The Cost of a Win in MLB

The amount of money in Major League Baseball is astonishing. The New York Yankees are worth $4.6 billion. The Los Angeles Dodgers, Boston Red Sox, Chicago Cubs, and San Francisco Giants are all worth over $3 billion each. The smallest valuation, the Miami Marlins, is worth $1 billion. The average annual salary for a player in 2019 was $4.36 million, but players like Mike Trout, Nolan Arenado, and Manny Machado were making upwards of $30 million.

My question is simple: Are these highest paid players worth the money?

The most common way to determine this has been to use Wins Above Replacement (WAR). According to, the idea behind WAR is to see “how much better a player is than a player that would typically be available to replace that player.” Players are compared to averages in a complex variety of ways, ultimately focusing on runs contributed offensively and saved defensively. One win is estimated to equal about ten runs, so WAR values are presented with decimals. As a scale to refer the values to, lists < 0 as replacement level, 0-2 as reserve, 2+ as starter, 5+ as All-Star quality, and 8+ as MVP quality.

A difficult aspect becomes assigning a dollar value per WAR. This value is different for pitchers versus position players, as well as starting pitchers versus relief pitchers. Younger players with high WARs can also throw off the value since, as Dave Cameron of FanGraphs puts it, “players with zero to six years of service time have an artificially depressed salary due to not being able to qualify for free agency.” The value changes year to year thanks to inflation. Matt Schwartz, another writer for FanGraphs, states how $/WAR can change for a player within a contract from year to year. He says that, “Unsurprisingly, players decline over time. As a result, the $/WAR in a deal’s first year is generally higher than the $/WAR in later years.” Dave Cameron used money spent on free agents along with a weighted average of their win values to create a value of $4.5 million/win for the 2008 season. John Edwards used Cameron’s formula along with FanGraphs community research to determine the $/WAR values for starting pitchers, position players, and relief pitchers from 2006 to 2017. He determined that the cost of a win is $4.2 million for starting pitchers, $5.7 million for position players, and $10.9 million for relief pitchers.

We can use these numbers, and the help of FanGraphs’ Contract Estimation Tool, to determine the value of certain players. The Tool factors in a 5% inflation rate for the first five years of the contract as well as an aging curve. The aging curve adds 0.25 WAR/year for players from 18 to 27, 0 WAR/year for players from 28 to 30, subtracts 0.5 WAR/year for players from 31 to 37, and subtracts 0.75 WAR/year for players over 37.

The values are up to 2017 so let’s look at some of the top free agents from that year.

Let’s start with Eric Hosmer. He was coming off his best year in terms of WAR, in which he played first base at 4.1 WAR for the Kansas City Royals. He truly stepped up in a contract year, and got paid for that level of play. The San Diego Padres signed him to an 8 year, $144 million contract. Using the Contract Estimation Tool and setting the $/WAR to start at $6 million, the estimated value of the contract is $171.1 million. Based on this model, the Padres got a deal for a talented player. However, the model also assumes the player will maintain that WAR and only have slight decreases with age. If we look at how Hosmer actually played in 2018 and 2019, we see a different story. According to, Hosmer’s WAR in 2018 fell to 1.4, and it fell even farther to -0.3 in 2019. With a WAR of 1.4 and a $6 million/WAR ratio, the Padres should have only had to pay Hosmer $8.4 million in 2018. Much less than the $18 million he was actually owed and the $24.6 million he was expected to make using the Tool.

FanGraphs’ Contract Estimation Tool

Another big free agent from 2017 was starting pitcher Yu Darvish. He spent 5 solid seasons with the Texas Rangers then had a partial season stint with the Los Angeles Dodgers, before he was signed by the Chicago Cubs for 6 years and $126 million. The minimum $/WAR available on the Tool is $5.5 million, so even though John Edwards calculated the cost of a win for starting pitchers to be about $4.2 million, we will use $5.5 million. The Tool estimated a contract for Yu Darvish to be valued at $77.5 million. Darvish struggled in 2018 and also had a shortened season due to an elbow injury. His WAR dropped to -0.1. After an OK year in 2019, he posted a 3.3 WAR. Contracts for starting pitchers are hardly ever based solely on $/WAR. Teams value starters highly and most age well enough to not have as steep drop-offs over the years.

