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Baseball-Reference.com WAR Explained

WAR EXPLAINED

Since we added Sean Smith's ("rallymonkey" to some) Wins Above Replacement measurement in 2010, we've seen its use expand in to many new areas and its popularity catch on in the media and the general population, but there have also been a lot of questions about how it's calculated and whether it has validity. In this tutorial, I'm going to run through the calculations in graphic detail and point out areas where our approach differs from some of the other popular WAR or WAR-like approaches.

How to Use WAR

The idea behind the WAR framework is that we want to know how much better a player is than what a team would typically have to replace that player. We start by comparing the player to average in a variety of venues and then compare our theoretical replacement player to the average player and add the two results together.

There is no one way to determine WAR. There are hundreds of steps to make this calculation, and dozens of places where reasonable people can disagree on the best way to implement a particular part of the framework. We have taken the utmost care and study at each step in the process, and believe all of our choices are well reasoned and defensible. But WAR is necessarily an approximation and will never be as precise or accurate as one would like.

We present the WAR values with decimal places because this relates the WAR value back to the runs contributed (as one win is about ten runs), but you should not take any full season difference between two players of less than one to two wins to be definitive (especially when the defensive metrics are included).

WAR Editions/Changes

This page and related pages give the gory details on how we calculate WAR.

Version 2.2, March 2013

Based on discussions with FanGraphs and others, we decided to drop the replacement level to .294 from .320. This means that 2013 MLB has 1000 WAR in the entire major leagues. This was applied retroactively, so that it was applied to all previous AL, NL, and NA seasons. Other Major Leagues (AA, UA, PL, FL) were maintained at the same level relative to the NL.

After the positional adjustment was applied we forced the major league average to be zero across the league.

A small amount of smoothing was done to transition between decade-long league-vs-league replacement levels.

Version 2.1, May 2012

After launching version 2.0 on May 4th, we immediately became aware of an issue that had concerned us, but we thought we still had right. Pitchers were being overvalued due to a runs to win estimate that broke down for extreme performances. A stingy pitcher drives down the runs per win, but not to the degree we were showing.

Version 2.01, May 2012

We made a minor change converting oWAR to afWAR (or average fielding WAR). This has been rolled back and is not in place now.

Version 2.0, May 2012

Previous to launch of 2012 WAR numbers we undertook a top to bottom evaluation of our WAR numbers and added a number of improvements.

Version 1.0, pre-May 2012

Sean Smith produced the original framework for the site and until May 2012 we used his numbers and methodology in all locations. We still use his replacement level and position levels, but we have changed much of the remainder of the system. Th

The Concept of Replacement Players

Average is a well-defined concept. You sum up all of the observations and then divide by the number of observations. We compute averages every day.

So why don't we compute Wins Above Average rather than Wins above Replacement? When computing the value of a major league player, average is a poor baseline for comparison. Average players are relatively rare and can be expensive to acquire. Average players don't make the league minimum. Plus, not all average performances are equal. A team would pay much more for 200 league average innings than for 50. When a star player is injured, they are rarely replaced by an average player--usually their replacement is much worse.

That last point is our premise here. Average players are relatively rare and difficult to obtain. Replacement level players, by their very definition, are players easy to obtain when a starter goes down. These are the players who receive non-roster invites at the start of the year or the players who are 6-year minor league free agents. Baseball talent among the population is generally distributed normally, but only the very right-end of that curve plays professional baseball.

There is some dispute over where to place the replacement level, but most sabermetricians agree that comparing players to a general replacement level is the best approach to valuing players. We'll talk more about this later.

Sports Reference sets replacement level at a .320 winning percentage for recent seasons. This means that we expect a team of replacement players to have a .320 win-loss percentage or a 52-110 record. We also set the value differently between the two leagues, since the AL has been shown to be the stronger league by inter-league play. This means that in the AL our replacement team might win 48 games while in the NL, 56 games.

Sports Reference sets replacement level at .294 or (48-114). This change was made in March of 2013 after deciding with FanGraphs.com to set a single replacement level between our sites. We also smoothed out the changes in replacement level between the two leagues where before the change from one decade to the next had been stepwise.

WAR: The General Idea

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. I just got done saying we don't want to use averages, but an equation should explain what we are doing here.

Players Runs over Replacement = Player_runs - ReplPlayer_runs = (Player_runs - AvgPlayer_runs) + (AvgPlayer_runs - ReplPlayer_runs)

This gives us two components, player runs above average (RAA) and then the average player's runs above replacement.

Ultimately, baseball teams are interested in wins and losses, and so is WAR. RAA is converted to wins above average by running the results through a PythagenPat win-loss estimator (a rundown of PythagenPat. This allows us to more accurately model the interaction between the player and league and the effect on wins. Generally, ten runs will give you one win, but that does not always hold.

Adding up all of the WAR on a team (adding in replacement level (48 wins for a full season)), should get you very, very close to the team's actual wins and losses, and should match up even more closely with their Pythagorean win-loss records.

