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Deviants At Work

By Bill James

June 11, 2013

The standard deviation of OPS for all players in baseball history with 300 plate appearances in a season is .111; the average is .743 with a standard deviation of .111.

On that scale the highest OPS of all time (1.477 by Bonds in 2002) is 6.59 Standard Deviations above the norm. ..quite an astonishing figure, and a number that would probably never occur if OPS had a "normal" bell-shaped curve. The lowest OPS ever (300 or more Plate Appearances) was .310 by Will White (primarily a pitcher) in 1879. The lowest OPS ever by a non-pitcher was .319, by Bill Bergen in 1909. White’s figure is 3.89 standard deviations below the norm; Bergen’s is 3.81.

Of course, some of the "spread" or deviation is accounted for by fluctuations in year-to-year norms. This chart gives the average OPS (for a player with 300 Plate Appearances) and the Standard Deviations of OPS for every year since 1876. The normal standard deviation now is .094:

YEAR	Count	Avg OPS	St Dev
1876	15	.727	.120
1879	41	.645	.126

1880	44	.631	.100
1881	44	.675	.096
1882	75	.659	.106
1883	117	.655	.106
1884	167	.654	.123
1885	103	.658	.113
1886	124	.665	.124
1887	121	.740	.121
1888	119	.638	.103
1889	118	.722	.102
1890	185	.719	.115

1891	122	.700	.105
1892	106	.669	.097
1893	89	.766	.102
1894	93	.840	.123
1895	91	.789	.123
1896	90	.773	.107
1897	99	.764	.106
1898	102	.703	.095
1899	105	.736	.105

1900	62	.743	.096
1901	129	.717	.117
1902	122	.703	.107
1903	129	.693	.103
1904	141	.644	.099
1905	135	.659	.094
1906	134	.651	.095
1907	133	.647	.079
1908	135	.626	.088
1909	134	.650	.091

1910	133	.680	.092
1911	126	.728	.107
1912	123	.734	.095
1913	126	.706	.097
1914	196	.696	.099
1915	199	.683	.089
1916	126	.672	.085
1917	136	.663	.088
1918	111	.678	.100
1919	115	.706	.087

1920	135	.733	.121
1921	133	.780	.111
1922	134	.780	.114
1923	139	.769	.122
1924	141	.769	.110
1925	136	.803	.114
1926	134	.774	.105
1927	131	.773	.119
1928	130	.782	.120
1929	132	.810	.124

1930	135	.822	.142
1931	137	.768	.119
1932	139	.772	.112
1933	133	.742	.111
1934	140	.771	.112
1935	141	.770	.100
1936	140	.786	.120
1937	142	.772	.122
1938	132	.778	.112
1939	143	.784	.106

1940	138	.763	.115
1941	134	.750	.118
1942	134	.711	.102
1943	131	.701	.088
1944	135	.718	.110
1945	132	.721	.096
1946	137	.729	.103
1947	135	.749	.101
1948	136	.761	.104
1949	134	.766	.103

1950	135	.791	.103
1951	131	.766	.096
1952	136	.731	.093
1953	134	.771	.104
1954	134	.757	.112
1955	135	.770	.109
1956	132	.772	.110
1957	139	.754	.113
1958	131	.763	.105
1959	135	.760	.096

1960	135	.751	.097
1961	157	.773	.112
1962	173	.761	.093
1963	171	.719	.095
1964	184	.727	.105
1965	174	.723	.102
1966	173	.728	.097
1967	174	.707	.106
1968	167	.679	.099
1969	199	.735	.114

1970	212	.752	.118
1971	209	.722	.101
1972	200	.707	.102
1973	227	.729	.101
1974	218	.718	.092
1975	216	.727	.098
1976	221	.705	.089
1977	238	.752	.105
1978	229	.728	.095
1979	238	.753	.102

1980	240	.739	.097
1981	156	.730	.093
1982	230	.738	.094
1983	245	.740	.090
1984	237	.729	.092
1985	229	.742	.087
1986	242	.745	.087
1987	240	.774	.104
1988	237	.722	.089
1989	240	.721	.088

1990	236	.739	.089
1991	230	.735	.092
1992	245	.722	.091
1993	250	.765	.100
1994	209	.796	.115
1995	232	.790	.106
1996	258	.797	.112
1997	251	.784	.106
1998	272	.783	.105
1999	281	.804	.110

2000	274	.814	.118
2001	267	.786	.118
2002	271	.774	.112
2003	272	.785	.107
2004	276	.793	.101
2005	284	.774	.093
2006	271	.798	.098
2007	279	.784	.098
2008	281	.776	.092
2009	284	.776	.092

2010	270	.762	.094
2011	265	.749	.094
2012	265	.757	.094

The highest-ever norm for OPS was .840, in 1894, and the highest standard deviation was .142, in 1930. 1894 and 1930 were both huge hitter’s seasons; 1930 also had the second-highest OPS norm of all time, .822.

