## Wins Above Replacement and Player Evaluation

David Price signed a 7 year contract for $217 million with the Boston Red Sox in the 2015 offseason. This is a large contract, in both absolute and relative terms, but how do we decide whether or not Price is worth it? The nice feature of the Advanced Pitcher Statistics and Advanced Hitter Statistics comes with the fact that they enable the assessment of players based on their specific ability to affect the game. Isolating the factors the player directly controls allows for a better estimate of the player’s unique ability. The few shortcomings of these metrics arise when trying to estimate a player’s worth to his team. In any business circumstance, worth is best understood as “two items of equivalent value”. For example, if someone purchases a piece of jewelry for$150, both the jewelry and the $150 are equivalent in worth to the parties exchanging them. The purchaser must be indifferent between the idea of having the jewelry or having the cash, which is why they are willing to offer the money for it. If the purchaser did not think that the jewelry was worth$150, they would not offer to buy it. Similarly, the selling party is indifferent between maintaining ownership of the jewelry or receiving $150. If the selling party thought the jewelry was worth more than$150, then they would not offer its sale for such a price. In order for an actual exchange to occur, the parties must have the same valuation system for both the item and the money exchanged. Baseball teams and their players function in the exact same way.

To a baseball team, a player is worth “X” wins over the course of a season. The team is willing to offer “Y” dollars in exchange for this production from the player. Similarly, the player knows his own talent and feels that his level of production for the team is worth some amount of money. If the team and the player agree on the valuations, the player will sign a contract and the team will pay him the money agreed upon.

## Why are Wins used as a statistic in Sabermetrics?

It is important to discuss why wins are used as the means of evaluation in the sabermetric community. To quantify a player’s contribution to the successes and failures of his team, a metric of evaluation must include every aspect of the game: pitching, hitting, running, and fielding. It must also include the value of a player’s position (some positions are more difficult than others).

These factors, as examined previously, are measured in runs. Runs are the common denominator when it comes to measuring output for a player. Batting and baserunning contribute runs for the team, while pitching and fielding prevent runs. It is not convenient in discussion to mention each of these factors separately however, and so each component is unified into a measure of wins.

## What does a Win represent in Sabermetrics?

It is important to note that when converting runs into wins, this does not mean that the player directly contributed to the earning of a win for his team. Rather, it means that on average, his game-to-game production led to the team winning one more game than it would have without him over the course of a season. This is one of the most frequently misunderstood and misrepresented aspects of sabermetrics and advanced statistics.

Looking at the average combined number of runs in games (by the winning and losing team), we can determine a rough gauge of how many runs are involved in a win. The information can be found here on Fangraphs, under the R/W column. Generally, it takes somewhere between 9-10 runs total to equal the value of a win. A win is nothing more than a unit of measurement. It does not represent a tangible impact on a specific individual baseball game. It does not represent a precise estimation of how many games a specific team will win because of a player. It does represent an estimation of a player’s effect over a season on the basis of how many runs he adds offensively and subtracts defensively.

## What is a Replacement Player?

The key to linking wins with player worth is the concept of the replacement player. The idea of “replacement value” may initially seem foreign, but it is not too different from decisions made at the supermarket or while purchasing other common items!

Going to the supermarket to purchase bread, milk, etc. generally leaves you with two options: the generic “store brand”, or the specific company “brand name” item. When making a decision between which to buy, there are a number of factors that run through someone’s mind. Most prominently among those are probably 1) cost and 2) value derived from the item. If the store brand bread is much less expensive than the brand name bread but tastes nearly as good, it likely makes more sense to the consumer to purchase this in lieu of the brand name. Alternatively, if the store brand milk is not at all enjoyable, then it probably makes sense to pay the small premium to purchase the brand name milk.

Baseball players work in the exact same way to the 30 MLB teams. A replacement player is one that can be easily and cheaply signed or acquired, like the “store brand” item. Sometimes these players are characterized as “AAAA” players. This term symbolizes their abilities lying somewhere in between that of a “Major League regular” and “AAA talent” [highest level of the minor leagues] player. These players are frequently either former prospects that did not meet their predicted abilities, or are veterans that, due to age or previous injury, have lost a step.