Unfortunately, the statistics at our disposal to compare Tris Speaker and Ken Griffey Jr. have changed over time. We now have exact data regarding types and location of batted balls, and this has led to improvements in various measurements (defensive measurements most notably). When we compute our metrics for the various components of WAR, we always use as much data as possible. For example, with baserunning this means that we'll use stolen bases alone when that is all we have, stolen bases and caught stealings when that is all we have, and full play-by-play accounts of steals by base, pickoffs, and advancements on passed balls, wild pitches, sac flies, doubles, singles, etc when we have that. Here is an up-to-date listing of our Data Coverage.

WAR is calculated separately for pitchers and for position players, so we'll deal with each of them separately.

WAR for Position Players

WAR for Pitchers

WAR Comparison

Converting Runs to Wins

Runs to Wins details.

Differences Between B-R WAR Version 2.1 and Version 2.2

Since replacement level was adjusted down more or less uniformly for all players, every player's WAR went up in proportion to their playing time. The largest I noted was a 5 WAR increase for Pete Rose.

Differences Between Old B-R WAR (1.0) and Version 2.1

Below are the players with the ten biggest changes in WAR both up and down for pitching and batting and then the top 50 for batting and hitting before and after.

20 hitters most hurt by changes

+------+----------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
| rk   | name_common    | player_ID | year_min | year_max | PA    | runs_bat | runs_br | runs_defense | runs_position | runs_replacement | runs_above_rep | WAR   | runs_bat_old | runs_br_old | runs_defense_old | runs_position_old | runs_replacement_old | runs_above_rep_old | war_rate_old | WAR_old | war_diff |
+------+----------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
|    1 | Mickey Mantle  | mantlmi01 |     1951 |     1968 |  9907 |    814.5 |    49.8 |        -41.0 |         -37.7 |            271.1 |         1056.7 | 105.5 |        879.0 |        55.0 |            -36.0 |             -37.0 |                272.0 |             1129.0 |  9.307948848 |   120.2 |    -14.7 |
|    2 | Ty Cobb        | cobbty01  |     1905 |     1928 | 13078 |    995.8 |    51.8 |          0.0 |         -96.1 |            433.0 |         1384.5 | 144.9 |       1063.0 |        84.0 |              0.0 |             -97.0 |                413.0 |             1463.0 |  9.316696600 |   159.4 |    -14.5 |
|    3 | Barry Bonds    | bondsba01 |     1986 |     2007 | 12606 |   1134.1 |    43.8 |        174.8 |        -125.1 |            352.3 |         1579.9 | 158.0 |       1213.0 |        45.0 |            190.9 |            -129.0 |                347.0 |             1665.0 |  9.699995186 |   171.8 |    -13.8 |
|    4 | Babe Ruth      | ruthba01  |     1914 |     1935 | 10620 |   1335.8 |   -11.8 |         79.0 |         -64.2 |            336.4 |         1675.2 | 159.2 |       1430.0 |       -14.0 |             79.0 |             -81.0 |                325.0 |             1739.0 | 10.128929839 |   172.0 |    -12.8 |
|    5 | Herman Long    | longhe01  |     1889 |     1904 |  8505 |    -83.1 |    19.6 |         72.0 |         118.9 |            242.7 |          370.1 |  33.4 |         10.0 |        43.0 |             72.0 |             114.0 |                228.0 |              467.0 | 10.348954325 |    44.6 |    -11.2 |
|    6 | Adam Dunn      | dunnad01  |     2001 |     2011 |  6561 |    200.3 |    -9.5 |       -147.5 |         -84.5 |            181.3 |          140.1 |  12.9 |        200.6 |        -7.9 |            -58.6 |             -82.7 |                182.7 |              234.1 |  9.755072998 |    24.0 |    -11.1 |
|    7 | Jim Edmonds    | edmonji01 |     1993 |     2010 |  7980 |    310.1 |   -11.1 |         37.1 |          16.8 |            232.5 |          585.4 |  57.2 |        342.8 |        -8.5 |             84.8 |              16.9 |                240.5 |              679.2 | 10.033501920 |    67.9 |    -10.7 |
|    8 | George Davis   | davisge01 |     1890 |     1909 | 10178 |    277.6 |    19.2 |        146.0 |          93.1 |            313.3 |          849.2 |  80.2 |        380.0 |        28.0 |            146.0 |              87.0 |                303.0 |              944.0 | 10.344520283 |    90.7 |    -10.5 |
|    9 | Willie Keeler  | keelewi01 |     1892 |     1910 |  9610 |    352.8 |    -6.8 |         30.0 |        -113.2 |            296.5 |          559.3 |  50.7 |        404.0 |        48.0 |             30.0 |            -114.0 |                274.0 |              642.0 | 10.103368113 |    60.8 |    -10.1 |
|   10 | Lou Gehrig     | gehrilo01 |     1923 |     1939 |  9663 |    971.1 |   -11.3 |          2.0 |         -99.9 |            302.2 |         1164.1 | 108.5 |       1046.0 |        -1.0 |              2.0 |             -96.0 |                289.0 |             1240.0 | 10.459118540 |   118.4 |     -9.9 |
