Cybermetrics: April 2018

See DiMaggio’s Mysterious Plunge by John B. Holway.

DiMaggio's average was .409 through Sept. 9th but he hit only .233 in his last 73 ABs to finish at .381. One report said he had a virus that had sidelined pitcher Red Ruffing and "Years later Joe would say the cold he had developed on the 9th had caused a painful eye twitch."

But manager Joe McCarthy would not give him a couple of games off to recuperate.

"Can we believe that McCarthy didn’t know that his greatest star — the brightest star in America — was in agony? If he did know, did he really make DiMag stay in the game and suffer? Why???!!! McCarthy was an alcoholic, who kept a brown bag with him on the end of the bench, where he sat alone while the coaches apparently ran the team. He was sometimes referred to as a “push button manager,” the closest anyone came to whispering the problem. Eleven years later he would be found literally in the gutter and was swiftly and quietly whisked home to Buffalo and oblivion. No one then, or now, uttered the word “alcoholism.”"

If the coaches ran the team, it seems like they could have taken DiMaggio out of the lineup or after just one AB to get him some rest.

DiMaggio finished with 462 ABs. That means he needed 185 hits to reach .400. He was 17 for his last 73, and finished with a total of 176 hits. So he was 9 hits short of .400. If he had gone 26 for his last 73, he would have made it. That is still a .356 average and even a guy at .400 has no guarantee of reaching that level for a short spurt.

Using the binomial distribution function in Excel, I get that there is a 15% chance of DiMaggio getting 25 or fewer hits in his last 73 ABs (assuming he was truly a .409 hitter).

But was he truly a .409 hitter that year? Or could have been expected to be in Sept? Players usually hit worse in Sept., perhaps due to colder weather. The Yankees as a team batted .270 in Sept. while it was .287 for the whole season (it was .290 thru Aug.). Using the Baseball Reference Play Index, it looks like the Yankee regulars were still used as much as usual in Sept. Maybe with a big lead, they did not quite have their usual incentive. They never lead by less that 11.5 games the whole month. Anyway, if we reduce DiMaggio by 20 points then we expect only a .389 average from Sept. 10th on.

DiMaggio himself batted .319 in Sept/Oct games in his career while it was .325 overall (.326 thru Aug. for his career). So we had to expect some drop off. Also, in his last 19 games, only 2 were on the road and Yankee stadium was not a good place for righties like DiMaggio (it was 467 feet to left center). In his career, he batted .315 at home and .334 on the road. So maybe we reduce him .008 for this. He is down to .381

DiMaggio also had 78 of his 109 ABs in Sept. against righties. That is 71.6%. It was 66.7% for the whole season. Maybe that is 5 ABs more than usual against righties. In his career, DiMaggio batted .342 vs. lefties and .316 vs. righties. This would be a slight effect. Maybe .001. So he is down to .380

That would get him a .400 AVG for the season (and he finishes at .403 or .404). But what are the odds he can still reach .356 if we assume he was a true .380 hitter?). Using the binomial distribution again, I get a 30% chance that he gets 25 or fewer hits in his last 73 ABs if he is a true .380 hitter. That is a high enough chance that we can't assume it was just his illness, eye twitch and lack of rest due to a bad manager that cost him his .400 season.

Now I might have penalized him too much for a lower Sept. average by the Yankees as a whole. If I cut that penalty in half and we make him a true .390 hitter, there is still a 24% chance he does not get the 26 hits he needed in those last 19 games to finish at .400.

(This was originally published at Beyond the Box Score in 2006)

Most fans know that Gibson had an incredibly low ERA of 1.12 in 1968. Even considering that the league ERA was just 2.98 that year, what he did is still great. What explains this performance? Did Gibson have a great “stuff” year? Was he lucky? Or was it a combination of luck and skill? If so, how much of each?

Luck is sometimes a factor in baseball. Some years a guy hits well with runners in scoring position (RISP), some years he doesn’t. In 2004, A.J. Pierzynski, for example, hit .272 overall but .307 with RISP. In 2005, he hit .257 overall but only .236 with RISP. Its not likely he forgot how to hit with RISP all of the sudden. For pitchers, the batting average they allow on balls in play may be out of their hands (as pointed out by Voros McCracken). A pitcher might get lucky on balls in play one year, with more getting caught than normal (or his fielders might be especially good one year). Is this what happened to Gibson?

