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# Statistically Significant: WAR

It's been a long, long time since I started this stat explanation series, so I might as well finish it. Previously, I covered the basics behind wOBA, FIP, and UZR. It's finally time to combine all three of these into what's probably the most popular sabermetric statistic in use today—WAR.

WAR stands for Wins Above Replacement, and it's yet another attempt at combining several statistics from several aspects of production to arrive at a one stop shop number that can be used to compare hitters to pitchers and players from different decades. I'm going to dive in with more detail below, but the basic gist is that if you pick a hitting, fielding, and pitching statistic, you can compare a player's figure to the league average, and translate that number into the amount of runs above average* a player is. From there, it's a simple adjustment to turn runs into wins, which is the final goal of WAR.

*Apologies for the Pozterisk, but I had to butt in and correct a common misconception about the terminology before I start. By "runs above average", I don't mean that someone keeps a running count of whenever a run is scored or is batted in. That wouldn't be context-independent, which is what we're shooting for. I'll use an example to illustrate what "runs above average" actually means: Tom Tango and co. found that from 1999-2002, when a double was hit, the team that was at bat scored an average of 0.776 more runs in that inning than the average team scored per inning. Therefore, a double is worth 0.776 runs above average. And if you keep a running total of a batter's actions, both positive and negative, you'll come to a "runs above average" figure that's independent from everything except what the hitter actually did.

Replacement Level

The other important concept about WAR is the third letter in the acronym—Replacement. The idea of a replacement player has been around for decades, but essentially, it's defined as the sort of player who's freely available to every team in AAA—your Matt Carsons and such. The amount of production that these guys give in the major leagues is a nice natural benchmark to compare everyone else to.

Another important point about replacement level is that it changes from position to position. Obviously, finding an average defensive shortstop is harder than finding an average defensive first baseman. Because of that scarcity, a replacement level shortstop is, on the whole, going to have a far worse bat than a replacement level first baseman. So when WAR calls someone a replacement level DH, it means that player would be a 3 WAR catcher, with the same bat and average defense behind the plate. A list of all of the positional adjustments can be found here.

fWAR and rWAR

Now, as you might have guessed, I said "if you pick a hitting, fielding, and pitching statistic" for a reason. WAR doesn't have a set definition. Depending on who's calculating it, WAR could be used with wOBA, FIP, and UZR, or it could be batting average, ERA, and fielding percentage. They're still both WAR, which is more of a calculation method than it is a strict statistic. There are two main applications of WAR freely available on the internet today, found on Fangraphs and Baseball-Reference: fWAR and rWAR, respectively. (The r stands for Rally, because it was originally found at Rally's WAR Database, on the same website as the CHONE projections.) For the rest of this article, I'm going to focus on the more popular version, fWAR, and because of that, any references to WAR from here on out refer to fWAR.

Benchmarks

I find it really helpful to give a sense of scale. Because of the definition of replacement level, a 0 WAR player is a freely available AAA player. The average major leaguer is generally around 2 WAR over a full season, and an average starter is at 3 WAR. The threshold for All-Star level is somewhere around 5 WAR, and an MVP-caliber season tends to be around 7 or more. Barry Bonds in 2001? 12.9, which means he produced as much as two All-Stars that year. The general rule of thumb for Hall of Fame inductees is 50 WAR over an entire career, so when Bill James famously said that "If you could split [Rickey Henderson] in two, you'd have two Hall of Famers.", he wasn't kidding. Rickey accumulated 114.1 WAR over his career, which is 16th among all batters in baseball history.

Putting It All Together

This section goes through a bit of the calculation process, and is more technical, which is why I've saved it for last. Feel free to skip it.

This will be a lot easier if you follow along on the Total WAR line at the bottom of Eric Chavez's Fangraphs page here. I'm going to go through this table, column by column. All figures current as of July 19, 2011. I may or may not agree to recognize his time as a Yankee, on account of the fact that it makes me cry at night.

• Batting: By wOBA, Eric Chavez was +105.1 batting runs above average (BRAA), where average is the average major league hitter for each year, independent of position. Therefore, we can credit that many runs to his total WAR figure.
• Base Running: The next column is baserunning by way of UBR, which is a new statistic developed by Mitchel Lichtman. It's a rather small factor, and UBR credits Chavez for being worth +1.9 runs above average.
• Fielding: Chavez was a sterling fielder, and UZR justly recognizes that. Chavez racked up +35.4 fielding runs above average (FRAA), as compared to the league average third baseman of each year.
• Replacement: If you'll notice, the batting runs figure was compared to league average, not replacement level. This column is a translation factor, adjusting Chavez's production so that it's runs above replacement, not runs above average. This factor represents the distance between average and replacement for each year, prorated for the amount of playing time Chavez had. Chalk up another +181.5 runs.
• Positional: As explained above, replacement level changes from position to position. Third basemen, according to Tom Tango, hit 2.5 runs worse than average over a full season (600 PAs), so they get a 2.5 run bump in this column over a full season. This number is prorated to reflect Eric Chavez's playing time at each position per year. Because he spent some time at other positions late in his career (like a lot of DH in 2010), this figure is sometimes negative, to account for the innings at other, easier positions. Add all these up, and you get +10.5 runs.
• Runs Above Replacement (RAR): This column is simply the sum of all of the columns to the left of it, which is the total amount of runs above replacement that Eric Chavez was worth throughout his career.
• Wins Above Replacment (WAR): This is it, the endpoint. Every year has a certain factor that dictates how many runs turn into one win, and this number comes from the Pythagorean Expectation formula. It changes from year to year, but it's roughly 10 runs to 1 win. Divide RAR by this factor, and you get WAR.

The A's travel to Detroit to take on the Tigers tonight. First pitch is at 4:05 PM Pacific Time.