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Custom wOBA and Linear Weights Through 2010: Baseball Databank Data Dump 2.1

By Matt Klaassen
Accountant-_old_medium

A rare photo of Tom Tango, seen here calculating linear weights.

You know what wOBA is, right? If not, get hip to it. In short, wOBA (weighted On-Base Average) was created by Tom Tango as a way of more accurately expressing a player's offensive value (according to the linear weights of offensive events) than more traditional stats like batting average, on-base percentage, OPS, or whatever. While those numbers have their uses, linear weights more accurately reflect what a player has contributed since it does a better job of noting the relative value of walks, singles, doubles, etc. than those stats. wOBA is simply linear weights expressed as a "rate stat" scaled on on-base percentage, so, for example (depending on the run environment) .320-.330 are usually around average, .300 is terrible, and .400 is awesome. 

While the "original recipe" uses some pretty standard and effective weights, since then Tango has published a script that "customizes" wOBA for seasonal run environments. This has been implemented at FanGraphs, for example. However, many people now prefer these "custom" versions, but the values aren't readily available. I'm no sabermetric or SQL wizard, but I do have the script that these things are based. Due to overwhelming demand from my massive fanbase (okay, a couple of people on Twitter), I've run the script and have the weights through this season. I take no great claim to have invented this method or the script, but below you will find the wOBA coefficients updated for each MLB season through 2010.


A Few Boring Historical and Methodological Details (Feel Free to Skip)

 

In the original formulation given in The Book,  the linear weights used for events were: HR 1.70, 3B 1.37, 2B 1.08, 1B 0.77, uBB 0.62. To scale this to something resembling OBP, Tango divided all of these by 1.15 and did other stuff to make plate appearances (rather than outs, as in traditional linear weights) the denominator to come up with this formula  for caculating a player's (or any other entity's) wOBA:

(0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR) / PA

To convert to linear weights runs above average (what is called 'wRAA' at FanGraphs), simply take the players wOBA, subtract the league wOBA from that, and then divide by 1.15 (the 'wOBAScale') and multiply by plate appearances to get back to the actual runs scale.

Those weights work fine, actually, but Tango later published a SQL (for Access) script using the free database from Baseball Databank to give specific weights for each season (the run values of each event change for season-to-season depending on the run environment. Colin Wyers later adapted this script for MySQL, which is the script I use here. Again, check out the various links given herein for more detailed (and likely more accurate) information.

The "original recipe" was created to give one simple "rate stat" type to get a hitter-batter matchups in The Book, so stolen bases weren't included. It was easy enough to include them, though. Reached on Error isn't included in this version because they aren't recorded in the Baseball Databank (there are differing opinions as to whether they should be credited to the player, I say yes, but it isn't a big deal). What is or isn't included in a linear weights/wOBA calculation isn't a simple matter of right or wrong, it depends on what you want to do with it. For figuring out a batting order, for example, you'd probably want to use wOBA without steals/caught stealing, for overall offensive value, including steals/caught stealing gives a more accurate picture.

Note that Tango's script uses 0.2 and 1.4 as every season's linear weights for the stolen base and home run, respectively. Those are "quickie" workaround, but they work well enough. It might look like they change because their wOBA coefficients change, but that's simply because the scaling of wOBA to OBP changes each season.

These numbers will get you pretty close to what is used at FanGraphs, but there are some differences (likely due to things like methods of excluding pitchers from the initial calculations, overall data sources, rounding, etc.). I know that the league wOBAs for seasons I get and what FanGraphs get are sometimes different, but they are close enough. This is not 'official.' And again, these are not "my" weights, I just ran the script and wrote this interminable post... I do think these weights are very good for the most part, in early baseball there might be some problems because pitchers took a larger offensive role, and prior to 1956 or so iBBs weren't distinguished in the from uBBs, which also throws things off, but for most of modern baseball, and certainly for 2010, these will do the trick.