To test this, I ran a regression in which a pitcher’s ERA was the dependent variable and his strikeouts, walks and HRs allowed per 9 IP were the independent variables. I used the regression equation to predict each pitcher’s ERA then found out how much it differed from his actual ERA. If a pitcher had an ERA lower than what his strikeouts, walks and HRs allowed per 9 IP predicted, he most likely gave up fewer hits on balls in play than average. Here is the regression equation

(1) ERA = 2.19 + 1.436*HR - .159*SO + .303*BB

Again, all stats are per 9 IP. BB includes both walks and HBP. The data includes all pitchers who qualified for the ERA title from 1963-68 (I used this period since it was an especially low scoring period). There were 420 pitchers. The r-squared was .548, meaning that 54.8% of the variation in ERA across pitchers is explained by the equation. The standard error is .469.

Plugging Gibson’s 1968 data into equation (1) leaves an ERA of 2.02. That is a very large 0.90 above his actual ERA of 1.12. So it appears that he must have done especially well on balls in play (more on this later). The table below shows the leaders in how much lower their predicted ERA was than actual their ERA.

Rank	Pitcher	YEAR	ERA	Pred	Diff
1	Rickey Clark	1967	2.59	3.81	-1.22
2	Joe Horlen	1968	2.37	3.48	-1.11
3	Carl Willey	1963	3.10	4.18	-1.08
4	Lee Stange	1963	2.62	3.68	-1.06
5	Jim Perry	1965	2.63	3.64	-1.01
6	Dave McNally	1968	1.95	2.92	-0.97
7	Tommy John	1968	1.98	2.91	-0.93
8	Bob Gibson	1968	1.12	2.02	-0.90
9	Bob Veale	1968	2.06	2.95	-0.89
10	Joe Horlen	1967	2.06	2.93	-0.87
11	Vern Law	1965	2.16	3.01	-0.85
12	Sonny Siebert	1967	2.38	3.21	-0.83
13	Pete Richert	1965	2.60	3.41	-0.81
14	Joe Horlen	1964	1.88	2.69	-0.81
15	Phil Niekro	1967	1.87	2.68	-0.81
16	Tracy Stallard	1965	3.39	4.19	-0.80
17	Bobby Bolin	1966	2.89	3.69	-0.80
18	Denny McLain	1968	1.96	2.75	-0.79
19	Eddie Fisher	1965	2.40	3.17	-0.77
20	Jim Perry	1966	2.54	3.29	-0.75
21	Luis Tiant	1968	1.60	2.34	-0.74
22	Jim Bouton	1963	2.53	3.26	-0.73
23	Jerry Koosman	1968	2.08	2.80	-0.72
24	Milt Pappas	1965	2.61	3.33	-0.72
25	Steve Blass	1968	2.13	2.85	-0.72

Gibson is not first in “Diff” but he did have a big one at #8 (something intersting is may be going on with the White Sox, with John, Horlen and Fisher all being up there). The table below shows the 25 lowest predicted ERAs.

Rank	Pitcher	YEAR	ERA	Pred
1	Bob Gibson	1968	1.12	2.02
2	Sandy Koufax	1963	1.88	2.06
3	Sandy Koufax	1964	1.74	2.16
4	Sandy Koufax	1965	2.04	2.18
5	Sandy Koufax	1966	1.73	2.20
6	Bob Moose	1968	2.74	2.22
7	Bob Bruce	1964	2.76	2.23
8	Bob Veale	1965	2.84	2.24
9	Bill Singer	1967	2.65	2.24
10	Don Sutton	1968	2.60	2.25
11	Mike Cuellar	1966	2.22	2.28
12	Chris Short	1964	2.20	2.28
13	Sam McDowell	1965	2.18	2.29
14	Gaylord Perry	1966	2.99	2.30
15	Dean Chance	1964	1.65	2.31
16	Luis Tiant	1968	1.60	2.34
17	Jim O'Toole	1964	2.66	2.35
18	Whitey Ford	1964	2.13	2.37
19	Gaylord Perry	1968	2.44	2.37
20	Tom Seaver	1968	2.20	2.38
21	Dean Chance	1968	2.53	2.39
22	Bob Gibson	1967	2.98	2.40
23	Don Drysdale	1964	2.19	2.40
24	Gary Peters	1963	2.33	2.41
25	Mike Cuellar	1968	2.74	2.42

