Tiger Tales: A Detroit Tigers Blog

One of the most confusing concepts for fans trying to learn sabermetrics is the replacement baseline used in the Wins Above Replacement (WAR) processes.  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 compare favorable to an average player, 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 difference 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.

Table 1 below clearly shows that 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.  This is because they had the same number of plate appearances. 

Table 1: Two Players: Average in Every Way but Hitting

Measure	Gary Great	Sammy Solid	Difference
Plate Appereances	600	600	0
wOBA	.398	.335	.063
Runs Above Average	40	10	30
Wins Above Average	4	1	3
Runs Above Zero	108	78	30
Wins Above Zero	10.8	7.8	3
Runs Above Replacement	60	30	30
Wins Above Replacement	6	3	3

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.  The results are summarized in Table 2 below.
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. 

Table 2: Two Players: Average in Every Way but Hitting, Playing Time

Measure	Gary Great	Sammy Solid	Difference
Plate Appearances	300	600	-300
wOBA	.398	.335	.063
Runs Above Average	20	10	10
Wins Above Average	2	1	1
Runs Above Zero	54	78	-24
Wins Above Zero	5.4	7.8	-2.4
Runs Above Replacement	30	30	0
Wins Above Replacement	3	3	0

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.

It was obvious to any fan watching the Tigers this year that they desperately needed help in the bullpen and they addressed the problem in a big way tonight by acquiring right-handed reliever Joakim Soria from the Texas Rangers (first reported by Kyle Bogie of Scout.com).  The Tigers had to give up two of the best pitching prospects in the system to get him - starter Jake Thompson and reliever Corey Knebel.  

Adam Wainwright of the Cardinals is the NL leader in runs prevented
(Photo credit: HardballTalk.NBCSports.com)

Earlier today, I posted the American League run prevention leaders through July 2.  Now, for the National League. 

There is no surefire way to determine the best pitchers in the league, but a pitcher's job is to prevent runs.  So, it's useful to estimate how many runs pitchers saved their teams compared to an average pitcher.  In the past, I have explored four different ways to do this:    

• Pitching Runs -  Runs Saved Above Average based on innings and runs allowed. 

• Adjusted Pitching Runs - Pitching Runs minus estimated Runs allowed by fielders. 

• Base Runs -  Runs Saved Above Average based on batters faced and hits, walks, total bases and home runs allowed.

• FIP Runs - Runs Saved Above Average based on innings, bases on balls, hit batsmen and home runs allowed and strikeouts.

These measured are discussed in more detail in an earlier post.  After computing each measure, I then take the average of the four. 

The current National League leaders are listed in Table 1 below.  Cardinals right hander Adam Wainwright leads the league in Pitching Runs (29), Adjusted Pitching Runs (24), and Base Runs (27) and is second with 20 FIP Runs.  That gives him an aggregate of 25 runs prevented compared to an average pitcher.  

Johnny Cueto of the Reds is second with 21 runs prevented.  He is tied for first in Base Runs (27), second in Pitching Runs (22) and Adjusted Pitching Runs (19) and third in FIP Runs (17).

Table 1: NL Run Prevention Leaders as of July 2, 2014
Data source: Baseball-Reference.com