Fun with park factors

Note: This article contains numerous factual errors. Please see the follow-up for clarification.

Among most sports, baseball is unique in that the stadium in which the game is played has a tangible effect on the game itself. This can be attributed to the paucity of defined standards for a park's construction, for which there are many reasons. In a nutshell, many parks date to a time when standards didn't exist for anything, and by the time people realized that standardization would be advantageous, it was too unfeasible to actually be completed. Hence, thirty different ballparks.

The fun part of this, for a statistically-inclined person such as myself, is that it gives us another angle of the game to analyze: park factors. For the sake of neutrality, we evaluate every player on an equal scale, which means that players are credited or debited for the park in which they play. All of the inherent benefits or costs of a particular stadium are boiled down into one simple number.

FanGraphs keeps track of these simple park factors for every year since 1871. The more complex ones, however, only go back to 1974, so our discussion will focus on those 40 years for now. As with many things statistical-y, 100 is the major-league average. In addition to the overall factors, FanGraphs provides figures for singles, doubles, triples, and home runs (each of these is also scaled to 100).

How well do these correlate to one another? As the following table shows, not particularly well:

	Overall	1B	2B	3B	HR
Overall	X	0.379	0.426	0.178	0.446
1B	0.379	X	0.061	0.053	0.045
2B	0.426	0.061	X	0.246	0.023
3B	0.178	0.053	0.246	X	0.009
HR	0.446	0.045	0.023	0.010	X

By using Pearson's r², we can measure the association between each of the variables. The strongest correlations to be found are between the overall park factors and the ones for doubles and home runs, but even they aren't all that significant — a good r² for this would be in the .5 range. For the most part, these park factors seem to exist independent of one another. They're still fairly consistent, though:

	Overall	1B	2B	3B	HR
SD	4.04	2.19	5.16	12.87	7.62
YTY (r²)	0.930	0.882	0.934	0.942	0.940

All five correlate extremely well year-to-year, and there isn't a whole ton of variation among them (except for triples).

Now let's look at the individual figures. Each team has one per season (obviously), and since there have been 1108 team seasons in the past 40 years, there are 1108 of each park factor over that span as well. Looking at the histogram of overall park factors over the past 40 years, there's definitely a positive skew:

While the histograms for the other factors vary in their spread, they all share the same positivity, to varying extents:

As was mentioned earlier, the histogram for triples has the widest spread and the most modes by far, as triples aren't nearly as consistent year-to-year. Singles and doubles are fairly tightly distributed, and home runs are spread more finely, although they're much more unimodal than triples.

The aforementioned 1108 seasons occurred in 55* different ballparks. How do these compare to one another? Which favor the hitting-folk, and which are more inclined toward the ones who hurl?

*Well, 54 — in 1974 and 1975, the Yankees and Mets shared Shea Stadium. It has different factors for each of them, though, so it's listed as two different parks.