Finally, the Coefficients and Weights

Here it is, your 2010 wOBA formula (drumroll please):

(0.70 x uBB + 0.73 x HBP + 0.89 x 1B +1.27 x 2B +1.61 x 3B + 2.07 x HR +0.25 x SB + 0.50 x CS) / PA

The "wOBAScale" for 2010 is 1.25 and the league wOBA is .320, so for runs above average, use

( (wOBA - .320) /1.25) x PA

The "weights proper" (rounded to two places) for this season are 0.30 uBB, 0.33 HBP, 0.46 1B, 0.76 2B, 1.03 3B, 1.4 HR, 0.2 SB, 0.4 CS.

...and here is the "big table" for all of MLB. Enjoy, nerds!

(Click here for the full list of weights as well as unrounded wOBA coefficients and whatnot.)

 

wOBA Coefficients Through 2010
Year wOBA wScale wBB wHBP w1B w2B w3B wHR wSB wCS
2010 0.320 1.25 0.70 0.73 0.89 1.27 1.61 2.07 0.25 0.50
2009 0.328 1.21 0.71 0.74 0.89 1.26 1.58 2.02 0.24 0.51
2008 0.328 1.21 0.71 0.74 0.89 1.26 1.58 2.02 0.24 0.51
2007 0.330 1.19 0.71 0.74 0.90 1.25 1.57 1.99 0.24 0.52
2006 0.330 1.17 0.71 0.74 0.89 1.24 1.56 1.96 0.23 0.52
2005 0.325 1.20 0.70 0.73 0.89 1.25 1.58 2.01 0.24 0.51
2004 0.329 1.18 0.71 0.74 0.89 1.24 1.56 1.98 0.24 0.52
2003 0.327 1.19 0.71 0.74 0.89 1.25 1.57 2.00 0.24 0.51
2002 0.325 1.21 0.70 0.73 0.89 1.26 1.58 2.02 0.24 0.51
2001 0.326 1.18 0.70 0.73 0.89 1.24 1.56 1.98 0.24 0.52
2000 0.339 1.15 0.72 0.75 0.90 1.25 1.56 1.95 0.23 0.53
1999 0.340 1.16 0.72 0.75 0.90 1.25 1.56 1.96 0.23 0.53
1998 0.331 1.20 0.71 0.74 0.90 1.26 1.58 2.01 0.24 0.52
1997 0.332 1.20 0.72 0.75 0.90 1.26 1.59 2.01 0.24 0.52
1996 0.334 1.17 0.72 0.75 0.90 1.25 1.57 1.97 0.23 0.53
1995 0.332 1.20 0.72 0.75 0.90 1.26 1.59 2.01 0.24 0.53
1994 0.333 1.18 0.72 0.75 0.90 1.25 1.57 1.99 0.24 0.53
1993 0.327 1.24 0.71 0.75 0.91 1.28 1.61 2.06 0.25 0.52
1992 0.316 1.33 0.71 0.74 0.91 1.31 1.67 2.17 0.27 0.51
1991 0.317 1.30 0.71 0.74 0.91 1.30 1.65 2.13 0.26 0.51
1990 0.319 1.30 0.71 0.74 0.91 1.30 1.65 2.13 0.26 0.51
1989 0.313 1.32 0.70 0.74 0.91 1.31 1.66 2.17 0.26 0.51
1988 0.312 1.32 0.70 0.73 0.90 1.30 1.65 2.16 0.26 0.51
1987 0.325 1.21 0.71 0.74 0.89 1.26 1.58 2.01 0.24 0.52
1986 0.320 1.26 0.71 0.74 0.90 1.28 1.62 2.09 0.25 0.52
1985 0.317 1.28 0.70 0.73 0.90 1.28 1.63 2.11 0.26 0.51