With this information we can easily state each player’s OPS in terms of standard deviations above or below the norm. This makes surprisingly little difference at the extremes. The average OPS in 2002 was .774, but the standard deviation was only .112—almost the same as the overall historical average--so Bonds was still 6.30 standard deviations above the norm that year, and 6.20 above the norm in 2004. It is interesting to look at Bonds and the steroid era in this light. In 1998, when McGwire hit 70 home runs, his OPS was 4.17 standard deviations above the norm for that season. This made him the first player in 41 years to be four standard deviations above the norm, the last previous being Ted Williams in 1957. At that time McGwire was only the 12^th "player" in history to be four standard deviations above the norm. The others were Babe Ruth (7 times) and Ted Williams (4 times).

Then came Bonds; he was +5.02 in 2001, +6.30 in 2002, +4.62 in 2003, and +6.20 in 2004. Do you know what it means to be six standard deviations above the norm? In a normally distributed population, only one data point in 500 million would be six standard deviations above the norm. There are only 22,500 player/seasons in baseball history with 300 plate appearances. Even though OPS is not normally distributed—nothing in baseball is—it is extraordinary to have data points which are six standard deviations above the norm. The public just revolted; they couldn’t deal with those kind of numbers, although, of course, they weren’t looking at the numbers in that form.

On the other end of the scale Bergen is still the worst, even normalizing for the year, and his number doesn’t change very much, either. With a .319 OPS in 1909, Bergen was 3.91 standard deviations below the norm. The average OPS for 1909 was just .650, but the standard deviation was .091, so, even normalizing for the era, Bergen is still 3.63 standard deviations below the norm, still the worst ever, and not really much less bad in this form than in the other.

The only seasons in history which are 3 standard deviations below the norm, year adjusted, are Bill Bergen in 1906 (-3.08) and Bill Bergen in 1908 (-3.63).

Here’s an interesting note for a 1980s Royals fan. In 1985 one of the Royals’ shortstops was Onix Concepcion, who had a .500 OPS, which was 2.76 standard deviations below the norm for 1985. At that time that was the 10^th-worst figure of all time. It would now be the 12^th-worst. In 1986 the Royals replaced Concepcion with Angel Salazar. In 1987 Salazar had an OPS of .465, which was 2.98 standard deviations below the norm—the third-worst figure of all time.

Through 2012 there have been 10,656 player/seasons which were above the league norm, and 11,808 which were below the league norm. 3,424 seasons have been at least one standard deviation above the norm, and 3,377 at least 1.0000 standard deviations below the norm. 69.8% of all seasons have been within one standard deviation of the norm.

In history (through 2011):

2 seasons have been 6.00 standard deviations above the norm (both by Bonds),

5 seasons have been 5.00 standard deviations above the norm (all by Bonds and Ruth),

16 seasons have been 4.00 standard deviations above the norm,

118 seasons have been 3.00 standard deviations above the norm,

732 seasons have been 2.00 standard deviations above the norm,

3424 seasons have been at least 1.00 standard deviation above the norm,

3377 seasons have been at least 1.00 standard deviation below the norm,

263 seasons have been 2.00 standard deviations below the norm,

2 seasons (both by Bill Bergen) have been 3.00 standard deviations below the norm.

The "elimination of the norms" discussed by the late, great Stephen Jay Gould is observable in the data, but not terribly significant. From 1876 to 1919 the average OPS was .696, and the average standard deviation was .103, so the deviation was 15% of the norm. From 1920 to 1968 the average OPS was .757 and the average standard deviation was .108, so the deviation was 14% of the norm. From 1969 through 2012 the average OPS was .756, and the average standard deviation was .100, so the deviation was 13% of the norm. In the 21^st century the standard deviation has been 12% of the norm.

Let’s look at the careers of twelve players, stating their OPS as standard deviations above and below the norm. ..I’ll do Cobb, Ruth, Bonds, Hornsby, Mantle, Musial, Miguel Cabrera, Mazeroski, Bergen, Hal Lanier, Tim Wallach and Steve Garvey, and I’ll put those in chronological order. What the heck; I’ll do Norm Cash, too; I should always do Norm Cash. And Bill Buckner. And Bill Bruton. OK, that’s 15. These numbers are not park- or position-normalized, so whoever led the league in OPS would have the highest OPS in terms of standard deviations above the norm. We’re not including any seasons with less than 300 plate appearances, since the study is of players with 300 or more plate appearances in a season.