|   11 | Bid McPhee     | mcphebi01 |     1882 |     1899 |  9429 |    105.4 |    12.2 |        154.0 |          40.2 |            226.5 |          538.3 |  48.3 |        150.0 |        37.0 |            154.0 |              42.0 |                220.0 |              603.0 | 10.354579742 |    57.9 |     -9.6 |
|   12 | Hugh Duffy     | duffyhu01 |     1888 |     1906 |  7841 |    249.5 |    18.3 |         67.0 |         -93.8 |            217.4 |          458.4 |  40.1 |        339.0 |        45.0 |             67.0 |             -95.0 |                206.0 |              562.0 | 11.011252007 |    49.6 |     -9.5 |
|   13 | Fred Clarke    | clarkfr01 |     1894 |     1915 |  9838 |    383.0 |    -1.4 |         91.0 |        -124.2 |            288.8 |          637.2 |  64.2 |        433.0 |        37.0 |             91.0 |            -123.0 |                275.0 |              713.0 | 10.108299812 |    73.4 |     -9.2 |
|   14 | Billy Hamilton | hamilbi01 |     1888 |     1901 |  7608 |    499.3 |    52.8 |         30.0 |         -84.3 |            213.3 |          711.1 |  61.1 |        585.0 |        70.0 |             30.0 |             -86.0 |                194.0 |              793.0 | 11.284017865 |    69.6 |     -8.5 |
|   15 | Joe DiMaggio   | dimagjo01 |     1936 |     1951 |  7673 |    525.9 |    14.2 |         49.0 |         -18.2 |            207.1 |          778.0 |  75.1 |        579.0 |        30.0 |             49.0 |             -19.0 |                200.0 |              839.0 | 10.011025302 |    83.6 |     -8.5 |
|   16 | Cap Anson      | ansonca01 |     1871 |     1897 | 11331 |    628.6 |   -28.5 |         59.0 |          10.0 |            345.8 |         1014.9 |  91.1 |        733.0 |       -47.0 |             59.0 |               7.0 |                326.0 |             1078.0 | 10.882601225 |    99.5 |     -8.4 |
|   17 | Honus Wagner   | wagneho01 |     1897 |     1917 | 11748 |    637.0 |    33.3 |         85.0 |         107.2 |            340.8 |         1203.3 | 126.2 |        699.0 |        45.0 |             85.0 |             104.0 |                333.0 |             1266.0 |  9.536208657 |   134.5 |     -8.3 |
|   18 | Bobby Lowe     | lowebo01  |     1890 |     1907 |  7766 |   -135.1 |    -5.8 |         88.0 |          13.3 |            231.9 |          192.3 |  16.8 |        -64.0 |         9.0 |             88.0 |              13.0 |                227.0 |              273.0 |  9.210300234 |    25.1 |     -8.3 |
|   19 | Joe Kelley     | kellejo01 |     1891 |     1908 |  8139 |    371.3 |     1.2 |         18.0 |         -88.6 |            240.1 |          542.0 |  47.3 |        437.0 |        20.0 |             18.0 |             -91.0 |                234.0 |              617.0 | 10.309779362 |    55.5 |     -8.2 |
|   20 | Ed Delahanty   | delahed01 |     1888 |     1903 |  8400 |    569.8 |    -3.0 |         20.0 |         -74.6 |            242.4 |          754.6 |  66.5 |        636.0 |        16.0 |             20.0 |             -76.0 |                231.0 |              827.0 |  9.955032326 |    74.7 |     -8.2 |
+------+----------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
20 Hitters most helped
+------+------------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
| rk   | name_common      | player_ID | year_min | year_max | PA    | runs_bat | runs_br | runs_defense | runs_position | runs_replacement | runs_above_rep | WAR   | runs_bat_old | runs_br_old | runs_defense_old | runs_position_old | runs_replacement_old | runs_above_rep_old | war_rate_old | WAR_old | war_diff |
+------+------------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
|    1 | Warren Spahn     | spahnwa01 |     1942 |     1965 |  2056 |   -143.7 |    -7.8 |          0.0 |         226.2 |             69.8 |          144.5 |   7.5 |       -151.0 |        -6.0 |              0.0 |              59.0 |                 72.0 |              -26.0 |  8.727302466 |    -3.7 |     11.2 |
|    2 | Torii Hunter     | hunteto01 |     1998 |     2011 |  7303 |     69.7 |    10.2 |         54.3 |           8.4 |            245.1 |          387.7 |  39.0 |         55.7 |        13.9 |            -29.5 |               6.0 |                251.9 |              298.2 |  9.987369024 |    29.7 |      9.3 |
|    3 | Alex Rios        | riosal01  |     2004 |     2011 |  4695 |    -23.0 |    15.9 |         70.0 |         -26.1 |            158.8 |          195.6 |  19.3 |        -29.1 |        12.5 |             -5.9 |             -27.9 |                156.2 |              105.3 | 10.106127482 |    10.5 |      8.8 |
|    4 | Lew Burdette     | burdele01 |     1951 |     1966 |  1123 |    -90.9 |    -2.7 |          0.0 |         124.7 |             37.5 |           68.6 |   3.2 |        -97.0 |        -2.0 |              0.0 |              14.0 |                 37.0 |              -48.0 |  8.569753900 |    -5.5 |      8.7 |
|    5 | Ozzie Smith      | smithoz01 |     1978 |     1996 | 10778 |    -93.4 |    79.2 |        238.7 |         138.8 |            318.4 |          681.7 |  73.0 |       -129.0 |        82.0 |            238.7 |             147.0 |                310.0 |              649.0 | 10.784130209 |    64.6 |      8.4 |