Field	Years Used	Overall (Average)	1B (Average)	2B (Average)	3B (Average)	HR (Average)
Coors Field	1995-	116.1	108.5	108.8	124.7	117.1
Mile High Stadium	1993-1994	114	106	104	163	106
Atlanta-Fulton County Stadium	1974-1996	105.4	102.9	100.6	89.5	114.4
Globe Life Park	1994-	104.7	102	102.2	116.7	105.2
Chase Field	1998-	104.4	100.9	105.4	125.7	103.9
Wrigley Field	1974-	104.2	101.6	100.8	98.6	109.7
Fenway Park	1974-	104.1	101.9	112.3	101	99.3
Jarry Park Stadium	1974-1976	104	104	99	108	103
Exhibition Stadium	1977-1989	103.2	98.5	107.8	117.9	103.2
Yankee Stadium (II)	2009-	103	100	97	84.8	110
Metrodome	1974-2009	102.1	100.5	103.5	111.6	99.8
Kauffman Stadium	1974-	101.9	101.7	105.7	121.2	92.9
Riverfront Stadium	1974-2002	101.7	98.2	105.4	98.2	104.2
Great American Ball Park	2003-	101.7	98.6	99.3	90.4	110.4
Kingdome	1977-1999	101.4	98	103.6	95	110.1
Citizens Bank Park	2004-	101.4	99.4	99.8	94.4	106.1
Rogers Centre	1990-	101.2	98	104	106.2	104.2
Comiskey Park	1974-1990	101.1	100.4	99.1	116.7	93.9
Veterans Stadium	1974-2003	101.1	98.1	104.7	107.6	101.1
Marlins Park	2012-	101	101	101	109	89
U.S. Cellular Field	1991-	100.8	99.1	97	93.9	105.9
Tiger Stadium	1974-1999	100.7	98	95.6	99.5	108.6
Cleveland Stadium	1974-1993	100.7	102	97.4	91.8	100.6
Three Rivers Stadium	1974-2000	100.6	99.1	102.8	102.7	100.4
Minute Maid Park	2000-	100.4	99.6	98.7	108.6	104.5
Miller Park	2001-	100.1	97.2	100.2	100	104.8
Olympic Stadium	1977-2004	100	98.5	104.5	103	96
Target Field	2010-	100	101	101	109	93
Nationals Park	2008-	100	101.5	101	97	99.5
Camden Yards	1992-	99.8	101.1	95.8	87.8	104.9
Comerica Park	2000-	99.6	101.9	96.9	119.1	96.6
Arlington Stadium	1974-1993	99.6	101.3	98.2	94.6	98.7
Milwaukee County Stadium	1974-2000	99.4	101	98.1	99.5	95.2
Busch Memorial Stadium	1974-2005	99.4	99.9	101.7	107	93.9
Progressive Field	1994-	99.2	100.4	101.1	87.9	97.2
Turner Field	1997-	99.1	100.5	97.9	97.6	97.7
PNC Park	2001-	98.6	101.7	102.9	93.8	93.2
Angel Stadium of Anaheim	1974-	98.3	100.5	96.6	86	100.7
Yankee Stadium (I)	1976-2008	98.2	99.7	96.6	93.1	100.1
Shea Stadium (Yankees)	1974-1975	98	98	101	97	97
Tropicana Field	1998-	97.9	99.1	98.4	108.7	97.9
Sun Life Stadium	1993-2011	97.9	99.2	97.8	109.6	95.1
Candlestick Park	1974-1999	97.5	98.7	97.5	94.7	96.8
AT&T Park	2000-	97.2	100.4	100.1	111.6	90.7
Busch Stadium	2006-	97	100.5	96.9	92.5	91.9
Shea Stadium (Mets)	1974-2008	96.9	99.6	96.9	91.9	97.2
Memorial Stadium	1974-1991	96.8	98.1	96.9	80.7	99.2
Citi Field	2009-	96.6	98.2	95.8	101	97
O.co Coliseum	1974-	96.2	98.6	94.5	91.3	95.9
Qualcomm Stadium	1974-2003	96.1	99	94.1	96.4	99.7
RFK Memorial Stadium	2005-2007	96	98	98	102	91
Safeco Field	2000-	95.7	98.4	95.9	88.3	95.2
Dodger Stadium	1974-	95.7	100.5	91.9	78.5	98.1
Astrodome	1974-1999	94.7	98.6	98.8	105.3	84.8
Petco Park	2004-	92.1	96.9	91.5	104.4	90.6

Obviously, some parks (Colorado, Texas) favor scoring, while others (San Diego, Los Angeles) don't. Some confirm their reputations, others don't — as an Orioles fan, Camden Yards' 99.8 overall factor was pretty surprising.

How about the consistency of each park from year to year?