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Bill	Bergen	1901	1	17	.179	.433	-2.42
Bill	Bergen	1902	0	36	.180	.438	-2.48
Bill	Bergen	1904	0	12	.182	.411	-2.37

Bill	Bergen	1906	0	19	.159	.359	-3.08
Bill	Bergen	1908	0	15	.175	.404	-2.52
Bill	Bergen	1909	1	15	.139	.319	-3.63

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Ty	Cobb	1906	1	34	.316	.749	+1.04
Ty	Cobb	1907	5	119	.350	.853	+2.59
Ty	Cobb	1908	4	108	.324	.842	+2.45
Ty	Cobb	1909	9	107	.377	.947	+3.25

Ty	Cobb	1910	8	91	.383	1.008	+3.56
Ty	Cobb	1911	8	127	.420	1.088	+3.35
Ty	Cobb	1912	7	83	.409	1.040	+3.22
Ty	Cobb	1913	4	67	.390	1.002	+3.06
Ty	Cobb	1914	2	57	.368	.979	+2.85

Ty	Cobb	1915	3	99	.369	.973	+3.25
Ty	Cobb	1916	5	68	.371	.944	+3.19
Ty	Cobb	1917	6	102	.383	1.014	+3.99
Ty	Cobb	1918	3	64	.382	.955	+2.78
Ty	Cobb	1919	1	70	.384	.944	+2.72

Ty	Cobb	1920	2	63	.334	.867	+1.11
Ty	Cobb	1921	12	101	.389	1.048	+2.42
Ty	Cobb	1922	4	99	.401	1.026	+2.16
Ty	Cobb	1923	6	88	.340	.882	+0.93
Ty	Cobb	1924	4	74	.338	.866	+0.88

Ty	Cobb	1925	12	102	.378	1.066	+2.29
Ty	Cobb	1927	5	93	.357	.912	+1.18
Ty	Cobb	1928	1	40	.323	.809	+0.23

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Rogers	Hornsby	1916	6	65	.313	.814	+1.66
Rogers	Hornsby	1917	8	66	.327	.868	+2.33
Rogers	Hornsby	1918	5	60	.281	.764	+0.86
Rogers	Hornsby	1919	8	71	.318	.814	+1.24

Rogers	Hornsby	1920	9	94	.370	.990	+2.13
Rogers	Hornsby	1921	21	126	.397	1.097	+2.86
Rogers	Hornsby	1922	42	152	.401	1.181	+3.53
Rogers	Hornsby	1923	17	83	.384	1.086	+2.59
Rogers	Hornsby	1924	25	94	.424	1.203	+3.95

Rogers	Hornsby	1925	39	143	.403	1.245	+3.86
Rogers	Hornsby	1926	11	93	.317	.851	+0.72
Rogers	Hornsby	1927	26	125	.361	1.035	+2.21
Rogers	Hornsby	1928	21	94	.387	1.130	+2.90
Rogers	Hornsby	1929	39	149	.380	1.139	+2.64

Rogers	Hornsby	1931	16	90	.331	.996	+1.92

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Babe	Ruth	1918	11	66	.300	.966	+2.89
Babe	Ruth	1918	29	114	.322	1.114	+4.37

Babe	Ruth	1920	54	137	.376	1.379	+5.36
Babe	Ruth	1921	59	171	.378	1.359	+5.22
Babe	Ruth	1922	35	96	.315	1.106	+2.87
Babe	Ruth	1923	41	131	.393	1.309	+4.42
Babe	Ruth	1924	46	121	.378	1.252	+4.39

Babe	Ruth	1925	25	66	.290	.936	+1.16
Babe	Ruth	1926	47	146	.372	1.253	+4.54
Babe	Ruth	1927	60	164	.356	1.258	+4.09
Babe	Ruth	1928	54	142	.323	1.172	+3.25
Babe	Ruth	1929	46	154	.345	1.128	+2.55

Babe	Ruth	1930	49	153	.359	1.225	+2.84
Babe	Ruth	1931	46	163	.373	1.194	+3.59
Babe	Ruth	1932	41	137	.341	1.146	+3.33
Babe	Ruth	1933	34	103	.301	1.023	+2.54
Babe	Ruth	1934	22	84	.288	.985	+1.90

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Stan	Musial	1942	10	72	.315	.888	+1.74
Stan	Musial	1943	13	81	.357	.988	+3.27
Stan	Musial	1944	12	94	.347	.990	+2.48

Stan	Musial	1946	16	103	.365	1.021	+2.84
Stan	Musial	1947	19	95	.312	.902	+1.51
Stan	Musial	1948	39	131	.376	1.152	+3.77
Stan	Musial	1949	36	123	.338	1.062	+2.88

Stan	Musial	1950	28	109	.346	1.034	+2.35
Stan	Musial	1951	32	108	.355	1.063	+3.09
Stan	Musial	1952	21	91	.336	.970	+2.57
Stan	Musial	1953	30	113	.337	1.046	+2.66
Stan	Musial	1954	35	126	.330	1.036	+2.49

Stan	Musial	1955	33	108	.319	.974	+1.88
Stan	Musial	1956	27	109	.310	.908	+1.23
Stan	Musial	1957	29	102	.351	1.034	+2.47
Stan	Musial	1958	17	62	.337	.996	+2.22
Stan	Musial	1959	14	44	.255	.792	+0.33

Stan	Musial	1960	17	63	.275	.841	+0.92
Stan	Musial	1961	15	70	.288	.898	+1.11
Stan	Musial	1962	19	82	.330	.926	+1.78
Stan	Musial	1963	12	58	.255	.747	+0.29

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Mickey	Mantle	1951	13	65	.267	.792	+0.27
Mickey	Mantle	1952	23	87	.311	.924	+2.08
Mickey	Mantle	1953	21	92	.295	.895	+1.20
Mickey	Mantle	1954	27	102	.300	.933	+1.57

