December 5, 2017

An Explanation Of WAR

To write this article, I leaned heavily on the FanGraphs website, as well as,, and Wikipedia.

An Overview of WAR (Wins Above Replacement)

Despite my love of baseball and statistics, I’ve always been intimidated by the advanced sabermetrics that are an increasingly important part of the game.  My favourite advanced stat is WAR, but until writing this article, I had a very cursory understanding of it. Much of the complexity still escapes me, but I take comfort in knowing that men and women determine these stats professionally. To personalize it and to help me get my head around it, I decided to analyse my favourite player’s best season. In short, I sought to determine what Jose Bautista’s 2011 WAR of 8.1 represented.

The Thousand Games Theory of WAR: Statisticians assume that a team stocked with low-level major leaguers should win 29.4% of its games, roughly 47 or 48 per season. Therefore, we start by granting each team roughly 47.5 wins and 47.5 losses before even stepping on the field.   This theoretical default floor and ceiling are Inot perfect, as the 2001 Mariners (46 losses) and the 2003  Tigers (43 wins) can attest. But we have to start somewhere. After theoretically pulling all of those games out of the analysis, we’ve removed 1430 games of the total 2430 played across the majors in a standard season. This leaves 1000 games up for grabs. If each player’s WAR is calculated perfectly, without any rounding, then the sum of all the WARs of every major league player should be 1000 at the end of the season. Since there are 750 players on major league rosters at any one time, then an average major leaguer who plays an entire season should have a WAR between 1 and 2.

How are those thousand games divided up? Different sources evaluate WAR slightly differently, but the broad strokes are the same. No one game is ever designated as going to a single player. The results of each game always result in tiny incremental increases in some players’ WAR ratings and tiny decreases for others. And a player’s WAR may increase even after a game his team loses. WAR deals in aggregate totals over time, not specific in-game scenarios. A hit in the first is worth the same as the same hit in the ninth.

The Difference Between Position Players and Pitchers: Given that approximately 43% of major league players are pitchers and that there are 1000 wins up for grabs in a season, the total WAR for all individual pitchers at the end of a season should be about 430. This leaves about 570 for position players. According to a player with a WAR of 0 is essentially a replaceable piece, while a player with a WAR of 8 should almost always be an MVP candidate.

In other words, Jose Bautista’s 3rd place finish in the 2011 AL MVP vote was fitting.


Analysing WAR for a Position Player

This article focuses on evaluating WAR for a position player. The process for pitchers is different and in my opinion is more confusing.

Formula: According to FanGraphs, for a position player

WAR = (batting runs + baserunning runs + fielding runs + positional adjustment + league adjustment + replacement runs)

/ (runs per win)

FanGraphs provides a great and extremely detailed analysis of Joey Votto’s WAR for one season and I would recommend it to anyone who wants a great WAR analysis. For position players, the first step is to evaluate how many of his team’s runs can be attributed to him offensively throughout the season. Then, advanced defensive metrics are used to determine how many runs can be attributed to him for his defensive work. The numbers are then adjusted for the player’s position, ballpark and league. Finally, the total is divided by the runs needed for a team to win a game.

Batting runs: The primary category for evaluating a player’s offensive contribution to his team’s wins is batting runs.  According to FanGraphs, this category measures a player’s ability to get on base and to help create runs for his team. A player’s success is then compared against the league average. The most important traditional statistic here is on base percentage. The term weighted on base average is used in the calculation.  In short,

wOBA = (0.690×uBB + 0.722×HBP + 0.888×1B + 1.271×2B + 1.616×3B +

2.101×HR) / (AB + BB – IBB + SF + HBP)

Those decimal constants change from year to year, but they reveal a lot. Since home runs are given a weight of 2.101 and singles are given a weight of 0.888, we deduce that a home run is slightly more than twice as important to a player’s WAR rating than a single. Therefore, Bautista’s 43 dingers in 2011 factored in nicely here. So did his .302 batting average. And since the concept that we are measuring more closely resembles on base percentage than batting average, his league leading 132 walks boosted his WAR rating. I often thought that his great eye for the strike zone and his willingness to take walks, i.e., his unselfishness, were underappreciated. Perhaps I was wrong. They were nicely accounted for in his WAR rating.