Field	Years Used	Overall YTY	1B YTY	2B YTY	3B YTY	HR YTY
Comerica Park	2000-	0.921	0.660	0.842	0.586	0.889
Coors Field	1995-	0.905	0.881	0.653	0.502	0.892
U.S. Cellular Field	1991-	0.901	0.438	0.516	0.875	0.942
Minute Maid Park	2000-	0.890	0.266	0.378	0.611	0.300
Tropicana Field	1998-	0.870	0.762	0.914	0.010	0.419
Wrigley Field	1974-	0.868	0.714	0.727	0.727	0.879
Qualcomm Stadium	1974-2003	0.864	0.413	0.739	0.332	0.913
Camden Yards	1992-	0.842	0.640	0.885	0.544	0.875
Sun Life Stadium	1993-2011	0.836	0.624	0.827	0.757	0.585
Tiger Stadium	1974-1999	0.825	0.760	0.879	0.892	0.472
Metrodome	1974-2009	0.817	0.562	0.734	0.644	0.812
Fenway Park	1974-	0.817	0.705	0.820	0.550	0.897
Progressive Field	1994-	0.753	0.660	0.538	0.735	0.662
AT&T Park	2000-	0.748	0.361	0.557	0.834	0.714
Memorial Stadium	1974-1991	0.744	0.788	0.507	0.613	0.868
Exhibition Stadium	1977-1989	0.715	0.737	0.745	0.627	0.111
O.co Coliseum	1974-	0.714	0.529	0.892	0.840	0.790
Candlestick Park	1974-1999	0.705	0.565	0.686	0.932	0.829
Atlanta-Fulton County Stadium	1974-1996	0.703	0.446	0.711	0.758	0.916
Dodger Stadium	1974-	0.693	0.853	0.880	0.698	0.827
Riverfront Stadium	1974-2002	0.691	0.670	0.711	0.769	0.660
Kauffman Stadium	1974-	0.680	0.824	0.774	0.850	0.897
Angel Stadium of Anaheim	1974-	0.671	0.596	0.763	0.685	0.881
PNC Park	2001-	0.660	0.350	0.860	0.407	0.798
Three Rivers Stadium	1974-2000	0.652	0.750	0.466	0.375	0.684
Rogers Centre	1990-	0.603	0.446	0.614	0.700	0.784
Milwaukee County Stadium	1974-2000	0.593	0.655	0.488	0.565	0.567
Arlington Stadium	1974-1993	0.551	0.758	0.532	0.883	0.786
Chase Field	1998-	0.528	0.325	0.596	0.311	0.605
Globe Life Park	1994-	0.513	0.682	0.653	0.258	0.664
Veterans Stadium	1974-2003	0.512	0.625	0.511	0.575	0.811
Astrodome	1974-1999	0.510	0.840	0.740	0.634	0.848
Yankee Stadium (I)	1976-2008	0.479	0.440	0.369	0.922	0.781
Kingdome	1977-1999	0.479	0.493	0.394	0.815	0.900
Shea Stadium (Mets)	1974-2008	0.462	0.527	0.423	0.775	0.759
Olympic Stadium	1977-2004	0.435	0.393	0.486	0.682	0.831
Comiskey Park	1974-1990	0.403	0.723	0.257	0.766	0.608
Busch Memorial Stadium	1974-2005	0.393	0.688	0.730	0.922	0.804
Miller Park	2001-	0.386	0.441	0.288	0.016	0.727
Great American Ball Park	2003-	0.340	0.643	0.413	0.904	0.614
Citi Field	2009-	0.333	0.333	0.333	0.333	0.333
Cleveland Stadium	1974-1993	0.229	0.780	0.715	0.676	0.708
Citizens Bank Park	2004-	0.190	0.654	0.527	0.391	0.610
Petco Park	2004-	0.003	0.135	0.521	0.257	0.096
Safeco Field	2000-	0.0004	0.252	0.006	0.026	0.169
Turner Field	1997-	0.0002	0.397	0.019	0.268	0.198
Busch Stadium	2006-	X	0.563	0.028	0.832	0.028
Marlins Park	2012-	X	X	X	X	X
Jarry Park Stadium	1974-1976	X	X	X	X	X
Nationals Park	2008-	X	0.444	X	0.444	0.444
Mile High Stadium	1993-1994	X	X	X	X	X
Target Field	2010-	X	X	X	X	X
Shea Stadium (Yankees)	1974-1975	X	X	X	X	X
Yankee Stadium (II)	2009-	X	X	X	X	X
RFK Memorial Stadium	2005-2007	X	X	X	X	X

(Note: Some ballparks have the "X"; this is because the park factor for them has been the same forever, as they haven't [or didn't] exist enough to have variation.)

For each stadium, there's a different level of constancy for each factor. Moreover, the amount of cohesive factors varies — Candlestick stays pretty steady across the board, while Safeco is inharmonious on every level.

Lastly, how consistent are they as a whole?