Mickey	Mantle	1955	37	99	.306	1.042	+2.51
Mickey	Mantle	1956	52	130	.353	1.169	+3.62
Mickey	Mantle	1957	34	94	.365	1.177	+3.73
Mickey	Mantle	1958	42	97	.304	1.035	+2.59
Mickey	Mantle	1959	31	75	.285	.904	+1.50

Mickey	Mantle	1960	40	94	.275	.957	+2.12
Mickey	Mantle	1961	54	128	.317	1.135	+3.22
Mickey	Mantle	1962	30	89	.321	1.091	+3.57
Mickey	Mantle	1964	35	111	.303	1.015	+2.74

Mickey	Mantle	1965	19	46	.255	.831	+1.06
Mickey	Mantle	1966	23	56	.288	.927	+2.05
Mickey	Mantle	1967	22	55	.245	.825	+1.10
Mickey	Mantle	1968	18	54	.237	.782	+1.04

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Bill	Bruton	1953	1	41	.250	.636	-1.30
Bill	Bruton	1954	4	30	.284	.701	-0.50

Bill	Bruton	1955	9	47	.275	.728	-0.39
Bill	Bruton	1956	8	56	.272	.723	-0.45
Bill	Bruton	1957	5	30	.278	.755	+0.01
Bill	Bruton	1958	3	28	.280	.696	-0.64
Bill	Bruton	1959	6	41	.289	.735	-0.25

Bill	Bruton	1960	12	54	.286	.758	+0.07
Bill	Bruton	1961	17	63	.257	.712	-0.54
Bill	Bruton	1962	16	74	.278	.776	+0.16
Bill	Bruton	1963	8	48	.256	.708	-0.11
Bill	Bruton	1964	5	33	.277	.745	+0.17

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Norm	Cash	1960	18	63	.286	.903	+1.57
Norm	Cash	1961	41	132	.361	1.148	+3.34
Norm	Cash	1962	39	89	.243	.894	+1.44
Norm	Cash	1963	26	79	.270	.856	+1.45
Norm	Cash	1964	23	83	.257	.804	+0.73

Norm	Cash	1965	30	82	.266	.883	+1.57
Norm	Cash	1966	32	93	.279	.829	+1.04
Norm	Cash	1967	22	72	.242	.783	+0.71
Norm	Cash	1968	25	63	.263	.816	+1.37
Norm	Cash	1969	22	74	.280	.831	+0.85

Norm	Cash	1970	15	53	.259	.823	+0.60
Norm	Cash	1971	32	91	.283	.903	+1.79
Norm	Cash	1972	22	61	.259	.802	+0.93
Norm	Cash	1973	19	40	.262	.828	+0.99

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Bill	Mazeroski	1957	8	54	.283	.725	-0.26
Bill	Mazeroski	1958	19	68	.275	.747	-0.15
Bill	Mazeroski	1959	7	59	.241	.621	-1.44

Bill	Mazeroski	1960	11	64	.273	.712	-0.40
Bill	Mazeroski	1961	13	59	.265	.678	-0.84
Bill	Mazeroski	1962	14	81	.271	.733	-0.30
Bill	Mazeroski	1963	8	52	.245	.629	-0.94
Bill	Mazeroski	1964	10	64	.268	.681	-0.45

Bill	Mazeroski	1965	6	54	.271	.641	-0.80
Bill	Mazeroski	1966	16	82	.262	.694	-0.34
Bill	Mazeroski	1967	9	77	.261	.644	-0.59
Bill	Mazeroski	1968	3	42	.251	.616	-0.63

Bill	Mazeroski	1970	7	39	.229	.607	-1.23

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Hal	Lanier	1964	2	28	.274	.630	-0.93

Hal	Lanier	1965	0	39	.226	.545	-1.74
Hal	Lanier	1966	3	37	.231	.546	-1.86
Hal	Lanier	1967	0	42	.213	.494	-2.00
Hal	Lanier	1968	0	27	.206	.461	-2.19
Hal	Lanier	1969	0	35	.228	.514	-1.95

Hal	Lanier	1970	2	41	.231	.543	-1.77

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Bill	Buckner	1971	5	41	.277	.672	-0.50
Bill	Buckner	1972	5	37	.319	.758	+0.50
Bill	Buckner	1973	8	46	.275	.648	-0.80
Bill	Buckner	1974	7	58	.314	.763	+0.49

Bill	Buckner	1975	6	31	.243	.644	-0.84
Bill	Buckner	1976	7	60	.301	.716	+0.12
Bill	Buckner	1977	11	60	.284	.739	-0.12
Bill	Buckner	1978	5	74	.323	.765	+0.39
Bill	Buckner	1979	14	66	.284	.756	+0.03

Bill	Buckner	1980	10	68	.324	.810	+0.74
Bill	Buckner	1981	10	75	.311	.829	+1.07
Bill	Buckner	1982	15	105	.306	.783	+0.48
Bill	Buckner	1983	16	66	.280	.746	+0.07
Bill	Buckner	1984	11	69	.272	.705	-0.26

