## Wednesday, February 11, 2015

### Using Runs Relative To Average To Determine The Best All Around Careers

See Using Runs Above Average To Determine The Best All Around Careers for a similar analysis.

The idea is to reward balance. I used the Baseball Reference Play Index in the post mentioned above.

In that study, I called up all the seasons with at least 0.1 in each of the following stats: fielding runs (Rfield), base running runs (Rbaser) and batting runs (Rbat). Those are all above average (no seasons came up from 1876-1885, maybe because they don't have SB data for those years).

Then all three stats were multiplied by each other. Then I took the cube root to get the geometric mean.  But that means that any seasons with a negative number or a zero in any of the three stats did not count.

If I use career totals, then there can still be negatives and zeroes so using the cube root probably does not make sense. So here I tried to convert each stat into a rate stat (the explanation is at the end in technical notes). It involved OPS+ and turning the running and fielding stats into something like OPS+. Also, OPS+ itself was adjusted to be an "above replacement" stat. The others were not as it is probably easy to find average runners and fielders in the minors.

That meant that OPS+ went up for most players (if not all). They got credit for more runs and that increased their estimated OPS+. If a player had negative fielding runs, his fielding OPS+ would be less than 100. If positive, above 100 (100 is average in OPS+). Then I found the geometric mean of all three stats. I used all players with 5000+ PAs and their career stats.

Here are the top 25. I don't know if this is better than the other method. Just different. If you look at the complete lists, some players move up quite a bit.

 Rank Player OPS+WAR Run Field Rating 1 Babe Ruth 227.71 98.40 105.51 133.15 2 Barry Bonds 197.59 102.22 110.86 130.76 3 Albert Pujols 184.56 100.50 111.81 127.46 4 Willie Mays 176.96 104.45 111.61 127.24 5 Ted Williams 214.00 99.49 96.58 127.10 6 Rogers Hornsby 198.70 98.54 104.06 126.71 7 Lou Gehrig 206.75 98.36 99.49 126.42 8 Billy Hamilton 177.94 105.10 102.60 124.20 9 Joe DiMaggio 180.51 100.93 104.63 123.93 10 Ty Cobb 186.43 102.64 99.32 123.81 11 Tris Speaker 179.95 99.40 105.70 123.59 12 Mickey Mantle 190.49 103.48 95.88 123.58 13 Jimmie Foxx 188.39 98.93 101.30 123.53 14 Dan Brouthers 197.65 97.42 97.80 123.43 15 Larry Walker 166.61 103.47 109.05 123.36 16 Hank Aaron 175.33 101.89 105.15 123.33 17 Shoeless Joe Jackson 187.26 98.55 100.93 122.98 18 Jeff Bagwell 175.24 102.06 104.05 122.94 19 Roger Connor 177.86 97.75 107.03 122.94 20 Hank Greenberg 182.26 100.15 101.64 122.82 21 Jackie Robinson 160.59 103.71 110.95 122.65 22 Stan Musial 181.03 99.17 102.58 122.51 23 Mel Ott 179.95 98.93 102.99 122.33 24 Chase Utley 148.97 104.06 118.24 122.32 25 Mike Schmidt 166.69 99.20 109.84 121.95