# Most Valuable Player: A Quantitative Approach

# Introduction

Every year MLB chooses a player in each league to receive the Most Valuable Player award. This year’s winners were Mookie Betts in the AL and Christian Yelich in the NL. The winners are chosen by members of the Baseball Writers Association of America (BBWAA). Voting takes place at the end of the regular season. Guidelines are posted here and have remained unchanged since the first ballot in 1931. The guidelines suggest the criteria should include: the actual value of a player to his team; strength of offense *and* defense; number of games played; and, general character, disposition, loyalty and effort. Individual voters use their subjective judgments for choosing their nominees.

The question addressed in this article is “** Aside from the assessment of character and personality traits, is there a fair measure and ranking of on-field performance that can replace the subjective evaluations of the individual voters?**”

First, we define what we believe is a fair measure. This is followed by a description of how this measure can be obtained using the RunPlusMinus statistic. We show the top 3 MVP choices for each team in MLB. We then show league-independent top and bottom MVPs for 2018 MLB players who played at least 25 games. Finally, recognizing that some players “run hot and cold” during the course of the season, we provide a listing of the most volatile performers.

# A Fair Measurement of MVP-ness

The object of each team in a game is to win the game by scoring more runs than its opponent. Therefore, one component of a fair MVP measure must be based on the number of wins contributed by a player. Leaving aside for the moment how that is measured, we cannot ignore that a player may also contribute to a loss by a poor performance. This means that poor performances should offset winning performances. The net effect is that *the MVP value for a player should be games won minus games lost*.

Suppose we have the following two statistics for each game and each participating player and each team:

- A player statistic that measures how well the player performed in each play relative to the average historical performance of all players taking the same role in similar plays. The value of (player performance - average performance) is: positive if the player performed above average in the play; zero for an average performance; and negative for a below average performance. This means that the sum of a player’s performance for a game defines whether the player’s performance was above average, average or below average for the game.
- A team statistic for each team in a game that:

a. Is the sum of all player values for the game

b. Is always positive for the winning team and negative for the losing team

c. Reflects the winning margin of runs

Given the existence of such a statistic — and it does exist — then one can answer the following question. “Was the player’s performance — compared to an average player’s performance — sufficient to cause his team to win (or lose) the game?”. In a game suppose the player’s statistic value is X and his team’s statistic value is Y. There are 3 cases.

**Case 1:** the player’s team won the game (Y is positive) and the player performed above average (X is positive). It follows that if X is greater than Y then the player’s performance was sufficient to win the game. The reason is simply that an average performance would reduce the team’s value by X making the team’s total negative meaning the team would have lost the game. In this case the player can be justifiably credited with a win.

**Case 2:** the player’s team lost the game (Y is negative) and the player performed below average (X is negative). It follows that if X is less than Y then the player’s performance was sufficient to lose the game. The reason is simply that an average performance would increase the team’s value by X making the team total positive which would mean the team would have won the game. In this case the player can be justly credited with a loss.

**Case 3:** Any other combination of X an Y values means that if the player’s performance had been an average performance, it would not have changed the outcome of the game (assuming other players’ performances did not change).

The table below illustrates the logic above.

Notes:

- A Team Value of zero cannot occur because there are no ties in MLB games and the team statistic is
*always*positive for the winning team and the negative of that value for the losing team. - In every game there may be zero or more players credited with a win or a loss.
- Over the course of a season, a player’s

**MVP Rating = Number of Wins - Number of Losses**On each team the player with the highest rating is the team’s MVP winner.

Is the MVP winner on a stronger team “more of an MVP” than the MVP winner on a weaker team? The answer is “No”. This is because: 1) *each MVP rating is a competition among players on the same team*; and 2) the MVP rating is *the difference between player wins and losses for that team*.

# MVP Calculations Using the *RunPlusMinus* Statistic

An explanation of the RunPlusMinus statistic can be found here and in the articles accessible from that page. For this discussion however, the RPM statistic is the only published statistic that satisfies the necessary criteria to calculate player MVP ratings defined by the rules above. Among other attributes the RPM statistic is: run-based, additive, includes every player’s contribution in every play in every game and is zero sum (offense values are equal and opposite to defense values).

# MVP Results

We present the following four charts:

- AL Team MVPs
- NL Team MVPs
- Top and bottom MLB MVPs

In each case, the players being ranked have played at least 25 games. For each team, the top 3 players including ties are listed unless a large number of players had the same rank. Ranking is based on the MVP rating shown in the “Won - Lost” column.

**AL MVPs**

For example, Andreltron Simmons and Mike Trout tied for the highest MVP rating on the Angels. Other attributes of player performance could be used to break the tie.

**NL MVPs**

MVP ratings and rankings for the NL teams are shown below.

The Pirates have 5 players tied for tops with a net (Won - Lost) of 3.

**MLB MVP**

The chart below shows the overall top and bottom MVP rankings in the combined AL and NL. Note that Mookie Betts is the clear winner and was chosen by the BBWAA as well. The NL winner Christian Yelich does not appear in the top group. He had a wins minus losses value of 4 on the Brewers. This is likely a consequence of not using a quantitative measure such as the RPM-based rating and/or subjective non-quantitative assessments used by BBWAA voting members.

# Volatility

Every baseball enthusiast can identify players who seem to have a lot of good games or bad games. That is, they lack consistency at the plate or on the mound. The RPM total of *games won plus games lost* is a good measure of this volatility. However if two players have the same total of wins plus losses, the player who had more wins than losses should be ranked higher than one with fewer wins than losses. This is shown by the colour highlights in the AL and NL charts which follow.

## AL Highest Volatilities

## NL Highest Volatilities

# Conclusions

This article:

- Argues that the component of MVP evaluation related to on-field performance can be based on calculating the value of games won minus games lost for each player.
- Games won or lost can be determined by determining whether the game winner would have changed if a player had had an average performance instead of his actual performance.
- A player’s MVP rating is the value of games won minus games lost.
- More that one player on a team may be credited with a game won or game lost in a game.
- The
*RunPlusMinus*methodology is (currently) the only published method of calculating the MVP rating described in this article. - The value of games won plus games lost is a measure of a player’s on-field performance volatility.