Bill	Buckner	1985	16	110	.299	.773	+0.35
Bill	Buckner	1986	18	102	.267	.733	-0.14
Bill	Buckner	1987	5	74	.286	.683	-0.89
Bill	Buckner	1988	3	43	.249	.616	-1.18

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Steve	Garvey	1972	9	30	.269	.734	+0.26
Steve	Garvey	1973	8	50	.304	.766	+0.37
Steve	Garvey	1974	21	111	.312	.811	+1.01

Steve	Garvey	1975	18	95	.319	.827	+1.03
Steve	Garvey	1976	13	80	.317	.813	+1.22
Steve	Garvey	1977	33	115	.297	.834	+0.78
Steve	Garvey	1978	21	113	.316	.852	+1.31
Steve	Garvey	1979	28	110	.315	.848	+0.93

Steve	Garvey	1980	26	106	.304	.808	+0.71
Steve	Garvey	1981	10	64	.283	.732	+0.03
Steve	Garvey	1982	16	86	.282	.718	-0.21
Steve	Garvey	1983	14	59	.294	.802	+0.70
Steve	Garvey	1984	8	86	.284	.680	-0.54

Steve	Garvey	1985	17	81	.281	.748	+0.07
Steve	Garvey	1986	21	81	.255	.699	-0.53

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Tim	Wallach	1982	28	97	.268	.784	+0.49
Tim	Wallach	1983	19	70	.269	.769	+0.33
Tim	Wallach	1984	18	72	.246	.706	-0.25

Tim	Wallach	1985	22	81	.260	.759	+0.20
Tim	Wallach	1986	18	71	.233	.704	-0.47
Tim	Wallach	1987	26	123	.298	.858	+0.80
Tim	Wallach	1988	12	69	.257	.690	-0.36
Tim	Wallach	1989	13	77	.277	.760	+0.45

Tim	Wallach	1990	21	98	.296	.810	+0.81
Tim	Wallach	1991	13	73	.225	.626	-1.18
Tim	Wallach	1992	9	59	.223	.627	-1.04
Tim	Wallach	1993	12	62	.222	.612	-1.52
Tim	Wallach	1994	23	78	.280	.859	+0.54

Tim	Wallach	1995	9	38	.266	.754	-0.34
Tim	Wallach	1996	12	42	.233	.666	-1.17

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Barry	Bonds	1986	16	48	.223	.746	+0.01
Barry	Bonds	1987	25	59	.261	.821	+0.45
Barry	Bonds	1988	24	58	.283	.859	+1.53
Barry	Bonds	1989	19	58	.248	.777	+0.64

Barry	Bonds	1990	33	114	.301	.970	+2.61
Barry	Bonds	1991	25	116	.292	.924	+2.06
Barry	Bonds	1992	34	103	.311	1.080	+3.92
Barry	Bonds	1993	46	123	.336	1.136	+3.70
Barry	Bonds	1994	37	81	.312	1.073	+2.40

Barry	Bonds	1995	33	104	.294	1.009	+2.06
Barry	Bonds	1996	42	129	.308	1.076	+2.50
Barry	Bonds	1997	40	101	.291	1.031	+2.34
Barry	Bonds	1998	37	122	.303	1.047	+2.51
Barry	Bonds	1999	34	83	.262	1.006	+1.84

Barry	Bonds	2000	49	106	.306	1.127	+2.67
Barry	Bonds	2001	73	137	.328	1.379	+5.02
Barry	Bonds	2002	46	110	.370	1.477	+6.30
Barry	Bonds	2003	45	90	.341	1.278	+4.62
Barry	Bonds	2004	45	101	.362	1.422	+6.20

Barry	Bonds	2006	26	77	.270	1.056	+2.65
Barry	Bonds	2007	28	66	.276	1.045	+2.67

First	Last	Year	HR	RBI	Avg.	OPS	OPS Vs. League
Miguel	Cabrera	2003	12	62	.268	.793	+0.08
Miguel	Cabrera	2004	33	112	.294	.879	+0.84

Miguel	Cabrera	2005	33	116	.323	.947	+1.85
Miguel	Cabrera	2006	26	114	.339	.998	+2.05
Miguel	Cabrera	2007	34	119	.320	.965	+1.85
Miguel	Cabrera	2008	37	127	.292	.887	+1.21
Miguel	Cabrera	2009	34	103	.324	.942	+1.80

Miguel	Cabrera	2010	38	126	.328	1.042	+2.97
Miguel	Cabrera	2011	30	105	.344	1.033	+3.01
Miguel	Cabrera	2012	44	139	.330	.999	+2.58

COMMENTS (26 Comments, most recent shown first)

MidnighttheCat
Bill, I suspect that OPS' appeal is that any fan or sports writer can add (especially with a calculator or computer) but not all can multiply fractions or percentages, at least not in their heads.

But yes, the vernacular, like it or not, is often the playing field we have to play on.