Another way to think of the AAAA player is as the one who is recalled from the minors when a Major League player (either starter or bench player) is temporarily injured. The AAAA player will take the injured player’s spot on the team until he is able to return to playing. Herein lies the origin of the term “replacement player”; the replacement player is the very common and easily accessible player that would replace the spot of the injured player.

It is important to not confuse the replacement player with the injured player’s “backup”. Pretend that Alan is the starting shortstop and Brian is his backup coming off the bench. If Alan gets hurt, Brian will likely become the team’s starting shortstop until Alan returns from injury, as he is the “next-man-up”, so to speak. Because Brian is now the starting shortstop, he has no backup off the bench. To correct for this, the team recalls Clark from their minor league team.

Because Clark is the variable that changed, he is the one that is considered the replacement player. Even though Brian is the one that took Alan’s spot on the field, he is not considered the replacement player because he already had a spot on the team. The level of contribution from Brian’s spot has not changed, just the amount (he is playing more frequently). In comparison, the level of contribution from Alan’s spot on the team has changed because Clark is a less-skilled player and the amount of contribution will likely decrease (as the spot is now devoted to the backup).

## How are Wins and Replacement Players related?

In order to understand what exactly a replacement player contributes to a team, it is necessary to create a metric that defines the minimum expectation of a player (i.e. replacement value). The metric that enables this is known as Wins Above Replacement (WAR). WAR (this is read as it appears, “war”) compares every player to that absolute minimum expectation. To continue with the metaphor from above, WAR defines how much better the brand-name milk tastes than the generic milk. It designates each individual’s performance as some degree “above replacement”, or better than the minimum alternative. A true replacement-level player will thus have 0 WAR, as he is 0 wins above replacement.

To determine the baseline, WAR imagines the production of a team full of replacement players, and then sets this as the “floor”. A team of only replacement players by definition is expected to win 48 games in a 162 game season for a .294 winning percentage. Because there are 30 teams in the majors, and the cumulative record of the league will be .500 (i.e. for every win there is a loss), this means that there are:

$30 \cdot 162 \cdot (.500 - .294) \approx 1000 \textrm{ WAR}$

to divide amongst the players in the majors for a season. This again is by definition and is designed to create a “nice” number to work with.

WAR is fractionally contributed to players over the course of an MLB season. The more a player plays, the more opportunities they have to earn WAR. It is also possible to earn negative WAR, the implication being that this player played even worse than replacement level (tastes even worse than generic milk). While this does occur, it is far from frequent, in the same way that you would ardently avoid a milk worse than the store-brand. A team will likely either 1) identify that the player is performing worse than what is cheaply and easily available and switch or 2) recover from whatever dire circumstances (player injury, emergency, etc.) forced the poorly performing player to enter games in the first place.

The distribution of the 1,000 WAR across the league’s players is done based on the contract allocation of major league free agents. In free agency, hitters receive approximately 57-59% of the money and pitchers the remaining 41-43%. Therefore, there are 570-590 WAR to divvy up amongst the hitters and 410-430 amongst the pitchers.

In terms of ranking performances in WAR, a general scale along with distribution across the league is as follows: (courtesy of Fangraphs) 70PA for hitter 20 IP (~10% of season)

WAR Level Pitchers % Distribution
< 0 (Below Replacement)  112  21.9%
0 – 1 (Replacement Level)  230  45.0%
1 – 2 (Role Player)  88  17.2%
2 – 3 (Solid Starter)  44  8.6%
3 – 4 (Good Player)  18  3.5%
4 – 5 (All-Star)  6  1.2%
5 – 6 (Superstar)  7  1.4%
6+ (MVP Candidate)  6  1.2%

WAR Level Hitters_ % Distribution
< 0 (Below Replacement)  119  24.6%
0 – 1 (Replacement Level)  144  29.8%
1 – 2 (Role Player)  88  18.2%
2 – 3 (Solid Starter)  59  12.2%
3 – 4 (Good Player)  32  6.6%
4 – 5 (All-Star)  21  4.3%
5 – 6 (Superstar)  9  1.9%
6+ (MVP Candidate)  11  2.3%