Notice that Gibson’s 1968 season, although the best, does not dominate the way his actual ERA dominates. The next table shows the lowest 25 actual ERAs from the period.

Rank	Pitcher	YEAR	ERA	Pred
1	Bob Gibson	1968	1.12	2.02
2	Luis Tiant	1968	1.60	2.34
3	Dean Chance	1964	1.65	2.31
4	Sandy Koufax	1966	1.73	2.20
5	Sandy Koufax	1964	1.74	2.16
6	Sam McDowell	1968	1.81	2.53
7	Phil Niekro	1967	1.87	2.68
8	Sandy Koufax	1963	1.88	2.06
9	Joe Horlen	1964	1.88	2.69
10	Dave McNally	1968	1.95	2.92
11	Denny McLain	1968	1.96	2.75
12	Bobby Bolin	1968	1.98	2.60
13	Gary Peters	1966	1.98	2.62
14	Tommy John	1968	1.98	2.91
15	Sandy Koufax	1965	2.04	2.18
16	Stan Bahnsen	1968	2.05	2.71
17	Joe Horlen	1967	2.06	2.93
18	Bob Veale	1968	2.06	2.95
19	Jerry Koosman	1968	2.08	2.80
20	Dick Ellsworth	1963	2.10	2.62
21	Whitey Ford	1964	2.13	2.37
22	Steve Blass	1968	2.13	2.85
23	Juan Marichal	1965	2.14	2.67
24	Don Drysdale	1968	2.15	2.63
25	Vern Law	1965	2.16	3.01

In predicted ERA, there are 24 pitchers within .40 or less of Gibson. But in actual ERA, it is only one!. So using only pitcher determined outcomes (strikeouts, walks and HRs allowed), brings Gibson back down to earth. He is the leader, but he is not so far away from the rest of the pitchers.

Now that we have seen these results, lets check to see if Gibson did indeed have a low batting average allowed on balls in play (BABIP) in 1968. The table below shows Gibson’s BABIP for each year of his career along with the BABIP of the entire Cardinal staff (including Gibson). Notice that his lowest BABIP was in 1968 as well as the difference from the Card’s staff. 1968 was also the biggest difference.

YEAR	BABIP-Gibson	BABIP-Cards	Diff
1961	0.283	0.276	0.007
1962	0.249	0.272	-0.023
1963	0.271	0.267	0.004
1964	0.272	0.275	-0.002
1965	0.256	0.273	-0.016
1966	0.240	0.267	-0.027
1967	0.280	0.268	0.012
1968	0.230	0.264	-0.034
1969	0.270	0.269	0.002
1970	0.299	0.293	0.005
1971	0.270	0.291	-0.021
1972	0.263	0.277	-0.014
1973	0.255	0.271	-0.015
1974	0.272	0.274	-0.002
1975	0.303	0.283	0.020

In some years Gibson had a lower BABIP than the Cards staff, in other years, higher. But he definitely had a low BABIP in 1968 (some of the numbers in the “Diff” column may look slightly wrong due to rounding). The next table shows the lowest 25 BABIPs of the period.