Ballpark Adjustment: An adjustment is then made to account for the ballpark and the league. Since some pitcher-friendly parks yield less runs than other parks, a run scored there should be given more value. In economic terms, a scarce resource is more valuable. To account for this, the parks are weighted differently in the WAR calculation. Each ballpark is assigned a score. A score of 100 in this context is neutral, and scores higher than that mean that more runs are required to win a game in that ballpark. Rogers Centre has a score of 102, tied for seventh highest in the majors. This means that while playing in the Rogers Centre likely helped Jose Bautista’s home run total in 2011, it was factored out while calculating his WAR.

Interestingly, the highest and lowest scores belong to Coors Field in Colorado and PNC Park in San Francisco with scores of 117 and 92 respectively. Remarkably, the park with the second highest score, Globe Life Park in Texas, has a ranking of 106. This means that the difference between the highest and second highest ranked park is almost the same as the difference between 2nd place and 30th.

Base Running Runs: The next measurement is a player’s base running runs. This category generally doesn’t have as great an impact on a player’s WAR rating as his batting runs. The base running runs category measures obvious concepts like stolen bases and times caught stealing. However, video tracking is also done to attempt to put a value on a player’s ability to advance from first to third on a single or to avoid hitting into double plays. Although Jose Bautista is a smart baserunner, it’s not likely that his baserunning in 2011 was particularly helpful or damaging.

Fielding runs are also measured. This category measures not only errors but also range. Different weights are also given to different positions, because some positions are simply more important defensively than others. The catcher position is most important, followed by shortstop. Third base, second base and centerfield are tied for third. The leftfield and rightfield positions are tied for sixth most important, followed by first base. Fittingly, the designated hitter position is given the lowest defensive rating. Interestingly, the outfield positions are park-adjusted to allow for the quirks in different ballparks. Being a rightfielder, I doubt that Bautista’s fielding runs stat was particularly significant, although his arm in right would have been factored in positively.

From my research, it would appear that the major league leader in defensive WAR usually has a score around 4, give or take 1. The greatest defensive WAR season in recent years was Atlanta shortstop Andrelton Simmons’ 5.4 ranking in 2013. He must have made some plays. Interestingly for Blue Jays’ fans, Kevin Pillar has been in the top 10 in each of the past three seasons, including 2017.

The league adjustment value is usually quite small.

Replacement Player: All of this is measured against a theoretical replacement player, who by definition is not an everyday major leaguer. To get an idea of a replacement player, think of a player that your favourite team might be able to call up should the team suffer injuries. Generally, this will be a minor league free agent or a fringe major leaguer.

Runs Per Win: When all of these results are tallied, you get a measure of a player’s runs above replacement. To determine wins above replacement, we need to divide that number by the number of runs per win. How many runs is that? FanGraphs suggests a fun way to consider this. We can guess that a .500 team likely has scored as many runs as it has allowed, but that a team one game ahead of them with an 82-80 record has on average scored about nine or ten more runs than they’ve allowed. Thus, the idea that nine or ten runs equals one win, in the aggregate.

Strengths and Weaknesses of WAR: On the plus side of the ledger, WAR is a rigorous attempt to encapsulate a player’s actual value to his team in terms of wins over the course of a season. Players, managers, coaches and fans generally just want to know whether someone will help their team win, and WAR sets out to do that in a comprehensive way. It’s a valiant attempt to do the impossible, and it’s tremendous fun. If advanced sabermetrics weren’t useful, they wouldn’t be used.

On the minus side of the ledger, WAR can’t measure chemistry. When the Blue Jays picked up Troy Tulowitzki and David Price two years ago, their WAR ratings with the Jays indicate an added three or four victories. But in reality, everything about the team changed. Rather than expecting to fight for a playoff spot, they expected to win the World Series. And they almost got there.

Also on the minus side, WAR does not account for clutch hitters that step up in key moments. The highest David Ortiz ever finished in the American League WAR leaderboard was 8th. But any baseball fan worth his or her salt could tell you that his presence in the lineup and ability to hit when his team absolutely needed him were huge. On a lesser scale, the same can be said for Jose Bautista in his prime. By 2011, teams were adjusting their game plans dramatically to account for what Bautista’s success. When he was raking, other teams had to adjust.

In summary, the WAR stat is great, but flawed. It’s a fabulous attempt to measure the unmeasurable. I tip my cap to the official scorers and sabermetricians that bring it to us.

And what does Bautista’s 2011 WAR rating of 8.1 mean? It means that we’ve been lucky to have him.


About The Author

Jim Beland is a Math Teacher and sports fantatic from Windsor, ON. A devout HABS and Blue Jays fan, Jim uses sports as a metaphor to teach his students about mathematics.

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