Thursday, January 24, 2013

WAR Baseline is All About Playing Time

For people trying to learn sabermetrics, one of the most confusing concepts is the replacement baseline used in the Wins Above Replacement (WAR) statistics.  In simple terms WAR is the wins a player contributed to his team's win total above what you would expect from a replacement level player - a theoretical player who could be acquired for league minimum salary.  An example of a replacement player would be a player in AAA, who is good enough to get some time in the majors, but is not regarded as a top prospect.  

Why is replacement used instead of average or zero?  When building a ball club, comparing players to league average can be problematic.  If a team is forced to replace a player due to an injury, he is not likely to be replaced by an average player or even a slightly below average player.  Average players are actually good players and are not generally available quickly or cheaply.   In most cases, the injured player will be replaced by a player who is substantially below average.

Comparing players to zero is also not generally a great idea because your replacement is not likely to bat .000 for any length of time.  Your replacement will usually be somewhere between zero and average.  Based on examination of data over several years, analysts determine how good a player typically needs to be to get a decent amount of playing time.  The threshold above which a player must perform in order to get consistent at bats is called replacement level.  Different people use somewhat different replacement levels, but I'll follow the FanGraphs.com definition here.

If you are interested in playing general manager and are concerned about roster construction or how much money a player is worth,the replacement threshold is the way to go.  If you want to do something else such as selecting hall of famers or award winners or you just want to know how many players on your favorite team are above average, you can use an alternative baseline.

If you do decide to shun replacement level for something more intuitive though, you should understand the consequences.  It all comes down to how much credit you want to give for playing time.  Whether you choose Wins Above Average (WAA) or Wins Above Zero (WAO) or WAR can make a substantial difference when there is a lot of variation in playing time among players.

Suppose, Gary Great and Sammy Solid were both second basemen with exactly 600 Plate Appearances (PA).  They were both average base runners and average defenders and played in neutral parks.  The only way they differed was that Gary was a much better hitter than Sammy.  Gary had a .400 OBP, .540 slugging average and .398 Weighted On-Base Average (wOBA).  Sammy had a .325 OBP, .450 slugging average and .335 wOBA. The question is how many wins was Gary worth compared to Sammy?

We would normally have to do a lot of calculations involving base running, fielding and park effects in order to calculate Wins, but the question is simplified by assuming that the two players were similar in every way except batting.  Based on PA and wOBA, Gary had 40 Batting Runs which means than he contributed an estimated 40 runs above what would be expected from an average player in the same number of plate appearances.  Since 10 runs is worth approximately one win, he was 4 WAA.

Sammy had 10 Batting Runs or 1 WAA.  So, there was a a gap of three wins between the two players.  (Note that we should actually be adding a fraction of a win for playing second base, but they both get the same fraction so we'll ignore it for simplicity.)

What if we use zero as the baseline rather than average?  An average player is worth 68 runs over 600 PA, so Gary was 40 + 68 = 108 runs above zero (also called Runs Created) or 10.8 WA0.  Sammy had 78  Runs Created or 7.8 WA0.  Again, the the two players were separated by three wins.

Finally, a replacement player is worth 20 runs per 600 PA below an average player, so Gary was 40 + 20 Runs Above Replacement or 6 WAR.  Sammy was 30 Runs Above Replacement or 3 WAR. So, one more time there were three wins between the two batters.  There was a very big disparity in the number of wins a each player was credited in WAA, WA0 and WAR, but no difference in the number of wins separating the two players because they had the same number of PA.

It's another story when players are far apart in their numbers of PA  Suppose Gary had a .398 wOBA in 300 PA while Sammy still had a .335 wOBA in 600 PA.  In that case, Gary had 20 Batting Runs compared to 10 for Sammy.  That comes out to 2 WAA for Gary and 1 WAA for Sammy.  So Gary was one win better by that measure.  Does this make sense? Is a great hitter who missed half the season worth more wins than an above average hitter in a full season?

Let's see what happens if we change the threshold.  An average player is worth 34 runs in 300 PA, so Gary was 20 + 34 = 54 Runs Above Zero.  Sammy was still 78 Runs Above Zero.  In terms of wins, Gary was 5.4 WA0 and Sammy 7.8 WA0.  In this case, Sammy was 2.4 Wins better than Gary.

Finally, if replacement is the baseline, Gary was 20 + 10 = 30 Runs Above Replacement or 3 WAR while Sammy was 10 + 20 = 30 Runs Above Replacement or 3 WAR.  So, they were considered equal contributors to wins by this metric.

The lesson learned is that the baseline you choose can make a large difference in your evaluation of players.  In the first case, Gary was the better player.  In the second instance, Sammy was the better player by a substantial margin.  In the third situation, they were equals. You don't have to use replacement level if you don't want, but it's important to be aware how much the results vary among baselines.

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