WAR - What Is It Good For

Tuesday, September 13 2011 @ 04:55 PM EDT

Contributed by: Magpie

Like I would know. I just thought I'd mess around and have some fun.

I just wanted to see what some of the implications might be. So watch my every move, because this sort of stuff is not my thing.

An individual's WAR is derived from his Runs Above Replacement. This has both an offensive and a defensive component. Brett Gardner's RAR, for example, is 46, from which his 4.4 WAR is derived. Most of Gardner's value, however, is held to be defensive. His oRAR (offensive Runs Above Replacement) is 13.

Now if we add up the oRAR of every hitter on the Yankees, we get... 233. So from this I assume that the Yankees hitters have generated 233 more runs than would have been produced by replacement level players. And if this doesn't make sense... what am I missing?

The Yankees have actually scored 799 runs (all numbers, by the way, are through Saturday's games.) So... I assume that the Replacement Level for the Yankees is 566, and the above replacement level skills of their hitters have contributed an additional 233 runs. Is this a reasonable assumption? (At first glance, expecting replacement level players to create 566 runs of offense... well, it seems kind of high to me. There are actual teams, with people like Joe Mauer and Andrew McCutcheon in their lineups, who haven't scored that many. This seems like a pretty potent band of replacements. On the other hand - I actually would expect a team that plays in a good hitter's park to have a high expectation for runs scored. With that in mind, I will expect that the assumed replacement levels in Texas and Colorado will be much, much higher. They had better be, at any rate.)

We also have a RAR figure for the pitchers, which incorporates "defensive support, opponents, and ballpark." Freddy Garcia has a RAR of 32, from which is derived his WAR of 2.9 (which places his RAR in the context of innings pitched, defense, leverage.) The Yankees pitchers have accumulated 255 RAR, and that suggests to me that the Replacement Level they're working against is 833 runs allowed.

Put it together - the Yankees Replacement Level is 566 runs scored, 833 runs allowed. Such a team should play roughly .403 ball. (Well, I don't know about that. I'm kind of stuck with using BB-ref's 1.83 component in its Pythagorean formulae, and that's where that leads us. I think they'd be more likely to play .350 ball.) Anyway - they'd have a record of about 58-86. If you're committed to measuring things against a hypothetical (it will always be hypothetical) replacement level, I suppose that's as good a place to set the bar as anywhere else.

Is that where the bar is for everyone? Let's do the exact same exercise for the other 29 teams, and look at all 30 replacement levels. We work our way backward to determine the implied expectation for runs scored and allowed, which will then provide an expected W-L record

Team              W    L     Pct.    RS      RA
                    
New York AL      58    86    .403    566    833
Boston           55    90    .379    475    787
Tampa Bay        53    91    .368    404    689
Toronto          56    90    .384    514    829
Baltimore        51    93    .354    472    861
Detroit          54    91    .372    461    783
Chicago AL       54    90    .375    482    810
Cleveland        56    87    .392    463    726
Kansas City      52    95    .354    444    823
Minnesota        57    88    .393    495    774
Texas            56    90    .384    509    814
Los Angeles AL   53    92    .366    400    687
Oakland          54    91    .372    479    818
Seattle          54    91    .372    437    741
                    
Philadelphia     56    86    .394    461    707
Atlanta          57    89    .390    468    726
New York NL      51    94    .352    431    785
Washington       56    87    .392    434    680
Florida          52    92    .361    428    746
Milwaukee        58    89    .395    467    726
St. Louis        54    91    .372    425    708
Cincinnati       59    86    .407    484    712
Pittsburgh       57    88    .393    479    749
Chicago NL       55    90    .379    449    735
Houston          56    89    .386    429    683
Arizona          60    86    .411    481    693
San Francisco    55    90    .379    406    674
Los Angeles NL   55    89    .382    421    679
Colorado         54    91    .372    523    878
San Diego        57    89    .390    441    686

I'm going to pause for now, and puzzle over this. There are things that don't make much sense to me, mostly concerning the somewhat flexible replacement levels applied to different teams.

Like, what is the Replacement Level supposed to be? BB-ref says they set the replacement bar at .320, but as you can see, none of these teams would play that badly if you use a Pythagorean equation with a 1.83 component. The records actually add up to .381.

So I'm going to proceed under the assumption that .381 is the desired Replacement level, and continue to use the 1.83 component.

If we want everyone playing .381 ball - and I guess we do - in the AL our average group of replacements would score 496 runs and allow 804 runs; in the NL they'd score 460 runs and allow 758 runs. We'll run Park Adjustments for everybody... and Voila!