|    6 | Brandon Phillips | phillbr01 |     2002 |     2011 |  4366 |    -21.1 |    12.5 |         44.4 |          20.0 |            121.1 |          176.9 |  17.9 |        -39.6 |        14.4 |            -22.3 |              19.8 |                122.7 |               94.1 |  9.976876088 |     9.5 |      8.4 |
|    7 | Chase Utley      | utleych01 |     2003 |     2011 |  4778 |    189.1 |    30.0 |        135.0 |          18.7 |            129.3 |          502.1 |  50.2 |        181.3 |        28.4 |             67.3 |              19.2 |                124.8 |              420.3 |  9.934868368 |    42.3 |      7.9 |
|    8 | Carlos Pena      | penaca01  |     2001 |     2011 |  4902 |    138.5 |    -1.6 |          8.8 |         -75.5 |            161.2 |          231.4 |  23.1 |        126.0 |        -3.1 |            -52.2 |             -78.5 |                164.5 |              154.9 | 10.217234406 |    15.2 |      7.9 |
|    9 | Orlando Hudson   | hudsoor01 |     2002 |     2011 |  5130 |      1.6 |    18.0 |         93.4 |          22.9 |            153.5 |          289.4 |  28.6 |         -0.1 |        20.5 |             15.2 |              23.3 |                155.5 |              213.9 |  9.796773959 |    21.7 |      6.9 |
|   10 | Adrian Beltre    | beltrad01 |     1998 |     2011 |  8043 |    107.0 |     1.1 |        171.7 |          22.4 |            247.6 |          549.8 |  54.1 |         92.8 |         2.8 |            114.5 |              22.4 |                247.5 |              479.7 | 10.047054342 |    47.6 |      6.5 |
|   11 | Ben Zobrist      | zobribe01 |     2006 |     2011 |  2458 |     50.0 |     8.2 |         57.0 |          -0.4 |             83.3 |          198.1 |  20.0 |         46.6 |         6.5 |             -1.2 |               0.6 |                 85.0 |              137.6 | 10.000945118 |    13.6 |      6.4 |
|   12 | Roberto Clemente | clemero01 |     1955 |     1972 | 10211 |    386.1 |    20.2 |        204.8 |        -106.1 |            339.0 |          844.0 |  89.8 |        351.0 |        21.0 |            204.8 |            -125.0 |                334.0 |              786.0 |  9.641412208 |    83.8 |      6.0 |
|   13 | Carl Crawford    | crawfca02 |     2002 |     2011 |  5934 |     73.7 |    43.2 |         78.9 |         -59.9 |            199.9 |          335.8 |  33.2 |         39.6 |        41.8 |             61.8 |             -61.6 |                191.6 |              272.7 | 10.029454904 |    27.2 |      6.0 |
|   14 | George McBride   | mcbrige01 |     1901 |     1920 |  6235 |   -223.1 |    -5.9 |         99.0 |         103.2 |            210.2 |          183.4 |  17.5 |       -244.0 |       -10.0 |             99.0 |             106.0 |                205.0 |              156.0 | 11.801048225 |    11.6 |      5.9 |
|   15 | Brian Giles      | gilesbr02 |     1995 |     2009 |  7836 |    360.6 |    21.0 |        -28.0 |         -69.3 |            218.3 |          502.6 |  48.4 |        342.3 |        14.4 |            -72.6 |             -71.0 |                213.0 |              425.1 |  9.904725110 |    42.5 |      5.9 |
|   16 | Alex Rodriguez   | rodrial01 |     1994 |     2011 | 10634 |    621.2 |    56.3 |         39.8 |          73.2 |            354.8 |         1145.3 | 110.2 |        616.8 |        56.1 |            -13.7 |              76.5 |                338.6 |             1073.6 | 10.258871865 |   104.6 |      5.6 |
|   17 | Bobby Wallace    | wallabo01 |     1894 |     1918 |  9612 |     66.9 |   -12.9 |        133.0 |         149.7 |            308.4 |          645.1 |  66.0 |         51.0 |       -26.0 |            133.0 |             138.0 |                304.0 |              600.0 | 10.211267162 |    60.5 |      5.5 |
|   18 | Bill Mazeroski   | mazerbi01 |     1956 |     1972 |  8379 |   -164.8 |    -5.8 |        147.2 |          58.3 |            280.5 |          315.4 |  32.3 |       -193.0 |        -6.0 |            147.2 |              57.0 |                286.0 |              291.0 |  9.794823607 |    26.9 |      5.4 |
|   19 | Steve Sax        | saxst01   |     1981 |     1994 |  7632 |    -11.2 |    22.9 |        -60.9 |          36.0 |            241.1 |          227.9 |  22.9 |        -55.0 |        22.0 |            -60.9 |              43.0 |                228.0 |              176.0 | 10.701560730 |    17.5 |      5.4 |
|   20 | Bob Buhl         | buhlbo01  |     1953 |     1966 |   953 |   -160.8 |    -2.2 |          0.0 |         106.5 |             32.1 |          -24.4 |  -6.2 |       -163.0 |        -2.0 |              0.0 |              30.0 |                 33.0 |             -102.0 |  8.373673033 |   -11.5 |      5.3 |
+------+------------------+-----------+----------+----------+-------+----------+---------+--------------+---------------+------------------+----------------+-------+--------------+-------------+------------------+-------------------+----------------------+--------------------+--------------+---------+----------+
20 Pitchers Most Hurt