What jumped out at me from this list is Bonds' 1992 season - it is, before the wacky numbers later on, the highest standard deviation and is up there with some famous seasons like Musial in 1948. Yet at first glance it appears merely to be a really good season, not quite MVP level.

Anyway, to learn that until Bonds there had only been 12 seasons four or more standard deviations above the norm and that 11 had been by arguably the two greatest hitters ever, Ruth and Williams adds some weight to these methods and also shows how special such seasons are. If McGwire's 1998 could be credited entirely to his own un-enhanced efforts, it would be a great accomplishment to rank even one season in a career in such elite company. That Bonds' pre-2000 best (in terms of standard deviations over OPS norm) previous season ranked with the best of other great hitters tells us something, and as far as the fans' revolt, in part it is about two things: 1) how can we tell anymore what a good or great season or career is if Bonds' 1992 or Musial's 1948 seem ordinary now? and 2) what good are records that can't be broken ever now except by cyborgs ?
5:02 AM Mar 11th

jollydodger
Is the MLB talent distribution (or whichever measure you'd prefer) not a pyramid? Is it a bell curve with everything below the lower first SD cut off?

I looked at the last 10 years or so of the data, and OPS numbers aren't higher. With the added emphasis (or sex appeal) of drawing walks in today's game, it doesn't seem to be helping overall. Of course we know players are taking more strikes, batting with 2 strikes more often, and thus, are striking out at all-time rates.

This leads me to make the leap that drawing walks while not striking out a ton is a trait a player simply has or doesn't have, not something effectively learned.

I'm surprised Cabrera's numbers aren't higher...unless he's just now hitting his groove, which would be amazing.
1:26 AM Jun 22nd

mauimike
After trying to write a funny line or two, creating havoc is one of my favorite things. "Cry Havoc, and let slip the dogs of war." Shakespeare. "Julius Caesar." Always quote Shakespeare when you want to appear smart. Recreational drug use is one of those terms that can mean so many things, that it means nothing. What is a drug? Is it what's legal? good? bad? a life enhancer? a life destroyer? It depends on the time, the government, etc. The, 'War on Drugs' should be called the, 'War on Some Drugs.' Its just another war that this government is losing, with all the new drugs that are being invented, with the drugs getting stronger and better and with hundreds of thousands of people in jail for doing the wrong ones and thousands dying while doing the prescribed ones. Be careful, your favorite drug could become illegal next, alcohol was once and smoking was the height of chic. Don't worry, the NSA, will straighten it all out. Hi, guys. Anyway, good stuff as usual. I don't chose to argue with your numbers.
2:48 AM Jun 19th

bjames
You all know perfectly well what is meant by the term "recreational drug use". Pretending that you don't know is just a way of trying to create havoc within the discussion.
9:16 AM Jun 17th

Brock Hanke
Excellent article, Bill. I do have a couple of comments on side issues that came up in the discussion. The term "recreational drugs" was, as far as I know, coined in the 1960s to describe pot, LSD, magic mushrooms and mescaline (peyote cactus). These drugs were not used for medical or (usually) religious purposes by hippies; they were used for fun - for recreation. I ought to know....

Also, OBP x SLG is not the complete story on estimating Runs Created, because it lacks a "volume of attempts" factor. It just gives you a rate, not RC. What you want, and which is nothing more than algebraic rearrangement of Bill's original Runs Created formula, is OBP x SLG x AB. I imagine that the reason sportswriters don't use this, and why OPS became so popular, is that you can calculate OPS with pencil and paper, if you can add. My formula here requires multiplication of 3-digit numbers, which means you have to use a calculator.

My guess as to why sabermetricians don't use it, other than that you can get an audience for OPS because of sportswriter exposure, is that you're multiplying by AB instead of (AB + BB). This is because OBP uses BB and SLG does not, but it does seem odd and wrong to use AB as the "volume of attempts" factor, instead of a simplified version of PA. - Brock Hanke

8:16 AM Jun 16th

mauimike
"Recreational drug use." What does that mean? Are they drugs taken when we play dodgeball, or ride swings, like soda and candy. Are they drugs that are used to enhance, recreation, like steroids or speed? Are they something that people do, when they're done, recreating? Is it harmful? Or does it help recreation? Does it matter if its legal or not? I don't have an ax to grind here, beer, my drug, is legal, but in 2009, 37,500, people died from prescription drugs and I think they're still trying to find the first person to die from smoking dope, in the history of the world. Does recreational, mean I had fun, doing it? Does it mean, I did it in private and no one measured it and I don't know how much I did and I don't remember what I did and should we just forget about it all, until the morning and like Hemingway, you say, "did the earth move for you?" and she smiles and you know you did good. Or is it something else?
5:08 AM Jun 15th

flyingfish
Ahah, I hadn't read ErnieSS's Ask Bill question, but 1.422 still is better than Lamar's 1.421, again based on ErnieSS's numbers.
4:04 PM Jun 14th

flyingfish
ErnieSS: I don't understand your math. When I add 0.812 and 0.609 your numbers for Lamar's 2004 season, I get 1.421, not 1.422, but in either case, when I compare 1.477, Bonds's record year, to either 1.421 or 1.422, I have to conclude that Bonds's record still stands.
4:00 PM Jun 14th

bjames
1) I’ve never liked OPS, and I do agree that On Base * Slugging would have been a better measure than On Base + Slugging, but OPS has become a accepted industry standard. It has its flaws, but all stats do; I still use winning percentage, ERA, RBI, and fielding percentages. They all have obvious flaws.

