I looked at some data for the NL and the Pirates during two time periods;

[numbers from "Sports Encyclopedia:Baseball", Total Baseball and "The Bill James Electronic Encyclopedia"] The Pirates played 2707 games in Mazeroski's 17 years (159.2/yr) so I projected totals to 160 games;

G PO2b A2b E2b DP2b PO A E DP othDP 1. NL 160 399.6 473.6 21.5 107.9 4295.5 1784.7 147.4 152.4 44.5 1.Pit 160 413.9 478.2 22.5 111.1 4283.1 1791.4 155.9 153.4 42.3 2. NL 160 380.5 465.1 20.7 104.6 4306.7 1755.2 144.0 149.8 45.1othDP is double plays turned not involving second basemen. Mazeroski's years with the pirates are in2.Pit 160 390.1 522.4 17.0 130.6 4303.2 1848.4 150.2 175.7 45.2

Many of the extra assists for the Pirates appear to come from their 2b. The others probably come from a slight GB tendency of the Pirate pitchers. As another check on this I looked at the A/PO ratio for pitchers, the A/PO ratio for the Pirate pitchers was 2.95, for all NL pitchers it was 2.84. (But see later for a better look into this)

How do the extra plays turned by Pirates 2b affect other total? (especially runs allowed and DPs) I looked at total outs per game (PO/G), outs involving 2b ((PO2b+A2b)/G) and outs no involving 2b ((PO/G-(PO2b+A2b)/G)) for 1956-72;

PO/G 2b others H BB K Approx. OBA NL 26.917 5.285 21.632 Pit 26.895 5.703 21.192 8.731 2.963 5.288 .3030Using the "others" as a "clock" (assuming that over the years the rest of the players come out as average fielders and make plays at the same rate), I estimate that an average 2b would make 5.178 plays in the same time that the Pirates 2b made 5.703 plays. This accounts for 26.369 outs. To get the rest of the outs will take another 1.99% "longer" giving the totals

PO/G 2b others H BB K Approx. OBA 26.895 5.281 21.614 8.905 3.022 5.2391 .3072Using Bill James' simple Runs Created estimate RC=OBA*TB, gives an increase of 3.401% in RC (OBA increased by 1.38% and TB by 1.99%) The Pirates allowed 628.533 runs per 160 games. A 3.4% increase sends this to 649.910 R/160G, indicating a saving of 21.377 runs per tear. Over 17 years this amounts to 363.4 runs, consistent with total baseball's 362 Fielding Runs for Mazeroski, though a bit lower than Mike Emeigh's figures. (I could also project this to account for the fact that more runs allowed means more losses ==> a few more outs at home, a few less on the road, but the effect is small enough that I'm not going to worry about it.)

Proj. DP= 83.269 +.0641*H - .0190*HR + .0944*BB - .0494*SO with R^2=.249, SE=16.67, F(4,161)=13.36Using this model, the Pirates turned an extra 351 DPs in Mazeroski's 17 years, with the worst values coming in 1956, '57 and '71. Looking only at the years 1958-70 gives 351 extra DPs in 13 years.

Michael also looked at this using a Dummy Variable for the Pirates data. When I looked at the 1956-1972 data I got:

Proj.DP=-19.939 + .116*IP + .103*BB - .0568*SO + 27.947*DV r^2=.412, SE=14.76, F(4,161)=28.20greatly "improving" the model and implying that the Pirates were turning an extra 27 double plays per year.

I also tried making the dummy variable a little smarter by replacing the "1" by the fraction of Pirates games played by Mazeroski that year (basically measuring the "Mazeroski-Ness" of each team) which gave the model

Proj. DP=-22.687+.117*IP+.104*BB-.0562*SO+33.813*MAZ r^2=.416, SE=14.71, F(4,161)=28.61implying that Mazeroski was worth 33.81DP (SE=4.58), with a 95% confidence interval of [24.88,42.75].