This confirms that exceptional players (>4 WAR) are difficult to come by. On average there are only enough for each of the 30 teams to have 1 or 2 that meet those standards. Around 60% of all players are replacement level or below. This leaves a smaller amount (those in the 1-4 WAR range) as the players a team relies on to put up dependable performances. As these players account for ~30% of the total players, there are enough for each team to employ 7 or 8, on average. This scarcity causes a competition for talent, and it is important to discussed on how teams value and compete for this talent will occur later on.

## Using WAR to Value Players

How do we tie all of this information together? We know that WAR measures how much a player plays above replacement (baseline) level. We also know that there is a limited amount of WAR for players to accrue in a season. Lastly we know that players that earn WAR at notable paces (>4 WAR per season) are rare. MLB Teams also recognize this, and there is a competition for the scare talent. How do teams use WAR gauge how competitive they should be in a bid for a player? In other words, how do you figure out the maximum amount you are willing to pay for the better taste of brand name milk?

#### Incentives, Options, and Aging: Contract-Makers and Deal-Breakers

Sometimes the parts of the contract that make it a good or bad deal are the “extras” that are thrown in. Offering incentives to a player can reward them for good performance, without actively costing the team money upfront. Player, team, and mutual options allow parties to opt-out of the contract based on performance, either good or bad. In Price’s case as we mentioned above, he has an option to opt-out after the 2018 season. “Why would David Price walk away from $30 million a year?!” some may ask. The answer lies in performance. If Price outperforms his projected output for the next 3 years (somewhere around 14-15 WAR total) and puts up closer to 17 or 18 WAR, then he will have been underpaid for his performance 3 years running as outlined above. If Price feels that he could opt-out of the contract and make more than$30MM/year after 2018, then he will likely do so. Generally at the initial signing, a team offering this type of option to a player is not seen as a detriment to the team. The only “risk” that the team assumes is that the player performs even better than they are paying him.

In the opposite way, a team can engineer a deal in which they have the option after a certain amount of time, and can opt-out. This gives the team an “escape route” to leave a deal that ends up not being worth it if the player’s performance declines due to injury or age. Lastly, there are the rare mutual options that are exercised when each party wants to opt out of the contract. This may occur if the team no longer has a use for the player or feels they are overvalued, and the player wants a change of scenery or feels that he is performing better than his contract.

One concept mentioned above that is important for contract evaluation is that of age decline. Many large contracts are awarded to players that are toward the end of their prime years. There is no guarantee that paying for a player’s recent performance will indicate that he continues to play at that level. This is where teams run into dangers with contracts and what makes them burdensome. Using the Price example again, David was 30 when he signed the contract and will be 37 when the contract expires. The Red Sox paid for the WAR production of his age 29 season! A lot can happen in 8 years, both naturally and because of injury. Should something happen to Price to cause him to decline, the Red Sox will be paying quite a premium for less talent than they were expecting. The Red Sox are able to take this huge risk however, because they are one of the few teams able to absorb it.

#### Market Size and Payroll: What Teams are Willing and Able to Undertake

This leads to the last major point of Contract Evaluation; a good/bad contract is not necessarily good/bad for each team. The MLB is the only major American professional sports league that does not have some form of a salary cap. Because of this, each of the 30 teams are able to spend whatever amount they can or want to on players. Teams based in big media markets (the New York teams, the Los Angeles teams, the Cubs, and the Red Sox are a few examples), are much more able to spend significant amounts of money on contracts than teams in smaller markets (such as the Twins, Royals, Pirates, etc.). It was out of this restriction that sabermetric use developed amongst teams. This was documented in the book (and later film), “Moneyball,” the main exposure to sabermetrics for casual fans. When discussing contracts at SaberBallBlog, market size will be an important component in assessing the feasibility of a contract.

## Coming Home: Participating in the Sabermetric Community

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