If you want to be a part of the general conversation, you have to speak the language that everybody else speaks. OPS is the language that everybody speaks now.

2) The real problem with using z-scores to identify steroid users is that it is unethical to speculate about matters such as steroid use based on something as flimsy as an unusual pattern of OPS production. Like speculation about other people’s sex lives or recreational drug use, it’s just gossip. It doesn’t belong in a knowledge- and learning-based environment.

8:22 AM Jun 14th

ErnieSS
Such a good article that I hate pointing out the little quibbles, but the all-time OPS season was not Bonds' 1.477 in 2002, as stated.

It was Lamar's 2004 year, when he combined an .812 SLG with that absurd OBP of .609...thus 1.422 is the record.
3:56 AM Jun 13th

Robinsong
What Bill has explained is that major league players are the upper tail of a distribution. There are many more players - most in the minor leagues or washed out - who can hit for one standard deviation below the major league average than can hit for one standard deviation above that average. Players who are two deviations below the average cannot play for long since they are well below replacement level. I would hit for 6 standard deviations below the major league average, but then I am an un-athletic 57-year-old. Someone like Hal Lanier can only stick around because the Giants had a shortage of talent in the middle of the infield, the management did a bad job of identifying alternatives, and he could field like a dream. The distribution of major league talent is not only not normally distributed; it is not symmetric around the average.

You also have to be careful using z-scores to identify steroid users. Babe Ruth did not use steroids (because they had not been invented, otherwise he probably would have), yet he set the records Bonds broke. Was Brian Downing a steroid user because he had a late-career surge in OPS? Maybe, but there are other possible explanations.
8:57 PM Jun 12th

keenanj
wovenstrap wrote:
Bill often emphasizes that MLB isn't normally distributed -- can someone explain how that fact affects the numbers we're seeing here? In other words, do they make a z-score of 5 a bit less astounding? Perhaps keenanj can explain?
---
This is a good question. The answer, in reality is that you can't use standard inferential statistics (like t-tests) and it becomes difficult to know exactly what the numbers are (in a precise manner) when you don't have a normal distribution

Let me use and example. If you have a normal distribution, the mean, mode, and median are equal. Thus if you are average (z-score of 0) such that your IQ is 100, you know that you are smarter than 50% of the people, and not as smart as the other 50%.
Without a normal distribution, you don't know this. There are other stats you can use for non-normally distributed data. If Jim Rice had an OPS that gave him a z-score of 0 in a non-normal distribution, he might be in the top 45% (extreme scores called outliers will typically ruin nice normal distributions). He may be in the top 55%.

The normal curve has other properties, such that a z-score of +1 would mean you are higher than 84.13% of the population. Thus if Jim Rice had a z-score of 1 (or was 1 SD above the mean) he would basically be in the top 15%. But we would only be able to be that precise if the data are normally distributed.

To address your question in another way, we don't know without the raw data if a the z-score is more or less extreme. However, normal or not, if you see z-scores like those of Barry Bonds with a fair number of population or sample observations, there is something pretty significant going. These numbers suggest freakish performance that others have talked about for years. Clearly, it is pointed out in the article how rare this is. Looking at the SDs it really is incredible. It may be that Barry was that great or he had access to steroids that no one else had. The IQ equivalent would be an IQ of 190 when an IQ of 100 was a typical MENSA IQ. Remember, his +6 is compared to a pool of (some) steroid users. If we compared his mid 2000 numbers to the dead ball era, a z-score of +6 would still be incredible. But, if I am understanding the article correctly, each z-score is against the year. Therefore, Bonds compared to other enhancers is still way ahead.

Had you gotten a z-score of +3 on your SATs, you would have had a good chance of going Harvard (or at least could have). Though the SAT's (back in my day) stopped at +3 SDs, if a person DID get a +6, it would raise every flag of cheating. Alarms would go off, computer programs would beep. Now, imagine getting that on your SATs while a good portion of the class is also cheating. I don't want to harp on the steroids other than to say this extreme event (Bonds' OPS) is made even more extreme because the mean is inflated by the other users.

Again, Mr. Bill James is much better at writing and explaining than I. I wasn't kidding in suggesting that this article is really the best explanation of extreme z-scores.