Simply looking at the correlations between the variables I found the following correlations significant at the 1% level; positive correlations: IP/SO, H/HR, H/E, H/DP, HR/BB, BB/DP, DP/DV negative correlations: IP/HR, H/SO, HR/SO, HR/DVar, SO/DP indicating that the model for projecting DPs should have H, BB, K and the Pirates dummy variable in it. The IP, HR and E variables probably don't belong. The presence of the HR variable in the non-DV model probably came about because the Pirates tended to give up fewer HR (Forbes Field) and the effect of the missing DV probably appeared as a HR coefficient. The negative correlations for IP/HR and HR/SO are probably due to the fact that early expansion (more IP) took place in the early '60s. (bigger strike zone, fewer HR)

Mixing this with the "effects of good fielding 2b", without the Pirates dummy variable I get, per 160 games;

IP H HR BB SO projDP actDP NL 1435.6 1374.3 128.9 490.0 889.4 149.2 149.8 Pit 1428.5 1390.2 110.0 471.9 842.0 154.3 175.7 PitnoMaz 1428.5 1417.9 113.2 481.3 858.5 155.7Indicating that playing for the Pirates was a DP inducing environment, but that Mazeroski was so good at turning the DP that he cost himself about 1.5 DP opportunities per year relative to other 2b. (and cost the pitchers 15-20 SO)

Projected DP/G = .8211 + .29567*IO - .048679*K/GUsing this, I find that the Pirates project to an extra .040 DP/G (6.4 per year). The rest was Mazeroski. Using these calculations to adjust the assists, I get

RF adj.RF FA DP/G Adj.play-ratio E-ratio McPhee +.48 +.45 +.019 +.123 1.077 1.34 Lajoie +.54 +.51 +.011 +.145 1.098 1.29 Maz +.54 +.40 +.006 +.181 1.080 1.34The "adjusted range factor" takes into account the ground ball tendencies of the Pirates as found above. I have not yet tried to account for putouts.

For another look at IO, I checked the Bill James Electronic Encyclopedia and the Franklin Electronic Baseball Encyclopedia for the totals for each team for the years 1956-1972 and found the following:

Assists non2b Team G DP P 1b 2b 3b SS Inf-A OF-PO 2b-DP -DP IO LH IP (#) Braves 2708 2478 4102 1838 7840 5581 8604 27,965 17,053 1782 696 1.64 7141.3(33) Cubs 2714 2565 4221 1898 8482 5701 8846 29,148 16,128 1789 776 1.81 5762.7(49) Reds 2700 2469 3798 1826 7381 5162 8144 26,311 16,934 1679 790 1.55 6857.7(37) Dodgers 2706 2460 3988 1823 7479 5859 8714 27,863 15,746 1698 762 1.77 9550.7(25) Phillies 2702 2525 3691 1849 7398 5364 8461 26,763 17,039 1757 768 1.57 6915 (27) Pirates 2707 2973 3951 1955 8838 5429 9024 29,197 16,504 2209 764 1.77 6158.7(31) Giants 2706 2353 4160 1775 7770 5350 8434 27,489 16,623 1595 758 1.65 7221.7(33) Cardinals 2705 2615 3876 1841 7938 5358 8582 27,595 16,597 1823 792 1.66 7198.3(55) Avg. 2706 2555 3973 1851 7891 5476 8601 27,791 16,578 1792 763 1.68 7100.7(36) Pir.diff +1 +418 +22 +104 +947 -47 +423 +1,406 -74 +417 +1 +.09 -942 (-5)Avg. is the average of the 8 teams rounded to the nearest integer

Pir.diff is the Avg. subtracted from the Pirate total

LH IP is the number of innings thrown by Left-handed pitchers (#) is the number of left-handed pitchers used by the team

Again, Mazeroski was helped by the Pirates being a groundball staff, but he was clearly a great fielder.