+------+---------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+------+------------------+----------------------+--------------------+--------------+---------+----------+
| rk   | name_common   | player_ID | year_min | year_max | IP        | G    | GS   | runs_allowed | xRA_ppf  | runs_defense | runs_above_rep | WAR  | runs_defense_old | runs_replacement_old | runs_above_rep_old | war_rate_old | WAR_old | war_diff |
+------+---------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+------+------------------+----------------------+--------------------+--------------+---------+----------+
|    1 | Bob Caruthers | carutbo01 |     1884 |     1892 | 2828.6667 |  340 |  310 |         1393 | 1644.274 |       84.005 |        462.012 | 40.1 |             59.0 |               2076.0 |              624.0 | 11.705965479 |    52.6 |    -12.5 |
|    2 | Tony Mullane  | mullato01 |     1881 |     1894 | 4531.3333 |  555 |  504 |         2523 | 2784.332 |      118.789 |        606.140 | 55.1 |             85.0 |               3320.0 |              712.0 | 12.170346324 |    65.1 |    -10.0 |
|    3 | Dave Foutz    | foutzda01 |     1884 |     1894 | 1997.3334 |  251 |  216 |         1068 | 1157.699 |       72.757 |        227.279 | 20.0 |             52.0 |               1459.0 |              339.0 | 11.459945575 |    30.0 |    -10.0 |
|    4 | Matt Kilroy   | kilroma01 |     1886 |     1898 | 2435.6666 |  303 |  292 |         1539 | 1617.458 |      -21.054 |        259.511 | 20.0 |            -14.0 |               1903.0 |              378.0 | 11.832972672 |    28.9 |     -8.9 |
|    5 | Gaylord Perry | perryga01 |     1962 |     1983 | 5350.0002 |  777 |  690 |         2128 | 2525.291 |      -27.019 |        921.394 | 87.5 |            -25.0 |               2967.0 |              864.0 |  9.242938454 |    96.3 |     -8.8 |
|    6 | Don Drysdale  | drysddo01 |     1956 |     1969 | 3432.0000 |  518 |  465 |         1292 | 1557.546 |       -1.871 |        622.745 | 57.4 |             -2.0 |               1869.0 |              579.0 |  8.859296421 |    65.7 |     -8.3 |
|    7 | Bob Gibson    | gibsobo01 |     1959 |     1975 | 3884.3334 |  528 |  482 |         1420 | 1828.790 |       11.794 |        791.869 | 77.5 |             15.0 |               2165.0 |              730.0 |  7.268684521 |    85.6 |     -8.1 |
|    8 | Don Sutton    | suttodo01 |     1966 |     1988 | 5282.3333 |  774 |  756 |         2104 | 2335.445 |       51.399 |        736.467 | 62.9 |             52.0 |               2721.0 |              565.0 |  8.056832817 |    70.8 |     -7.9 |
|    9 | Bob Lemon     | lemonbo01 |     1946 |     1958 | 2850.3333 |  460 |  350 |         1185 | 1334.249 |       43.919 |        403.861 | 34.7 |             31.0 |               1690.0 |              474.0 |  9.563891205 |    42.4 |     -7.7 |
|   10 | Adonis Terry  | terryad01 |     1884 |     1897 | 3514.3333 |  440 |  406 |         2303 | 2258.098 |       18.806 |        271.772 | 24.2 |             15.0 |               2660.0 |              347.0 |  9.202283211 |    31.8 |     -7.6 |
|   11 | Nolan Ryan    | ryanno01  |     1966 |     1993 | 5386.0000 |  807 |  773 |         2178 | 2497.233 |      -37.617 |        854.942 | 77.4 |            -36.0 |               2912.0 |              770.0 |  9.274636545 |    84.8 |     -7.4 |
|   12 | Warren Spahn  | spahnwa01 |     1942 |     1965 | 5243.6669 |  750 |  665 |         2016 | 2375.835 |       38.650 |        934.983 | 86.0 |             44.0 |               2879.0 |              819.0 |  8.880594243 |    93.4 |     -7.4 |
|   13 | Al Atkinson   | atkinal01 |     1884 |     1887 |  915.0000 |  106 |  106 |          656 |  604.294 |      -15.183 |         -7.807 | -0.3 |            -12.0 |                680.0 |               67.0 | 14.909080611 |     7.0 |     -7.3 |
|   14 | Larry Jackson | jacksla01 |     1955 |     1968 | 3262.6666 |  558 |  429 |         1405 | 1598.624 |        0.572 |        533.776 | 48.7 |              2.0 |               1927.0 |              520.0 |  8.476979721 |    55.6 |     -6.9 |
|   15 | Chris Short   | shortch02 |     1959 |     1973 | 2324.9999 |  501 |  308 |          991 | 1086.885 |      -36.245 |        329.169 | 28.6 |            -36.0 |               1295.0 |              340.0 |  8.958960458 |    35.5 |     -6.9 |
|   16 | Bob Friend    | frienbo01 |     1951 |     1966 | 3610.6668 |  602 |  497 |         1652 | 1745.388 |       16.871 |        479.918 | 42.1 |             21.0 |               2098.0 |              425.0 |  7.353200671 |    48.9 |     -6.8 |
|   17 | Ed Seward     | sewared01 |     1885 |     1891 | 1485.6667 |  176 |  169 |          823 |  945.767 |       -2.482 |        223.386 | 19.1 |             -3.0 |               1130.0 |              310.0 | 12.437591039 |    25.7 |     -6.6 |
|   18 | Rick Wise     | wiseri01  |     1964 |     1982 | 3127.3331 |  506 |  455 |         1455 | 1507.566 |      -28.760 |        356.050 | 28.5 |            -27.0 |               1774.0 |              346.0 |  8.507057171 |    35.1 |     -6.6 |
|   19 | Vic Raschi    | raschvi01 |     1946 |     1955 | 1819.0001 |  269 |  255 |          828 |  852.573 |       30.486 |        193.517 | 14.8 |             21.0 |               1109.0 |              260.0 | 10.652756307 |    21.4 |     -6.6 |
|   20 | Guy Hecker    | heckegu01 |     1882 |     1890 | 2924.0000 |  336 |  322 |         1726 | 1794.538 |      -14.564 |        233.354 | 24.2 |             -6.0 |               2091.0 |              382.0 | 14.387767003 |    30.7 |     -6.5 |
+------+---------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+------+------------------+----------------------+--------------------+--------------+---------+----------+
20 pitchers most helped

