Wins Above Replacement (WAR)
The Baseball Guage uses Baseball-Reference's WAR system. For more information on their calculation, please visit this page.
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Win Shares (WS)
Win Shares are calculated using the formula in the book Win Shares by Bill James. If you don't have the book and would like to take a look at the calculations, "Patriot" has a very detailed seven part walk through on his site.
If you are wondering why the Win Shares totals do not exactly match those totals in the Win Shares Book, there are a couple of reasons:
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The first, and possibly the biggest reason is that this site uses different park factors than Bill James did. Any difference in park factor can alter the distribution of offensive and defensive Win Shares as well as other parts of the formula.
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Possibly, the second biggest reason is that this site keeps decimal points, where as Bill James rounded to the whole number. This is done to keep the values as accurate as possible.
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Next, when figuring Catcher's claim points, the book only uses opponent's stolen base data from 1987 until present. This site uses this data from 1954 until present. On the flip side, the book uses sacrifice allowed data from 1931 until present, while this site only uses it from 1956 until present. This difference in data available will alter catcher claim points, which will also slightly alter the other positions as well.
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When calculating Runs Created for offensive Win Shares, the same RC formula is used except for that RISP data is not included.
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When calculating Pitching Win Shares, the book includes an adjustment for pitchers hitting below a certain level. This site does not make that adjustment since a pitcher's offense (or lack of) should not affect his pitching Win Shares.
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Finally, Catcher's ERA is not included in calculating claim points. This is done mainly because of lack of data available, but also because of possible inaccuracies. Some pitchers use a "personal" catcher, which will cause the games caught for each pitcher to be unequal. For example, Eddie Perez was Greg Maddux's personal catcher while Javy Lopez caught the majority of the other games. It is inaccurate to compare their catcher's ERA's since they caught different pitchers.
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Win Shares Above Bench (WSAB)
Bench level is set at 75% of league average for all players except Starting Pitchers, whose bench level is 60%
For more information on WSAB, check out the glossary entry at The Hardball Times.
For Offensive WSAB, find the league average of Offensive Win Shares per Plate Appearance. This is done separately for Non-pitchers and pitchers. For explanation purposes, let's say that the league average is .014 WS/PA.
Suppose that player X had 600 Plate Appearances and 12 Offensive Win Shares. Multiply his Plate Appearances by the league average WS/PA. This would give him 8.4 (600 * .014) Expected Offensive Win Shares. To find expected bench, multiply that by the bench level (8.4 * .75 = 6.3 Win Shares). Simply subtract the bench level offensive Win Shares from player X's actual offensive Win Shares to find Offensive WSAB (12 - 6.3 = 5.7).
The same process is done for Fielding WSAB, except that defensive innings is used for the rate instead of Plate Appearances. Bench level is still 75% for fielding.
It is important to note that Fielding Win Shares for each position played are compared to the league at that position. For example, suppose player X played primarily at 2B, but also played some SS and 3B. His total Fielding Win Shares are not just compared to other 2B. Instead, his Fielding Win Shares at 2B are compared to the league at 2B, while his Fielding Win Shares at SS are compared to the league at SS. This is also done for 3B. Once each position's WSAB are calculated, they are added together to find total Fielding WSAB.
For Pitching WSAB, Innings Pitched is used to find the league rate. Starters are compared to other starters while relievers are compared to other relievers. As mentioned earlier, the bench level for starters is 60% while it's still 75% for relievers.
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Components Above Replacement
Replacement Levels
Replacement level for each component is based on the standard deviation of each rate stat. Using the 82.5% from the WAR calculation as a baseline, we can figure that replacement level is approximately .5 standard deviations below league average. Each rate stat's corresponding percentage is calculated based on half of it's standard deviation below (or above in some cases) league average.
The reason that standard deviation is used is because not all rate stats are distributed equally. For example, the replacement level for batting average comes out to 92.8%. If the league average is .260, the replacement level would be a .241 batting average (.260 * .928 = .241). If we just used 82.5%, the replacement level would be .215 which would cause the vast majority of the league to be above replacement and this would not be consistent with our other replacement levels.
Component Stat Calculation
Each
component is calculated using a corresponding rate stat. For example, Hits Above Replacement uses Batting Average (H/AB), Times On Base Above Replacement uses On Base Percentage (H + BB + HBP) / (AB + BB + HBP + SF). The rate stats are needed in order to compare each player to the league.
Let's take Hits Above Replacement for example. Suppose Player X has 150 hits in 500 at bats (.300 Avg). The league's average is .265 and the replacement level is .246 (.265 * .928 = .246). In 500 at bats, a replacement player would collect 123 hits (.246 * 500 = 123). Hits Above Replacement would then be 27 (150 - 123 = 27).
This is done with all Components Above Replacement. Each component just needs a corresponding rate stat so that the denominator can be applied to the replacement level.
To complicate things a little bit more, prior to the calculation, the numbers are also park adjusted for each player. To calculate park adjusted stats, the "Willie Davis Method" is used with an additional adjustment for Home run Factor. The "Willie Davis Method" is explained in The New Bill James Historical Baseball Abstract (pgs 740-743). Essentially, it uses the simple Runs Created formula, a park adjustment is applied and then the quadratic formula is used to find hits. The other stats (2B, BB, etc) are then adjusted at the same rate.
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