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

Click here to see the complete rankings.

Technical notes: I ran a regression with OPS+ as the dependent variable and batting runs above average per PA as the independent variable. Here is the equation

OPS+ = 832.14*BattingRuns/PA + 99.32

So for all three stats, the runs per PA was plugged into this equation.