+------+-------------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+-------+------------------+----------------------+--------------------+--------------+---------+----------+
| rk   | name_common       | player_ID | year_min | year_max | IP        | G    | GS   | runs_allowed | xRA_ppf  | runs_defense | runs_above_rep | WAR   | runs_defense_old | runs_replacement_old | runs_above_rep_old | war_rate_old | WAR_old | war_diff |
+------+-------------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+-------+------------------+----------------------+--------------------+--------------+---------+----------+
|    1 | Walter Johnson    | johnswa01 |     1907 |     1927 | 5914.0001 |  802 |  666 |         1902 | 2683.354 |       34.225 |       1367.877 | 144.7 |             25.0 |               3128.0 |             1201.0 |  9.547638204 |   127.7 |     17.0 |
|    2 | Cy Young          | youngcy01 |     1890 |     1911 | 7356.0001 |  906 |  815 |         3167 | 4093.024 |       85.040 |       1716.233 | 162.3 |             61.0 |               4731.0 |             1503.0 |  9.840410945 |   146.0 |     16.3 |
|    3 | Ted Breitenstein  | breitte01 |     1891 |     1901 | 2973.3334 |  380 |  342 |         1848 | 2082.538 |      -23.250 |        601.554 |  49.0 |            -18.0 |               2299.0 |              472.0 | 10.029087369 |    39.1 |      9.9 |
|    4 | Kid Nichols       | nichoki01 |     1890 |     1906 | 5067.3333 |  621 |  562 |         2480 | 3148.820 |      134.190 |       1250.571 | 111.6 |             96.0 |               3619.0 |             1046.0 | 10.039165824 |   102.3 |      9.3 |
|    5 | Jim Devlin        | devliji01 |     1876 |     1877 | 1181.0000 |  129 |  129 |          597 |  827.066 |       69.409 |        292.139 |  30.9 |             49.0 |                809.0 |              163.0 |  7.318936892 |    22.2 |      8.7 |
|    6 | Pete Alexander    | alexape01 |     1911 |     1930 | 5186.3332 |  696 |  600 |         1852 | 2475.385 |       32.571 |       1077.211 | 112.8 |             20.0 |               2797.0 |              926.0 |  9.010410044 |   104.9 |      7.9 |
|    7 | Rube Waddell      | wadderu01 |     1897 |     1910 | 2961.3335 |  407 |  340 |         1063 | 1321.281 |        3.357 |        522.711 |  57.7 |              3.0 |               1516.0 |              450.0 |  8.928551325 |    50.2 |      7.5 |
|    8 | Jim McCormick     | mccorji01 |     1878 |     1887 | 4275.6667 |  492 |  485 |         2095 | 2463.247 |       69.311 |        665.177 |  72.2 |             48.0 |               2865.0 |              722.0 | 11.642536001 |    64.7 |      7.5 |
|    9 | Jim Whitney       | whitnji01 |     1881 |     1890 | 3496.3333 |  413 |  396 |         2026 | 2135.774 |      -50.468 |        399.456 |  43.2 |            -34.0 |               2400.0 |              408.0 |  4.979419898 |    35.9 |      7.3 |
|   10 | Casey Patten      | patteca01 |     1901 |     1908 | 2062.3334 |  270 |  238 |         1079 | 1013.832 |      -56.244 |        125.370 |  12.1 |            -40.0 |               1076.0 |               37.0 |  6.064685380 |     4.8 |      7.3 |
|   11 | Al Orth           | orthal01  |     1895 |     1909 | 3354.6668 |  440 |  394 |         1704 | 1790.417 |      -58.680 |        415.651 |  40.5 |            -41.0 |               1958.0 |              295.0 |  7.934372933 |    33.3 |      7.2 |
|   12 | Win Mercer        | mercewi01 |     1894 |     1902 | 2484.6667 |  335 |  300 |         1753 | 1710.229 |      -78.656 |        256.094 |  21.3 |            -55.0 |               1851.0 |              162.0 | 11.579619581 |    14.1 |      7.2 |
|   13 | Curt Schilling    | schilcu01 |     1988 |     2007 | 3261.0000 |  569 |  436 |         1318 | 1819.832 |       -0.080 |        835.285 |  76.9 |             19.0 |               2052.0 |              715.0 |  9.912305038 |    69.7 |      7.2 |
|   14 | Tommy Bond        | bondto01  |     1876 |     1884 | 2779.6666 |  322 |  314 |         1339 | 1615.609 |       14.817 |        414.962 |  47.9 |             11.0 |               1806.0 |              456.0 |  6.497058282 |    40.8 |      7.1 |
|   15 | Burleigh Grimes   | grimebu01 |     1916 |     1934 | 4177.6668 |  616 |  497 |         2050 | 2165.777 |      -29.575 |        510.727 |  44.2 |            -22.0 |               2396.0 |              370.0 |  9.604876188 |    37.2 |      7.0 |
|   16 | Pud Galvin        | galvipu01 |     1879 |     1892 | 5941.3333 |  697 |  681 |         3315 | 3577.832 |       -7.797 |        744.021 |  77.5 |             -6.0 |               4110.0 |              798.0 | 10.665223530 |    70.5 |      7.0 |