1984 0.317 1.30 0.71 0.74 0.91 1.30 1.65 2.14 0.26 0.51
1983 0.319 1.29 0.71 0.74 0.91 1.29 1.64 2.12 0.26 0.51
1982 0.317 1.29 0.71 0.74 0.91 1.29 1.64 2.13 0.26 0.51
1981 0.313 1.36 0.71 0.74 0.92 1.33 1.69 2.22 0.27 0.51
1980 0.320 1.30 0.71 0.74 0.91 1.30 1.65 2.13 0.26 0.51
1979 0.324 1.26 0.71 0.74 0.91 1.29 1.63 2.09 0.25 0.52
1978 0.317 1.33 0.71 0.74 0.91 1.31 1.67 2.17 0.27 0.51
1977 0.322 1.26 0.71 0.74 0.91 1.28 1.62 2.09 0.25 0.52
1976 0.314 1.38 0.71 0.75 0.93 1.34 1.71 2.25 0.28 0.51
1975 0.320 1.33 0.72 0.75 0.92 1.32 1.68 2.18 0.27 0.52
1974 0.317 1.35 0.71 0.75 0.92 1.33 1.69 2.21 0.27 0.52
1973 0.317 1.32 0.71 0.75 0.92 1.31 1.67 2.17 0.26 0.52
1972 0.303 1.41 0.70 0.73 0.92 1.34 1.72 2.28 0.28 0.50
1971 0.310 1.37 0.70 0.74 0.91 1.33 1.70 2.23 0.27 0.50
1970 0.318 1.29 0.71 0.74 0.91 1.30 1.65 2.13 0.26 0.52
1969 0.312 1.35 0.71 0.74 0.92 1.32 1.68 2.20 0.27 0.52
1968 0.291 1.46 0.68 0.72 0.91 1.35 1.74 2.34 0.29 0.48
1967 0.298 1.39 0.69 0.72 0.91 1.32 1.70 2.25 0.28 0.50
1966 0.303 1.33 0.69 0.72 0.89 1.29 1.65 2.17 0.27 0.50
1965 0.303 1.34 0.69 0.72 0.90 1.30 1.66 2.18 0.27 0.50
1964 0.306 1.32 0.69 0.72 0.90 1.29 1.65 2.16 0.26 0.50
1963 0.303 1.34 0.69 0.72 0.90 1.30 1.66 2.18 0.27 0.50
1962 0.321 1.27 0.71 0.74 0.91 1.29 1.63 2.10 0.25 0.52
1961 0.321 1.25 0.71 0.74 0.91 1.28 1.62 2.07 0.25 0.52
1960 0.318 1.30 0.71 0.74 0.91 1.30 1.65 2.13 0.26 0.51
1959 0.318 1.27 0.71 0.74 0.91 1.29 1.63 2.10 0.25 0.52
1958 0.319 1.28 0.71 0.74 0.90 1.29 1.63 2.11 0.26 0.51
1957 0.318 1.29 0.71 0.74 0.91 1.29 1.64 2.13 0.26 0.51
1956 0.325 1.27 0.71 0.75 0.91 1.29 1.64 2.10 0.25 0.52
1955 0.326 1.27 0.72 0.75 0.92 1.30 1.64 2.11 0.25 0.53
1954 0.333 1.29 0.73 0.76 0.93 1.32 1.67 2.14 0.26 0.52
1953 0.335 1.26 0.73 0.76 0.92 1.30 1.64 2.10 0.25 0.53
1952 0.326 1.35 0.73 0.76 0.94 1.34 1.70 2.21 0.27 0.52
1951 0.335 1.28 0.73 0.77 0.93 1.32 1.66 2.13 0.26 0.54
1950 0.345 1.22 0.74 0.77 0.93 1.30 1.63 2.06 0.24 0.54
1949 0.343 1.27 0.74 0.77 0.94 1.32 1.67 2.12 0.25 0.54
1948 0.340 1.28 0.74 0.77 0.94 1.32 1.67 2.13 0.26 0.54
1947 0.335 1.30 0.73 0.77 0.94 1.33 1.68 2.16 0.26 0.53