Here are more of the pitching numbers to help set the context:Team G IP LHIP H HR SO BB E Braves 2708 24272 7141.3 23369 2346 13962 8001 2260 Cubs 2714 24250 5762.7 23931 2461 14390 8403 2481 Reds 2700 24275 6857.7 23450 2301 14859 8419 2151 Dodgers 2706 24389.3 9550.7 22321 2128 16771 8005 2414 Phillies 2702 24219.3 6915 23959 2239 15224 8167 2323 Pirates 2707 24284 6158.7 23634 1887 14314 8022 2542 Giants 2706 24388.7 7221.7 22931 2260 15202 8102 2651 Cardinals 2705 24325.3 7198.3 23225 2126 15175 8625 2448 Avg. 2706 24300.5 7100.7 23353 2219 14987 8218 2409 Pir. diff. +1 -16.5 -942 +281 -332 -673 -196 +133For more context, I looked at the team statistics for National League teams 1956-1972 and found the following regression model:

DP2b = -.0740 + .0268*LH + .0410*H + .0727*BBHB - .193*E + .0767*A + .0170*Maz + .0161*pir R^2=.61 SE=.0079Where

(i.e. if Maz played 108 of the Pirates' 162 games, Maz is 2/3, pir is 1/3, any Cubs games, Maz and pir are both 0)

This has Mazeroski accounting for an extra 318 DP (18.7 per year, or 24.3 per 160G) and the Pirates "context" (Pitchers, ball park, etc.) contributed 89 DP (5.2 per year) The SE on the Mazeroski coefficient is .00270, about 50.7 DP over his career, 3.0 per year or 3.9 per 160 G.

If we remove the "Maz" and "pir" variables from the model, the R^2 drops below 50% (without the LH IP it's 44%)

Rel.DP | Year | Team | Regular 2b |
---|---|---|---|

+41 | 1966 | Pirates | Mazeroski |

+34 | 1972 | Pirates | Cash |

+34 | 1961 | Pirates | Mazeroski |

+32 | 1965 | Pirates | Mazeroski |

+30 | 1963 | Pirates | Mazeroski |

+28 | 1962 | Pirates | Mazeroski |

+27 | 1958 | Dodgers | Neal |

+26 | 1971 | Braves | Millan |

+24 | 1960 | Pirates | Mazeroski |

+23 | 1971 | Giants | Fuentes |

+22 | 1972 | Astros | Helms |

+21 | 1959 | Pirates | Mazeroski |

+20 | 1961 | Cubs | Zimmer |

+20 | 1971 | Reds | Helms |

+19 | 1957 | Cardinals | Blasingame |

+17 | 1961 | Phillies | Taylor |

+17 | 1958 | Pirates | Mazeroski |

+16 | 1969 | Pirates | Mazeroski/Alley/Martinez |

+16 | 1969 | Expos | Sutherland |

+16 | 1956 | Cardinals | Blasingame |

+15 | 1958 | Cubs | Taylor |

Consider the `best' model that dos not include the dummy variables;

DP2b = -.0916 + .0121*LH + .0405*H + .0623*BBHB - .174*E + .0955*A R^2=.45 SE=.0092Using this, I found the predicted number of double plays for each National League team for the years 1956-1972. I then compared this number to the actual number of DPs turned by the team's second baseman. There were 21 teams whose second basemen turned 15 "extra" double plays. The table at right lists the teams and their regular secondbaseman. The secnodbasemen who appeared on the list more than once were

Bill Mazeroski 8 times Tommy Helms 2 times Don Blasingame 2 times Tony Taylor 2 timesI did not included the 1969 Pirates in the Mazeroksi count because he played fewer than half the Pirates games. The annual "relative DPs" for the Pirates beginning in 1956, were

Year: 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 DP: +6 +12 +17 +21 +24 +34 +28 +30 +6 +32 +41 +0 -2 +16 +11 +14 +34Suggesting that Mazeroski took a few years to learn how to turn the pivot and that his skill considerably diminished after 1966.

- Comparison of several long-time second basemen to an average 2b
- A year-by-year list of average shortstop numbers
- comparisons of several shortstops with the "average" shortstop
- Back to my baseball page