|   17 | Randy Johnson     | johnsra05 |     1988 |     2009 | 4135.3334 |  618 |  603 |         1703 | 2320.554 |       -4.384 |       1069.386 |  98.6 |             12.0 |               2645.0 |              930.0 |  9.808965187 |    91.8 |      6.8 |
|   18 | Jack Powell       | powelja01 |     1897 |     1912 | 4388.9999 |  578 |  516 |         1991 | 2096.815 |       38.617 |        532.918 |  51.3 |             30.0 |               2443.0 |              422.0 |  7.235229481 |    44.5 |      6.8 |
|   19 | Clarence Mitchell | mitchcl01 |     1911 |     1932 | 2222.6667 |  390 |  278 |         1215 | 1235.432 |      -37.174 |        231.583 |  18.7 |            -27.0 |               1269.0 |               81.0 |  4.579240793 |    11.9 |      6.8 |
|   20 | Red Faber         | faberre01 |     1914 |     1933 | 4086.6666 |  669 |  483 |         1813 | 2088.854 |       13.835 |        721.292 |  61.9 |              9.0 |               2394.0 |              572.0 | 10.377306458 |    55.2 |      6.7 |
+------+-------------------+-----------+----------+----------+-----------+------+------+--------------+----------+--------------+----------------+-------+------------------+----------------------+--------------------+--------------+---------+----------+
Top 20 hitters before and then after
+------+------------------+---------++------------------+-------+
| rk   | name_common      | WAR_old || name_common      | WAR   |
+------+------------------+---------++------------------+-------+
|    1 | Babe Ruth        |   172.0 || Babe Ruth        | 159.2 |
|    2 | Barry Bonds      |   171.8 || Barry Bonds      | 158.0 |
|    3 | Ty Cobb          |   159.4 || Willie Mays      | 150.8 |
|    4 | Willie Mays      |   154.7 || Ty Cobb          | 144.9 |
|    5 | Hank Aaron       |   141.6 || Hank Aaron       | 137.3 |
|    6 | Honus Wagner     |   134.5 || Tris Speaker     | 127.8 |
|    7 | Tris Speaker     |   133.0 || Honus Wagner     | 126.2 |
|    8 | Stan Musial      |   127.8 || Rogers Hornsby   | 124.6 |
|    9 | Rogers Hornsby   |   127.8 || Stan Musial      | 123.4 |
|   10 | Eddie Collins    |   126.7 || Ted Williams     | 119.8 |
|   11 | Ted Williams     |   125.3 || Eddie Collins    | 118.5 |
|   12 | Mickey Mantle    |   120.2 || Alex Rodriguez   | 111.1 |
|   13 | Lou Gehrig       |   118.4 || Lou Gehrig       | 108.5 |
|   14 | Rickey Henderson |   113.1 || Rickey Henderson | 106.8 |
|   15 | Mel Ott          |   109.3 || Mickey Mantle    | 105.5 |
|   16 | Mike Schmidt     |   108.3 || Mel Ott          | 104.0 |
|   17 | Frank Robinson   |   107.4 || Mike Schmidt     | 103.0 |
|   18 | Alex Rodriguez   |   104.6 || Nap Lajoie       | 102.2 |
|   19 | Nap Lajoie       |   104.2 || Frank Robinson   | 100.9 |
|   20 | Joe Morgan       |   103.5 || Joe Morgan       |  97.1 |
+------+------------------+---------++------------------+-------+
Top 20 pitchers before and after
+------+-------------------+---------++-------------------+-------+
| rk   | name_common       | WAR_old || name_common       | WAR   |
+------+-------------------+---------++-------------------+-------+
|    1 | Cy Young          |   146.0 || Cy Young          | 162.3 |
|    2 | Roger Clemens     |   128.4 || Walter Johnson    | 144.7 |
|    3 | Walter Johnson    |   127.7 || Roger Clemens     | 133.1 |
|    4 | Tom Seaver        |   105.3 || Pete Alexander    | 112.8 |
|    5 | Pete Alexander    |   104.9 || Kid Nichols       | 111.6 |
|    6 | Kid Nichols       |   102.3 || Lefty Grove       | 103.7 |
|    7 | Lefty Grove       |    98.3 || Tom Seaver        | 101.1 |
|    8 | Phil Niekro       |    96.8 || Greg Maddux       |  99.4 |
|    9 | Greg Maddux       |    96.8 || Randy Johnson     |  98.6 |
|   10 | Gaylord Perry     |    96.3 || Phil Niekro       |  91.7 |
|   11 | Warren Spahn      |    93.4 || Christy Mathewson |  90.8 |
|   12 | Randy Johnson     |    91.8 || Bert Blyleven     |  90.7 |
|   13 | Bert Blyleven     |    90.1 || Gaylord Perry     |  87.5 |
|   14 | Christy Mathewson |    87.7 || Warren Spahn      |  86.0 |
|   15 | Bob Gibson        |    85.6 || Tim Keefe         |  84.0 |
|   16 | Nolan Ryan        |    84.8 || Pedro Martinze    |  82.6 |
|   17 | Steve Carlton     |    84.4 || Eddie Plank       |  82.0 |
|   18 | Tim Keefe         |    82.5 || John Clarkson     |  81.1 |
|   19 | John Clarkson     |    82.1 || Steve Carlton     |  78.6 |
|   20 | Fergie Jenkins    |    81.3 || Mike Mussina      |  78.1 |
+------+-------------------+---------++-------------------+-------+

