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# Fun with park factors

You've probably heard a lot about park factors, but you might not know exactly what they are. Here's what you need to know.

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.

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