Field	Years Used	Overall SD	1B SD	2B SD	3B SD	HR SD
Coors Field	1995-	5.59	2.64	1.60	4.05	7.17
Wrigley Field	1974-	3.24	1.82	2.90	4.89	7.18
U.S. Cellular Field	1991-	3.08	0.740	1.67	7.10	7.67
Qualcomm Stadium	1974-2003	2.69	1.20	1.78	3.82	8.82
Camden Yards	1992-	2.39	1.18	3.16	3.36	3.43
Atlanta-Fulton County Stadium	1974-1996	2.39	1.23	2.28	4.95	9.61
AT&T Park	2000-	2.37	1.11	1.22	7.43	1.98
Candlestick Park	1974-1999	2.34	1.17	2.10	11.29	4.07
Tiger Stadium	1974-1999	2.26	1.18	3.72	6.42	2.32
Tropicana Field	1998-	2.25	0.99	3.22	1.96	1.89
Comerica Park	2000-	2.22	0.88	2.47	5.90	4.19
Milwaukee County Stadium	1974-2000	2.18	1.54	2.21	3.49	1.88
Minute Maid Park	2000-	2.16	0.73	1.28	6.53	0.50
Progressive Field	1994-	2.10	1.28	1.09	5.51	3.23
Fenway Park	1974-	2.02	1.26	2.80	3.62	5.33
Sun Life Stadium	1993-2011	1.96	1.10	2.50	4.68	1.94
Metrodome	1974-2009	1.92	0.90	4.69	6.17	3.17
Angel Stadium of Anaheim	1974-	1.86	1.02	2.40	4.10	5.23
Three Rivers Stadium	1974-2000	1.85	1.20	1.20	2.93	3.35
Olympic Stadium	1977-2004	1.84	0.73	1.88	5.59	4.08
Memorial Stadium	1974-1991	1.80	0.99	1.43	3.06	4.06
Kauffman Stadium	1974-	1.80	1.61	3.47	8.84	5.75
Dodger Stadium	1974-	1.77	2.14	2.92	3.96	4.41
Kingdome	1977-1999	1.74	0.91	3.39	5.53	8.73
Exhibition Stadium	1977-1989	1.66	1.28	2.63	5.70	2.32
O.co Coliseum	1974-	1.60	0.89	3.15	5.89	2.96
Safeco Field	2000-	1.53	1.11	2.31	1.62	1.90
Veterans Stadium	1974-2003	1.49	0.92	1.81	4.92	3.01
Yankee Stadium (I)	1976-2008	1.49	0.82	1.39	8.84	3.32
Riverfront Stadium	1974-2002	1.47	1.50	2.60	7.26	4.17
Arlington Stadium	1974-1993	1.47	1.37	1.47	8.03	4.10
Globe Life Park	1994-	1.39	0.67	1.33	5.62	2.79
Astrodome	1974-1999	1.39	1.55	2.06	7.24	4.66
Chase Field	1998-	1.32	0.70	1.37	3.49	2.18
Comiskey Park	1974-1990	1.28	1.03	1.32	4.61	3.06
PNC Park	2001-	1.21	0.82	1.94	1.56	1.92
Shea Stadium (Mets)	1974-2008	1.18	1.20	1.36	5.45	2.47
Busch Memorial Stadium	1974-2005	1.17	1.07	2.00	13.11	3.97
Rogers Centre	1990-	1.11	0.84	1.97	7.92	3.41
Petco Park	2004-	1.04	0.54	1.57	2.33	2.54
Great American Ball Park	2003-	0.98	0.46	1.40	8.03	1.20
Cleveland Stadium	1974-1993	0.91	1.32	1.42	3.03	4.10
Citizens Bank Park	2004-	0.80	1.02	0.87	2.01	2.26
Miller Park	2001-	0.73	0.77	0.66	2.54	3.14
Turner Field	1997-	0.54	0.50	1.08	1.85	0.75
Citi Field	2009-	0.49	0.98	1.47	9.80	4.90
Busch Stadium	2006-	0	0.50	0.33	2.18	0.33
Marlins Park	2012-	0	0	0	0	0
Jarry Park Stadium	1974-1976	0	0	0	0	0
Nationals Park	2008-	0	0.50	0	2.00	0.50
Mile High Stadium	1993-1994	0	0	0	0	0
Target Field	2010-	0	0	0	0	0
Shea Stadium (Yankees)	1974-1975	0	0	0	0	0
Yankee Stadium (II)	2009-	0	0	0	0.43	0
RFK Memorial Stadium	2005-2007	0	0	0	0	0

Like for the aggregate figures, the Triples are more inconsistent than any of the other factors. Some parks don't even have standard deviations, and those that do differ wildly. For the most part, the highest deviations seem to go to parks that are hitter-friendly in that area, and vice versa.

So, there's a lot to learn about park factors, and the best part? This is all subject to change! That's right — the 3-year regression that FanGraphs uses to derive their park factors means that all of this data will probably be worthless by this time next year. Until then, though, you've probably learned something; at least I have.

. . .

All statistics courtesy of FanGraphs.

Ryan Romano writes for Beyond the Box Score, the FanGraphs Community blog, and Camden Chat that one time. Follow him on Twitter at @triple_r_ if you enjoy angry tweets about Maryland sports and live tweeting about Community, Thursdays at 8/7c after the Olympics. Cool. Coolcoolcool.