Top 20 Total WAR before and after
+------------------+---------++------------------+-------+
| name_common      | WAR_old || name_common      | WAR   |
+------------------+---------++------------------+-------+
| Babe Ruth        |   190.0 || Babe Ruth        | 178.3 |
| Barry Bonds      |   171.8 || Cy Young         | 160.8 |
| Ty Cobb          |   159.5 || Barry Bonds      | 158.0 |
| Willie Mays      |   154.7 || Walter Johnson   | 157.8 |
| Cy Young         |   143.2 || Willie Mays      | 150.8 |
| Hank Aaron       |   141.6 || Ty Cobb          | 145.0 |
| Walter Johnson   |   139.8 || Hank Aaron       | 137.3 |
| Honus Wagner     |   134.5 || Roger Clemens    | 133.9 |
| Tris Speaker     |   132.9 || Tris Speaker     | 127.7 |
| Roger Clemens    |   128.8 || Honus Wagner     | 126.1 |
| Stan Musial      |   127.8 || Rogers Hornsby   | 124.6 |
| Rogers Hornsby   |   127.8 || Stan Musial      | 123.4 |
| Eddie Collins    |   126.7 || Ted Williams     | 119.8 |
| Ted Williams     |   125.3 || Eddie Collins    | 118.5 |
| Mickey Mantle    |   120.2 || Pete Alexander   | 115.9 |
| Lou Gehrig       |   118.4 || Kid Nichols      | 111.6 |
| Rickey Henderson |   113.1 || Alex Rodriguez   | 111.1 |
| Mel Ott          |   109.3 || Lou Gehrig       | 108.5 |
| Mike Schmidt     |   108.3 || Rickey Henderson | 106.8 |
| Frank Robinson   |   107.4 || Mickey Mantle    | 105.5 |
+------------------+---------++------------------+-------+
  3 pitchers of 20              5 pitchers

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