FanGraphs’ Contract Estimation Tool

Picking on all of the 2017 free agents would be interesting, but I want to check on one of the best players in the game with the largest contract in MLB history, Mike Trout. He has played for the Los Angeles Angels for his whole career, which began in 2012, and has been an MVP level player every year since then. He signed a 12 year, $428 million contract extension with the Angels in 2018. His “worst” year was 2017 when he was forced to sit out almost 50 games with a thumb injury, and posted a WAR of 6.6. Using that value, the Contract Estimation Tool still predicted a 12 year contract for him to be worth $453.7 million. When I used his career average WAR of 9.0, his 12 year contract value rose to $655.7 million. I then changed the Tool to say he ages well, meaning his WAR would not decrease with age as much, and his 12 year contract value jumped to $706.8 million. Seeing as he posted WAR values of 10.2 and 8.3 in 2018 and 2019, respectively, the contract estimations with the higher WAR seem more accurate.

Assigning the proper value to player contracts to determine the of wins they are worth is impossible. Teams pay players for much more than wins. They can pay an old veteran more than his expected $/WAR if they want some added leadership in the clubhouse. They can pay a relief pitcher more than his expected $/WAR if they are trying to make a playoff push. Teams can invest in a player to become the face of the franchise and improve fan engagement. A popular, but low WAR player may drive ticket sales better than an unknown, high WAR prospect. The variables that go into $/WAR are constantly changing. In order to properly analyze a players worth, many factors must be considered. The answer to my “simple” question is more complex than I could’ve imagined.

Continue Reading

The Impact of Weather on Mendenhall’s Football Team

Teeth are chattering, hands and toes are becoming numb and large amounts of hot chocolate are being consumed as football fans watch their teams play on a cold fall night. While the fans are freezing, they wonder if the cold is impacting the football players. Rain and cold are two weather conditions that football players face when playing in a game. The question I am trying to analyze is whether environmental factors like temperature and precipitation make a difference on offensive performance in a football game.

Coach Mendenhall took over the University of Virginia football team in 2016 and before UVA he was the coach for Brigham Young University for eleven years. Mendenhall is a student of the game of football and uses an adaptive style of coaching that incorporates the current resources that are available to his program. During his first two year at UVA, Mendenhall primarily used a run and gun offense, which is a type of offense that has a receiver suddenly changing positions by running left or right, parallel to the line of scrimmage, just before the ball is snapped. The traditional tailback runs with a pocket passer. Once Bryce Perkins was recruited to play for the University of Virginia, the offense changed to primarily a run-pass offense because of Perkin’s mobility. Teams playing against UVA had to account for not only the tailback runs but also the quarterback runs and passes. 

I was curious to examine the impact of temperature and weather on the offense while Mendenhall was the coach for both UVA and BYU. I analyzed six years of Mendenhall’s coaching career with two years at BYU and four years at UVA. Overall, Mendenhall won 55% of these games and lost 45% of them. For each game I looked at temperature, weather, total passing yards, passing yards attempted, passing yards completed, total rushing yards, average per rush, touch downs, fumbles, interceptions, total points and whether the team won or lost. I used temperature and weather (rain or clear) as the variables to compare the offense statistics to in order to see if there was a correlation.

The first set of data I analyzed was the impact of temperature on passing and rushing yards. 

When the temperature is below 25 degrees Fahrenheit, both rushing yards and passing yards are negatively affected. The offense was not as effective in achieving yards when the temperature was extremely cold. As temperature increases, both passing and rushing yards per game increase. Between temperatures 26 to 100 degrees, there is not a large difference between passing and rushing yards, however, in general the offense tends to have more passing yards than rushing yards. 

The next set of data was the impact of rain on passing and rushing yards.

When it was raining, the offense ran the ball more and when the weather was clear with no rain the offense passed the ball more. Before starting this project I hypothesized that the offense would rush the ball more when it was raining due to a higher chance of mistakes in the rain with less visibility and grip on the ball. The offense had to adapt to the weather conditions in order to have the best chance of winning.

I also looked at the impact of temperature on fumbles and interceptions (turnovers).

Interceptions were minimally affected by temperature and remained relatively constant. The offense had the greatest number of fumbles per game in cold weather. As the temperature increased, the average fumbles per game decreased. Overall there is a correlation between cold temperatures and number of fumbles.

The final set of data I analyzed was the impact of rain on fumbles and interceptions (turnovers).

When it was clear outside there were more interceptions compared to when it was raining. This makes sense because when the weather is clear the offense is passing the ball more. Greater passing leads to more opportunities for interceptions. There is less of a difference between rainy weather and clear weather with fumbles. However, there were slightly more fumbles per game when it was clear compared to when it was raining.

The weather and temperature are two factors that affect the style of play.  When it is raining outside, offense tends to rush the ball more. When it is clear outside, offense tends to pass the ball more. It will be interesting to see if these statistics hold up going forward as Mendenhall continues his time at UVA. 

Data from all the games

Continue Reading