1946 0.328 1.38 0.73 0.76 0.94 1.36 1.73 2.26 0.28 0.52
1945 0.329 1.38 0.74 0.77 0.95 1.36 1.73 2.26 0.28 0.53
1944 0.325 1.37 0.73 0.76 0.94 1.35 1.73 2.25 0.27 0.53
1943 0.322 1.42 0.73 0.77 0.95 1.38 1.76 2.32 0.28 0.52
1942 0.323 1.39 0.73 0.77 0.95 1.36 1.74 2.27 0.28 0.53
1941 0.334 1.30 0.74 0.77 0.94 1.33 1.68 2.15 0.26 0.54
1940 0.334 1.25 0.73 0.76 0.92 1.30 1.63 2.08 0.25 0.53
1939 0.342 1.23 0.74 0.77 0.93 1.30 1.64 2.07 0.25 0.55
1938 0.342 1.23 0.74 0.77 0.93 1.30 1.63 2.06 0.25 0.55
1937 0.344 1.23 0.74 0.77 0.93 1.30 1.63 2.06 0.25 0.54
1936 0.348 1.19 0.75 0.78 0.94 1.29 1.62 2.02 0.24 0.56
1935 0.341 1.23 0.74 0.77 0.93 1.30 1.63 2.06 0.25 0.55
1934 0.340 1.23 0.74 0.77 0.93 1.30 1.63 2.06 0.25 0.55
1933 0.329 1.30 0.73 0.76 0.93 1.33 1.68 2.15 0.26 0.54
1932 0.336 1.22 0.73 0.76 0.92 1.29 1.62 2.05 0.24 0.54
1931 0.339 1.25 0.74 0.77 0.93 1.31 1.65 2.09 0.25 0.55
1930 0.354 1.13 0.75 0.78 0.92 1.26 1.56 1.93 0.23 0.56
1929 0.352 1.18 0.75 0.78 0.93 1.28 1.60 2.00 0.24 0.55
1928 0.343 1.25 0.74 0.77 0.93 1.31 1.65 2.09 0.25 0.54
1927 0.344 1.25 0.74 0.78 0.94 1.31 1.65 2.10 0.25 0.54
1926 0.343 1.27 0.74 0.77 0.94 1.32 1.66 2.12 0.25 0.54
1925 0.353 1.21 0.76 0.79 0.94 1.31 1.63 2.05 0.24 0.56
1924 0.347 1.27 0.75 0.78 0.95 1.33 1.68 2.13 0.25 0.55
1923 0.346 1.27 0.75 0.78 0.95 1.33 1.68 2.13 0.25 0.55
1922 0.347 1.25 0.75 0.78 0.94 1.32 1.66 2.10 0.25 0.55
1921 0.347 1.26 0.75 0.78 0.94 1.32 1.66 2.11 0.25 0.55
1920 0.334 1.37 0.74 0.78 0.96 1.37 1.73 2.25 0.27 0.54
1919 0.318 1.38 0.72 0.75 0.93 1.34 1.72 2.25 0.28 0.51
1918 0.316 1.47 0.72 0.75 0.95 1.38 1.78 2.37 0.29 0.50
1917 0.311 1.47 0.71 0.75 0.94 1.38 1.77 2.36 0.29 0.50
1916 0.312 1.48 0.72 0.75 0.95 1.39 1.79 2.39 0.30 0.50
1915 0.318 1.46 0.73 0.77 0.96 1.40 1.79 2.36 0.29 0.53
1914 0.321 1.42 0.73 0.76 0.95 1.37 1.76 2.31 0.28 0.52
1913 0.324 1.35 0.72 0.75 0.93 1.34 1.70 2.22 0.27 0.51
1912 0.337 1.28 0.74 0.77 0.93 1.32 1.66 2.13 0.26 0.53
1911 0.336 1.29 0.73 0.77 0.93 1.32 1.67 2.14 0.26 0.53
1910 0.316 1.42 0.72 0.75 0.94 1.36 1.75 2.30 0.28 0.51
1909 0.306 1.48 0.71 0.75 0.94 1.38 1.78 2.38 0.30 0.51
1908 0.296 1.51 0.70 0.74 0.93 1.39 1.80 2.42 0.30 0.50