Rank	Pitcher	YEAR	BABIP
1	Dave McNally	1968	0.202
2	Joe Horlen	1967	0.214
3	Wally Bunker	1964	0.214
4	Joe Horlen	1964	0.216
5	Luis Tiant	1968	0.216
6	Phil Ortega	1966	0.221
7	Denny McLain	1966	0.221
8	Juan Marichal	1966	0.221
9	Bobby Bolin	1966	0.222
10	Dick Hughes	1967	0.224
11	Carl Willey	1963	0.224
12	Sonny Siebert	1967	0.225
13	George Brunet	1968	0.225
14	Sonny Siebert	1968	0.225
15	Jim Bouton	1964	0.226
16	Ernie Broglio	1963	0.229
17	Lew Krausse	1968	0.229
18	Bob Gibson	1968	0.230
19	Rickey Clark	1967	0.231
20	Pete Richert	1966	0.231
21	Denny McLain	1968	0.231
22	Jim Bouton	1963	0.231
23	Ken McBride	1963	0.233
24	Bobby Bolin	1968	0.233
25	Moe Drabowsky	1963	0.233

Gibson did not have the lowest BABIP, but he was #18.

If we try to predict Gibson’s ERA using regression analysis and also include hits on balls in play, we will be able to predict his ERA much more accurately. I ran a regression in which a pitcher’s ERA was the dependent variable and his non-HR hits, walks and HRs allowed per 9 IP were the independent variables (since I am using what happens on balls in play here, it is not necessary to put stikeouts in-every strikeout means one less chance for a hit and the number of hits is already accounted for in the model).

(2) ERA = -2.17 + 1.397*HR + .466*NONHR + .310*BB

The r-squared was .811, meaning that 81.1% of the variation in ERA across pitchers is explained by the equation. The standard error is .303. I then predicted each pitcher’s ERA using equation (2) and found how much that differed from their actual ERA. It predicted Gibson to have a 1.49 ERA. This is only .37 above his actual ERA, much more accurate than equation (1), which was off by .90. But the point here is not to find which equation is most accurate. The point is that once you include what happens on balls in play, we get a much more accurate picture of Gibson’s performance. And in this case Gibson was off by just 1.22 standard errors (.37/.303) while he was off by 1.92 standard errors with equation (1) (.90/.469). This supports the thesis that Gibson was helped quite a bit by his low BABIP.

A few weeks ago a I posted an article about the best seasons in something called “Fielding Independent ERA” or FIP ERA (see sources at the end of this article). In that article I used a more sophisticated approach than I used here. The lowest 25 FIP ERAs of this period are in the table below.

Rank	Pitcher	YEAR	FIP ERA
1	Sam McDowell	1965	1.96
2	Bob Gibson	1968	2.21
3	Sandy Koufax	1963	2.23
4	Al Downing	1963	2.25
5	Sandy Koufax	1966	2.28
6	Bob Veale	1965	2.30
7	Gary Peters	1963	2.32
8	Sonny Siebert	1965	2.32
9	Gaylord Perry	1966	2.32
10	Sandy Koufax	1964	2.38
11	Dick Radatz	1964	2.39
12	Luis Tiant	1968	2.39
13	Steve Hargan	1966	2.43
14	Dean Chance	1964	2.46
15	Mike Cuellar	1966	2.49
16	Chris Short	1964	2.50
17	Whitey Ford	1964	2.51
18	Bill Singer	1967	2.53
19	Sam McDowell	1968	2.55
20	Sam McDowell	1966	2.56
21	Bob Bruce	1964	2.57
22	Bob Moose	1968	2.60
23	Dean Chance	1968	2.62
24	Jim O'Toole	1964	2.63
25	Jim Maloney	1963	2.67

Notice that Gibson is only second (the FIP ERA’s do not completely correspond to predicted or actual ERAs mentioned earlier since all ERAs in the FIP ERA study are normalized to a league with an ERA of about 3.70). The FIP ERAs here are also different because HRs allowed were adjusted for park effects, something not done for the above analysis.

We can tell from the following stats that Gibson’s performance in 1968 was not as far above his other seasons as ERAs alone would indicate. The table below shows his strikeouts, walks and HRs allowed per batter faced for each year in his career with 100 or more IP. 1968 is clearly his best, but some other seasons rival it. In 1970, for example, his strikeout and HR rates are very close to 1968. In 1967, his strikeout rate and BB rate were similar to that of 1968. But 1970 was a much higher scoring season than 1968 with the NL ERA being 4.05. Gibson’s fielding independent stats in 1970 are almost as good as they were in 1968.

