Wins Above Replacement (WAR)
Offensive WAR
For Offensive WAR, we calculate BaseRuns for each player and make an adjustment for ballpark and compare them to a replacement level player. The default Replacement level is set at a .380 Winning %.
Finally, Runs above replacement are then converted to wins through a run conversion formula. One win is generally worth around 10 runs, but can fluctuate based on the run scoring environment.
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Fielding WAR
Fielding WAR is derived from Runs Saved data in the Defensive Regression Analysis system created by Michael Humphreys.
The Baseball Gauge uses a 3-year average, which increases the sample size to give a more accurate representation of the player’s ability. If the player does not meet a certain number of Innings in that 3-year span, the sample increases to 5 years.
The amount of Runs Saved is then converted to wins through a run conversion formula. One win is generally worth around 10 runs, but can fluctuate based on the run scoring envioronment.
For more information on Michael Humphrey’s Defensive Regression Analysis, check out the book Wizardry, or read his series at The Hardball Times.
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Pitching WAR
Pitching WAR begins with the pitcher’s original Runs Allowed and then adjustments are made for Fielding, Bullpen, Ballpark, and League Difficulty.
Each team’s total Fielding Runs Saved are divided amongst its pitchers based on each pitcher’s balls in play, handedness, groundball/flyball ratio, and number of base runners.
The bullpen adjustment estimates the number of runners on base that were stranded or allowed to score. This is based off of each bullpen member's BaseRuns compared to the league. Other factors included are each pitcher's number of pitching changes (non-complete games for SP's and non-games finished for RP's) as well as the base runners allowed rate for each pitcher. Since not all pitching changes come in the middle of an inning, this adjustment is generally very small except for extreme situations where a bullpen is very good or bad.
The default Replacement level is set at a .410 Winning % for Starting Pitchers and .480 for Relief Pitchers.
Finally, Runs above replacement are then converted to wins through a run conversion formula. One win is generally worth around 10 runs, but can fluctuate based on the run scoring environment.
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Positional Adjustment
A Positional Adjustment is needed to make up for the difficulty of each position. Take a look at the Defensive Spectrum to see the order of difficulty of each position.
Positional adjustments are based off of the difficulty to play each position and the offensive production at each position.
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Replacement Level
Replacement levels change over time based on a league difficulty factor. This difficulty factor comes from a study done by David Gassko at The Hardball Times. It calculates the year by year and league by league change in wOBA to show how Baseball has gradually become more difficult over time. We have reproduced this study for both hitters and pitchers and applied it to replacement level.
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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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