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# Further differences between WAR variants

What happens when we take WAR variants and break 'em down per game over the past few years? FUN, that's what.

As I go forward and compare / contrast the different WARs, I learn more and more about the different ways in which the WARs function. Comparing single players against the three systems (fWAR, rWAR and WARP) is great, but now it might help to look at how the systems, overall, compare.

Last week, Tom Tango requested that I break down the scores for each of the three major WAR systems by game. This would let us see (1) how WAR breaks down on a per-game basis and (2) how stable these systems are in terms of WAR from year-to-year. So I did that, at least for the past ten years. Here's what I found:

#### Pitcher WAR/9

Year fWAR/9 rWAR/9 WARP/9
2012 0.096 0.074 0.052
2011 0.097 0.074 0.051
2010 0.098 0.075 0.060
2009 0.096 0.074 0.061
2008 0.095 0.074 0.064
2007 0.095 0.074 0.066
2006 0.096 0.075 0.072
2005 0.097 0.075 0.076
2004 0.097 0.074 0.072
2003 0.096 0.075 0.074

As you can see, pitcher fWAR/9 stays incredibly stable from year to year. rWAR/9 stays incredibly stable from year to year. But WARP? WARP does not. WARP changes a substantial amount from season to season. So how about hitters?

#### Hitting / Defense WAR/9

Year fWAR/9 rWAR/9 WARP/9
2012 0.139 0.107 0.090
2011 0.138 0.107 0.085
2010 0.137 0.108 0.132
2009 0.135 0.107 0.130
2008 0.134 0.107 0.128
2007 0.132 0.107 0.127
2006 0.132 0.108 0.123
2005 0.135 0.108 0.121
2004 0.132 0.107 0.120
2003 0.133 0.107 0.121

Note: To compute this, I found the average number of PA/9 for each season.

Again, rWAR is very stable. fWAR is a little less stable, and has risen rather consistently over the last 10 years. Again, WARP is kind of all over the place. You can see an extreme change between 2010 and 2011, especially.

What does it mean that WARP fluctuates so much from year to year? Honestly, I'm not sure. It could mean that there are adjustments being made to the methodology that aren't being made to previous seasons, but if I know BP, I'd guess that is not the case. Hitter WARP cratered in 2011 and 2012, which were considered great pitching seasons, perhaps that is having a big effect on WARP?

Speaking of pitching, I noticed something else kind of interesting, and that's the ratio between position player WAR and pitcher WAR. For every system, there's a larger hitter WAR value per nine innings than pitcher value. I can rationalize this in my head that the contributions of hitters, as a whole, are slightly more valuable than that of pitchers. But look at the ratios for each system in 2012:

Year fWAR H-P Ratio rWAR H-P Ratio WARP H-P Ratio
2012 1.45 1.45 1.73

Now that's kind of interesting, isn't it? In both fWAR and rWAR, we see a ratio of 1.45 hitter / defense WAR to every 1.00 pitcher WAR. But for WARP, we see a larger ratio, a ratio of 1.73:1. To me, that looks like Baseball Prospectus's system weighs hitting as even more valuable than FanGraphs's system or Baseball-Reference's system. I'm not sure whether that's "wrong" or "right", but it's probably something that's important to know about the system in general.

Lastly, here's some data comparing the American League to the National League, for fWAR and rWAR. (Over the last few days, I haven't been able to pull PWARP from BP. I'll add it when I can.)

#### Pitcher WAR/9 - AL/NL

Year fWAR/9 AL fWAR/9 NL rWAR/9 AL rWAR/9 NL
2012 0.097 0.094 0.081 0.068
2011 0.107 0.089 0.082 0.067
2010 0.097 0.098 0.082 0.068
2009 0.109 0.083 0.082 0.067
2008 0.110 0.082 0.082 0.068
2007 0.113 0.080 0.082 0.067
2006 0.111 0.082 0.083 0.068
2005 0.109 0.086 0.082 0.068
2004 0.109 0.085 0.082 0.068
2003 0.104 0.089 0.083 0.068

Pitcher rWAR stays in roughly the same ratio between the AL and NL over each of the last 10 years. However, pitcher fWAR vacillates from season to season. In 2012, the AL and NL were very close together, but in 2009 and before, there was quite a bit more being generated by the AL, at least when it comes to pitcher fWAR.

#### Hitting / Defense WAR/9 - AL/NL

Year fWAR/9 AL fWAR/9 NL rWAR/9 AL rWAR/9 NL
2012 0.132 0.145 0.117 0.098
2011 0.139 0.138 0.118 0.098
2010 0.129 0.145 0.118 0.099
2009 0.135 0.135 0.117 0.098
2008 0.127 0.139 0.118 0.098
2007 0.120 0.142 0.118 0.097
2006 0.129 0.137 0.119 0.098
2005 0.124 0.145 0.118 0.098
2004 0.129 0.135 0.117 0.098
2003 0.123 0.143 0.117 0.098

Once again, we see that rWAR for hitters keeps the same ratio between AL and NL consistently over the 10-year period. fWAR, again, is a bit of a different story. It fluctuates from year to year. In rWAR, there's a consistent pattern that the AL is racking up more pitcher / hitter WAR than the NL. Now, I know we've all heard for years that the AL is the superior league to the NL, that's not new news. But has the AL really been at (nearly) the exact same level of dominance in both areas of the game over each of the ten past years? That sounds ... counter-intuitive, right?

And look at fWAR. fWAR varies quite a bit from year to year between the leagues, which actually makes quite a bit of sense to me. I mean, I would think that the level of competition between the leagues would vary, as teams and players rise and fall, and talent moves back and forth between teams in different leagues. But what stands out the most is that the National League has, more or less, been worth a substantive amount more hitter fWAR per game! Remember what I said earlier about the NL being the inferior league? Well quite a bit more fWAR is being assigned to the NL, rather than the AL, on a yearly rate basis. This isn't just because the NL has more teams, this is a rate basis. Should we really advocate that the NL is the hotbed of offense (yes, pitchers hitting ARE included), while the AL isn't?

Yes, this post is a bit of a data dump, but there's some use in taking a look at how these different systems work. What do you think we should do with this data? What conclusions can you draw? And is there a particular path of inquiry you'd like us to take moving forward?