YEAR	SO/BFP	BB/BFP	HR/BFP
1961	0.181	0.136	0.014
1962	0.215	0.109	0.016
1963	0.188	0.100	0.017
1964	0.206	0.080	0.021
1965	0.219	0.092	0.028
1966	0.201	0.074	0.018
1967	0.209	0.061	0.014
1968	0.231	0.059	0.009
1969	0.212	0.083	0.009
1970	0.226	0.076	0.011
1971	0.180	0.081	0.014
1972	0.186	0.081	0.013
1973	0.180	0.076	0.015
1974	0.124	0.105	0.023
1975	0.120	0.132	0.020

The next table shows his FIPERAs for the years 1961-1974 (season when he had at least 150 IP).

Year	FIP ERA
1961	3.08
1962	2.56
1963	3.31
1964	3.15
1965	3.47
1966	3.08
1967	2.69
1968	2.21
1969	2.46
1970	1.96
1971	3.03
1972	2.90
1973	3.12
1974	4.87

As mentioned earlier, these FIP ERAs are all normalized for a league with about a 3.70 ERA. According to this, Gibson was better in 1970 than in 1968. That is, taking park effects into account to adjust HRs, using only pitcher controlled stats and comparing to the league average shows his 1970 season to be even better. This, too, suggests that 1968 was helped quite a bit by a very low BABIP. The big difference between the two seasons was his BABIP of .230 in 1968 and his .299 BABIP in 1970. The 1968 BABIP was far below the team BABIP while his 1970 BABIP was above the team BABIP.

I also broke down his performance into RISP and non-RISP situations to try to understand how his ERA could have been so low. He allowed a batting average of .184 overall but just .141 with RISP (and .193 in non-RISP situations). To see if this made any difference, I ran a regression with ERA as the dependent variable and on-base percentage (OBP) and slugging percentage (SLG) were the independent variables. That predicted Gibson to have an ERA of 1.25 (just using pitchers from 1968). Then I broke down OBP and SLG into RISP and non-RISP situations. The resulting regression equation predicted Gibson to have an ERA of 1.13. So his RISP performance also helped a little in making his ERA so low since the regression that took RISP into account was more accurate. His career average allowed overall was .228 while with RISP it was .219. Those two are pretty close, indicating that Gibson probably did not have any special ability with RISP. He just happened to do very well in those situations in 1968.

I also took the natural log of ERA in one of the regressions in case ERA had a non-linear relationship with the other stats. Doing this did not improve the results.

There is one other issue with the fielding in 1968. It appears that Gibson got a little lucky in 1968 with more balls in play than average being turned into outs. Perhaps the fielders were playing better or trying harder behind Gibson that year than they were for the other Cardinal pitchers. But Gibson actually gave up more unearned runs than would be expected as compared to the entire Cardinal staff. The staff ERA was 2.49 or 1.37 above Gibson. But if we include all runs, Gibson gave up 1.45 runs per 9 IP while it was 2.87 for the whole staff or 1.42 higher than Gibson. So by adding in unearned runs, the difference between Gibson and the team grows. Gibson’s runs per 9 IP was 29.46% above his ERA while for the whole staff it was 15.26% higher. So Gibson was hurt more by unearned runs than the whole team, indicating that his fielders hurt him. Perhaps they were hustling more and simply got to more balls, leading to more errors. Maybe official scorers called more errors than expected to protect Gibson’s ERA (it is true that Gibson’s runs per 9 IP is .33 higher than his ERA while it is .38 for the whole staff, possibly showing that Gibsons was hurt less by unearned runs-but with fewer base runners allowed, any given error should have hurt him less so a .33 increase is proportionally worse for him than a .38 increase was for the whole team).

Sources:

The Complete Baseball Encyclopedia from Lee Sinins

The Best Fielding Independent Pitching Seasons From 1920-2005

http://www.beyondtheboxscore.com/story/2006/5/23/143235/740

Cybermetrics

Friday, April 27, 2018

Shortstops with at least 120 OPS+ thru age 22

Sunday, April 22, 2018

Did a cold and related eye twitch prevent Joe DiMaggio from batting .400 in 1939?

Friday, April 6, 2018

Explaining Bob Gibson’s 1968 Season

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