1907 0.304 1.48 0.71 0.75 0.94 1.39 1.79 2.38 0.30 0.51
1906 0.306 1.46 0.71 0.75 0.94 1.38 1.77 2.35 0.29 0.51
1905 0.307 1.41 0.71 0.75 0.93 1.35 1.73 2.28 0.28 0.52
1904 0.299 1.43 0.70 0.74 0.92 1.35 1.74 2.30 0.29 0.51
1903 0.315 1.31 0.72 0.76 0.93 1.32 1.67 2.15 0.26 0.55
1902 0.322 1.32 0.73 0.76 0.93 1.33 1.68 2.17 0.26 0.54
1901 0.324 1.25 0.74 0.77 0.93 1.30 1.64 2.07 0.25 0.57
1900 0.338 1.20 0.75 0.78 0.93 1.29 1.62 2.02 0.24 0.57
1899 0.341 1.19 0.76 0.79 0.94 1.30 1.62 2.01 0.24 0.58
1898 0.333 1.26 0.75 0.78 0.95 1.33 1.67 2.10 0.25 0.58
1897 0.353 1.11 0.76 0.79 0.94 1.27 1.57 1.91 0.22 0.59
1896 0.353 1.09 0.76 0.79 0.93 1.26 1.56 1.88 0.22 0.59
1895 0.359 1.04 0.77 0.80 0.94 1.25 1.53 1.82 0.21 0.62
1894 0.377 0.96 0.79 0.81 0.93 1.22 1.48 1.72 0.19 0.62
1893 0.356 1.08 0.78 0.81 0.95 1.27 1.56 1.87 0.22 0.62
1892 0.314 1.27 0.74 0.77 0.93 1.31 1.66 2.09 0.25 0.59
1891 0.329 1.19 0.76 0.78 0.94 1.30 1.62 1.99 0.24 0.61
1890 0.334 1.15 0.76 0.79 0.94 1.28 1.59 1.94 0.23 0.62
1889 0.332 1.14 0.75 0.78 0.93 1.27 1.57 1.92 0.23 0.60
1888 0.291 1.26 0.70 0.73 0.89 1.27 1.61 2.05 0.25 0.56
1887 0.330 1.07 0.74 0.76 0.90 1.22 1.51 1.82 0.21 0.60
1886 0.300 1.22 0.73 0.76 0.92 1.29 1.62 2.01 0.24 0.61
1885 0.286 1.33 0.73 0.77 0.94 1.34 1.69 2.14 0.27 0.62
1884 0.276 1.31 0.72 0.75 0.92 1.32 1.67 2.12 0.26 0.62
1883 0.284 1.24 0.73 0.76 0.92 1.29 1.63 2.02 0.25 0.63
1882 0.274 1.31 0.72 0.75 0.92 1.31 1.66 2.10 0.26 0.62
1881 0.287 1.33 0.72 0.76 0.93 1.33 1.69 2.15 0.27 0.60
1880 0.265 1.38 0.70 0.73 0.91 1.32 1.70 2.19 0.28 0.59
1879 0.269 1.33 0.71 0.74 0.91 1.31 1.67 2.13 0.27 0.60
1878 0.279 1.38 0.72 0.76 0.94 1.35 1.72 2.21 0.28 0.60
1877 0.290 1.30 0.73 0.76 0.93 1.32 1.67 2.11 0.26 0.61
1876 0.277 1.31 0.73 0.77 0.94 1.33 1.68 2.10 0.26 0.65
1875 0.257 1.32 0.73 0.76 0.93 1.33 1.68 2.11 0.26 0.66
1874 0.283 1.16 0.76 0.79 0.94 1.29 1.60 1.90 0.23 0.72
1873 0.303 1.05 0.79 0.82 0.95 1.27 1.55 1.77 0.21 0.76
1872 0.299 1.04 0.80 0.82 0.96 1.27 1.55 1.75 0.21 0.78
1871 0.312 0.92 0.80 0.82 0.94 1.22 1.47 1.61 0.18 0.78

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