runs and outs above average are projected. Statcast data is an important component of the projections. Principal component analysis is used to find similar players to Judge at each age. This helps to provide a midpoint, floor, and ceiling projection for Judge at each age, based on the range of outcomes provided by the comps.
Introduction
The purpose of this research is to project a contract extension value for Aaron Judge. Judge is one of the top of players in baseball, and his team control ends upon the conclusion of the 2022 season. Due to baseball’s economic system, he has been one of the greatest bargains in baseball to this point in his career. However, as one of the best and most influential players in baseball, he will receive a large contract to cover his free agent years. This research was conducted from the perspective of his current team, the New York Yankees. They will need to decide if they want to offer him a contract extension before his free agency, and if so what the value of their offer should be.
The goal of this work is put together all aspects of the Yankees to decision to come up with a reasonable contract offer. Projecting the offensive performance, defensive performance, and expected number of games played for Judge will help determine his expected value to the team in future seasons. Novel methods that help perform risk and cost analysis are used for the projections.
Method
Principal Component Analysis
The primary technique that is used to build the offensive and defensive projection systems is principal component analysis (PCA). PCA captures the variation in a dataset with many variables in a smaller number of principal components. The principal components each represent a certain percentage of variation in the data. It is possible to see how each of the variables in the original dataset is correlated with each principal component. Ultimately, this technique is very useful as it reduces a large number of variables into a small number of principal components that expand the possibilities for further analysis.
In the case of the offensive projection system, the principal components represent the offensive profile for each player in the sample. For example, if the variables in the dataset that have the highest positive correlation with the principal component are exit velocity and hard hit percentage, that principal component is most representative of players that hit the ball hard. Therefore, players that tend to have the highest contact quality would have a high value for that principal component, while players with lower contact quality will have lower values. Players with similar principal component values to Judge in each of the principal components that account for at least 10% of the variation in the data are considered his comps at each age. The defensive method uses the same process, but the principal components represent defensive profiles for outfielders instead of offensive profiles.
This is the selected method because it creates a distribution of values that could represent the change in Judge’s stats from one year to the next. As a result, the best and worst case scenario can be analyzed in addition to the most likely changes in Judge’s performance. Another benefit of this methodology is that predictions are based on players that have the most similar offensive and defensive profiles to Judge. This helps capture any unique advantages or disadvantages that Judge’s unique skillset provides as he ages.
Other Methods
To estimate the number of games Judge will play each season, a group of probit models are used. This method is useful because it provides odds that Judge will reach certain games played thresholds. Like with the offensive and defensive projections, this makes it possible to evaluate a variety of scenarios for the number of games Judge will play each season.
WAR values were determined by looking at WAR for players in the sample who had an OPS within 20 points of Judge’s projected OPS and outs above average within 2 points of Judge’s projected outs above average.
Results
| Age | Projected OPS | Projected wOBA | Projected HR/G |
| 28 | 0.9015 | 0.3705 | 0.268575 |
| 29 | 0.9375 | 0.3825 | 0.29041 |
| 30 | 0.9215 | 0.3785 | 0.2768 |
| 31 | 0.851 | 0.3465 | 0.246392 |
| 32 | 0.825 | 0.3255 | 0.2479 |
| 33 | 0.823 | 0.3225 | 0.24644 |
| 34 | 0.7815 | 0.3065 | 0.230225 |
| 35 | 0.7595 | 0.2885 | 0.21231 |
The first table is the results for the measures of future overall offensive productivity for Judge. An average league average OPS is considered to be about .770, while a league average wOBA is considered to be about .320. In terms of home runs, 0.1-0.15 is the average range. Based on the results, it is clear that Judge will remain an elite offensive force in his prime years of 28-30. In his early 30s, he will being to decline, but still be a well above average hitter. In his mid 30s he projects to be an average offensive or slightly below average hitter. Power will be a strength for Judge throughout his career.
| Age | Projected OAA |
| 28 | 9 |
| 29 | 11 |
| 30 | 11 |
| 31 | 8.5 |
| 32 | 7.5 |
| 33 | 7.5 |
| 34 | 8 |
| 35 | 2.5 |
The second result are the projection for Judge’s future outs above average statistics. This is the main statistic that was used to measure overall defensive value. An average OAA for an outfielder is about 0. Judge will be one of the top defensive outfielders in his prime years, and continue to be well above average in his early 30s. As he begins, to age he will be more of an average defensive outfielder.
| Age | Games with at least 50% probability | WAR |
| 28 | 140 | 4.8 |
| 29 | 140 | 5 |
| 30 | 140 | 5 |
| 31 | 140 | 4.8 |
| 32 | 140 | 3.5 |
| 33 | 130 | 3.3 |
| 34 | 130 | 2.8 |
| 35 | 110 | 1.4 |
The third tables represent Judge’s WAR and games played projections. The game played numbers displayed in the tables represent the highest number of games he has a 50% chance of playing. For the WAR projections, they predict the FanGraphs version of WAR. Judge is projected to be an all star from ages 28-31, an above average contributor from ages 32-34, and a role player after age 34.
Conclusions
Judge projects to be a valuable player that the Yankees should attempt to keep if they can agree on a fair contract value with Judge. His offensive and defensive production project to remain strong as he ages, though they will see some decline. In his prime he will remain one of the best players in baseball. In the period shortly following his prime, he will be a strong contributor but not one of the very best players in the game. Once he reaches his mid to late 30s, he will a role player.
Considering that the literature supports that 1 WAR is typically valued at about 8-9 million dollars per season, the recent signing of similar player George Springer for 6 years and 150 million seems to be a fair baseline offer for Judge. Going slightly above this value would make sense, given how difficult it is to acquire great players and Judge’s intangibles. Anything below 150 million is a bargain for the Yankees. The goal for the Yankees should be to keep the contract value below 200 million dollars. A six year term also aligns well with Judge’s expected aging curve.