Team               W    L     Pct.    RS    RA
                    
New York AL       55    89    .382    518    840
Boston            55    90    .379    533    864
Tampa Bay         55    89    .382    446    724
Toronto           56    90    .384    536    868
Baltimore         55    89    .382    506    820
Detroit           55    90    .379    506    820
Chicago AL        55    89    .382    503    816
Cleveland         55    88    .385    489    792
Kansas City       56    91    .381    484    784
Minnesota         55    90    .379    479    776
Texas             56    90    .384    593    961
Los Angeles AL    55    90    .379    454    736
Oakland           55    90    .379    484    784
Seattle           55    90    .379    471    764
                    
Philadelphia      54    88    .380    460    758
Atlanta           55    91    .377    446    735
New York NL       55    90    .379    446    735
Washington        54    89    .378    446    735
Florida           54    90    .375    455    750
Milwaukee         56    91    .381    467    769
St. Louis         55    90    .379    432    713
Cincinnati        55    90    .379    476    785
Pittsburgh        55    90    .379    455    750
Chicago NL        55    90    .379    449    739
Houston           55    90    .379    472    777
Arizona           55    91    .377    488    803
San Francisco     55    90    .379    405    667
Los Angeles NL    54    90    .375    439    724
Colorado          55    90    .379    554    913
San Diego         55    91    .377    421    694

Hmm. Having levelled the Replacement playing field, what else can I do? I know....

The obvious thing to do is determine the true level of runs above replacement, for both offense and defense.

Previously, we had simply added up the contributions of individual players to discover the team's RAR figures. That led us down the rabbit hole. This time we're going to begin with the team's Replacement Level, and look at how many runs the team actually scored. That will tell us what each team's True RAR really is, and we can compare it to the sums we originally started with...

Team           RepLevel Actual Added Actual          RepLevel Actual Added  Actual    
                 Runs   Runs    RAR   RAR    Error      RA      RA    RAR    RAR    Error

New York AL      518    799    233    281     48        840    580    253    260    - 7
Boston           533    782    307    249    -58        864    629    158    235    -77
Tampa Bay        446    616    212    170    -42        724    545    144    179    -35
Toronto          536    681    167    145    -22        868    681    148    187    -39
Baltimore        506    609    137    103    -34        820    759    102     61     41
Detroit          506    690    229    184    -45        820    645    138    175    -37
Chicago AL       503    587    105     84    -21        816    599    211    217    - 6
Cleveland        489    601    138    112    -26        792    639     87    153    -66
Kansas City      484    648    204    164    -40        784    710    113     74     39
Minnesota        479    555     60     76     16        776    714     60     62    - 2
Texas            593    757    248    164    -84        961    631    183    330   -147
Los Angeles AL   454    594    194    140    -54        736    558    129    178    -49
Oakland          484    592    113    108    - 5        784    621    197    163     34
Seattle          471    499     62     28    -34        764    598    143    166    -23
                                            
Philadelphia     460    651    190    191      1        758    461    246    297    -51
Atlanta          446    592    124    146     22        735    537    189    198    - 9
New York NL      446    645    214    199    -15        735    659    126     76     50
Washington       446    551    117    105    -12        735    601     79    134    -55
Florida          455    574    146    119    -27        750    637    109    113    - 4
Milwaukee        467    642    175    175      0        769    585    141    184    -43
St. Louis        432    673    248    241    - 7        713    625     83     88    - 5
Cincinnati       476    672    188    196      8        785    640     72    145    -73
Pittsburgh       455    549     70     94     24        750    620    129    130    - 1
Chicago NL       449    586    137    138      1        739    691     44     48    - 4
Houston          472    553    124     82    -43        777    710    -27     67    -94
Arizona          488    656    175    168    - 7        803    608     85    195   -110
San Francisco    405    484     78     79      1        667    510    164    157      7
Los Angeles NL   439    564    143    125    -18        724    550    129    174    -45
Colorado         554    667    144    113    -31        913    682    196    231    -35
San Diego        421    542    101    121     20        694    566    120    128    - 8

There's a very rough 10-1 ratio between RAR and WAR, but I'm not going to bury myself in those weeds. It's not a practical possibility, anyhow - I've separated the offensive and defensive components, and I wouldn't want to hazard a guess as to how many RAR we should give to Brett Gardner of the 281 from the Yankees' offense and the 260 from the Yankees defense.

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