4:19 PM Jun 12th

mvandermast
In 1961, all hitters except one had an OPS below the Norm...
3:56 PM Jun 12th

Arrojo
Somewhat off topic, but isn't OTS (on base x slugging) actually a closer estimate of Runs Created (and thus a better indicator of offensive worth) than OPS?
2:52 PM Jun 12th

wovenstrap
Responding to danfeinstein: I think Bill has it about right, there was widespread irritation about Bonds. It's pretty amazing to consider that Bonds broke Henry Aaron's career record for home runs but ESPN and other outlets mostly pretended it wasn't happening. It was just a terribly contradictory and frustrating situation which resulted in Bonds not being signed when he clearly could play and so on. I don't take record-keeping type stats that seriously and I'm not particularly anti-steroid or anything, but that "762" at the top of the career HR list just bothers me, it's a kind of stain.
12:46 PM Jun 12th

wovenstrap
Bill often emphasizes that MLB isn't normally distributed -- can someone explain how that fact affects the numbers we're seeing here? In other words, do they make a z-score of 5 a bit less astounding? Perhaps keenanj can explain?
12:42 PM Jun 12th

KaiserD2
What jumped out at me was that higher standard deviations correlated very strongly with jumps in offense--see 1930, 1969-70, 1987, and then, of course, the steroid era.

What then occurred to me, in re the discussion of Bonds and McGwire, was that this method could be used to develop a reasonable approximation of who benefited substantially from drugs. The tip-off would be exceeding a high, and unprecedented, number of standard deviations relatively late in life. Of course, as time went on people began using them earlier---A Rod's biography claims he used them before he was in organized baseball--so this won't help identify more recent players.

Lastly, based on one presentation I heard at SABR in particular, OPS isn't a particularly accurate measure of total value because, according to the presenter, an extra point of OBP is worth two extra points of SLG.
8:09 AM Jun 12th

danfeinstein
Bonds in his final season was better, per PA, than Cabrera was last year in his Triple Crown season, then offered to play the next season for the league minimum ... sure there wasn't collusion keeping him from one more year.

And I'm not sure that I'd agree with Bill's assertion that "[t]he public just revolted ..." There was a lot of ink spilled and talk radio waves filled, but fans kept going to games in record numbers and the value of franchises skyrocketed. If there was a meaningful revolt, the elephant would have left tracks all over the room, but I don't see that in the data.

My pet theory - without any proof whatsoever - is that fans love having a 'heel' to root against and that Barry Bonds was just about the perfect heel; haughty, arrogant, aloof, and amazingly good. Football misses the Raiders, college hoops is better when Duke is good, and Barry Bonds was loved to be hated.
7:59 AM Jun 12th

keenanj
I teach statistics. I think I am going to use this for my class. The # of standard deviations away from the mean is often called a z-score (Cabrera has a z-score of +1.85 in 2005). Typically, if the data have a normal distribution, anything above +2 or below -2 is rare (less than 5% occurrence).
Bonds has such insane numbers. Given that he wasn't the only one doing steroids, it is incredible to think that he could be so outside the norm.
This is a great, simple presentation of why SD is important. I wonder how many GMs understand what SD is.

6:39 AM Jun 12th

rgregory1956
Bergen was so bad, I wonder if the Dodgers' owner was on the take.
9:25 PM Jun 11th

hotstatrat
Under a corollary of the Norm Cash rule, I am obliged to point out that the '68 World Champion Tigers' most regular shortstop Ray Oyler was -2.83 standard deviations from the norm, but didn't quite make 300 PA.

It's interesting that so many players in your sample had their best OPS seasons near the end of their career as a regular. Of course, that doesn't consider how many plate appearances they were over 300 or how much their range had deteriorated in the field.

Billy Bruton's best OPS season by this way of looking at it was his last (1964), yet he still had enough speed to play center-field and steal 14 out of 19 bases. The '64 Tigers also had Al Kaline, Don Demeter, and George Thomas all of whom could play center and Gates Brown, who was probably the fastest runner on the team. Bruton was released at the end of the season to make way for their impressive September call-ups Willie Horton and Jim Northrup. By the following September they called-up-for-good a gold glove center-fielder: Mickey Stanley.

I noticed one of your favorite players, Bill: Ed Charles had his best season in standard deviations from the norm in his final year of 300 PA producing a +0.83. By the next season (1969), he was a 36 year old New York Met making way for the 21 year old Wayne Garrett. Perhaps, that wasn't such a good plan. Garrett's OPS was a -1.55 standard deviations from the norm, but the Mets won the World Championship that year.

9:23 PM Jun 11th

chuck
Bergen's standard deviation is so bad in 1906 and 1909... makes me wonder if he was on the take. Like Bonds, that kind of performance just isn't natural.
6:46 PM Jun 11th

Robinsong
Note that in 1992, Bonds beat Musial's best season. He was an all-time great talent, even without steroids.
5:12 PM Jun 11th

Robinsong
Wonderful analysis. I will try and look and the standard deviation of OPS+ (park and era adjusted) both aggregate and by position. Bonds would not be quite as far an outlier adjusted for position.
5:09 PM Jun 11th

bjjp2
Would love to see this for other sports. Gretzky? Chamberlain?
12:12 PM Jun 11th

kimchi
What does the data look like if you multiply OBP & SLG, rather than add them? Wouldn't that be more meaningful?
8:53 AM Jun 11th

Deviants At Work

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