The other night I tweeted that Prince Fielder's 50-homer season in 2007 -- when he hit .288/.395/.618 -- rates as the lowest wins above replacement total among the 42 seasons a player has hit at least 50. His 3.4 WAR on Baseball-Reference is one of just three of those 42 seasons the site evaluates as worth fewer than 5.0 wins, Mark McGwire's 4.9 in 1997 and Sammy Sosa's 4.5 in 1999 being the other two.
I followed up that factoid by mentioning that in 2012 Mariners shortstop Brendan Ryan -- who hit .194 with a .277 on-base percentage and three home runs -- was worth 3.3 WAR. How can two players of such extreme differences in offensive production be valued so similarly? As somebody mentioned in a follow-up tweet, it's numbers like this that make many fans skeptical of WAR or completely dismissive.
With that in mind, I thought it would be a good idea to do a rough example of how WAR is calculated, using Fielder and Ryan -- and why it does work and why it (hopefully) makes sense. (For a much more thorough description, here is the Baseball-Reference explanation page, including the idea behind WAR and the concept of replacement level, and here's the specific page on the steps used for rating position players.)
As Sean Forman writes on Baseball-Reference, "The basic currency of WAR is runs. We start with runs added or lost versus an average player and then compare the average player to a replacement player." The formula is this:
Players Runs over Replacement = Player_runs - ReplPlayer_runs = (Player_runs - AvgPlayer_runs) + (AvgPlayer_runs - ReplPlayer_runs)
OK, we'll start with runs on offense.
Using the linear weights method of evaluating offense -- giving value to each single, double, triple, home run, walk, hit by pitch, sacrifice and even reached on error -- Fielder created 143 runs in 2007. Ryan created 35 runs, so Fielder is off to a 108-run advantage right off the bat.
But remember that we have to factor in the context those runs were created in. The National League in 2007 hit .266/.334/.423 (and even higher when you filter out pitcher hitting) and the American League in 2012 hit .255/.320/.411, which means Fielder will be compared to a better average hitter than will Ryan. Fielder also played in Miller Park, which is rated as a neutral park for the three-year park factors Baseball-References uses (park factor of 100), while Ryan played in Safeco Field, an extreme pitchers' park (park factor of 90, decreasing run scoring by 10 percent). So Ryan played in a tougher offensive environment, which means his batting runs are accordingly adjusted.
Also, playing time -- Fielder produced his runs in 681 plate appearances while Ryan had 470. When each hitter is then compared to what a league-average hitter would produce in that amount of playing time, Fielder ends up at plus-44 runs and Ryan at minus-18, so the difference on offense is now 62 runs.
Baserunning and runs on avoiding double plays
It should not surprise you that a guy coming in somewhere close to 300 pounds doesn't earn extra value with his baserunning (including stolen bases and caught stealing). Fielder is minus-3 runs on baserunning, but plus-1 on double plays as he grounded into just nine that year. Ryan was average (zero runs) in both areas, so picks up two more runs in value, leaving Fielder at plus-60 runs.
This is the aspect of the game where Ryan shines. Baseball-Reference uses defense runs saved from Baseball Info Solutions, which evaluates every batted ball in a variety of categories, and then compares each player to the average fielder at his position. Ryan is rated at plus-27 runs, a very high figure -- the second highest of any fielder in 2012, and the fifth highest by a shortstop in the past decade.
Fielder, meanwhile, is rated at 15 runs worse than an average first baseman, a very poor total.
Look, are defensive stats perfect? No. Are they pretty good these days? Yes. Should one-year defensive stats in particular be viewed with some reservations? Sure. Was Ryan's 2012 season a defensive fluke? I don't think so. Defense runs saved has him at plus-25, plus-22, plus-18 and plus-27 in his four seasons as a regular, the first two with St. Louis, so it has consistently given high marks to his glove work.
As for Fielder, everyone would agree that he's not exactly Keith Hernandez at first base. He's a big, heavy guy without much quickness who also made 14 errors that year. It's certainly plausible that he was 15 runs below an average first baseman (his defense has rated better in recent seasons).
So Ryan has a huge 42-run advantage on defense, leaving Fielder at plus-18 runs.
There are those who will argue that the value of defense is being overrated, that the margins between the best and worst fielders can't be that high. Well, why not? Ryan had 601 total chances in the field in 2012 -- about a full season's worth of plate appearances for a hitter. Sure, many of those are routine grounders and easy pop-ups that any competent major league shortstop can field. But a certain percentage of possible plays are not routine, and that's where defensive value comes in to play. As for Fielder, he made 423 outs at the plate in 2007, so he's not obtaining any value in about two-thirds of his plate appearances, as well.
Final adjustments and wins
The final adjustment made is a positional adjustment. Obviously, it requires more ability to play shortstop than first base, as reflected by the fact teams will play lesser hitters there. Since Ryan was being compared only to other good fielders at his position, and Fielder only to other first basemen, that has to be factored in. Baseball-Reference's current values for positional adjustment are plus-7.5 runs for shortstops (per 1,350 innings played) and minus-10 for first basemen. This ends up giving Ryan plus-6 runs and Fielder minus-10.
Which puts us at Fielder at plus-2 runs.
From there, runs are converted to wins, and Fielder ends up at 3.4 wins above replacement and Ryan at 3.3. It's important to keep in mind that WAR is an approximation of value, not a definitive answer, but I hope this helps in explaining why a player who hit .194 can be viewed with the same value as a player who hit 50 home runs.
By the way, Fielder's WAR in 2012: 4.4. Even though he hit only 30 home runs.