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May 24, 2009

Prospectus Idol Entry

Baseball Prospectus Basics: Park Factors

by Brian Cartwright

The new Yankeee Stadium has received a lot of press this spring for the large number of homeruns hit there so far. On April 21, 2009, Buster Olney wrote at ESPN http://sports.espn.go.com/mlb/news/story?id=4080195 "The New York Yankees might have a serious problem on their hands: Beautiful new Yankee Stadium appears to be a veritable wind tunnel that is rocketing balls over the fences...including 17 in the first three games in the Yankees' first home series against the Indians. That's an average of five home runs per game and, at this pace, there would be about 400 homers hit in the park this year -- or an increase of about 250 percent. In the last year of old Yankee Stadium, in 2008, there were a total of 160 homers."

The first mistake in Olney's analysis is to take the homerun rate of five games and extrapolate that over a full season, and the second is to refer to how many were hit in the old Yankee Stadium last year, without considering if there might be different players on the field. The accepted method of measuring park factors, on any statistic, is to compare the home totals of both the batters and pitchers to those compiled on the road, where playing in fifteen or more different parks minimizes the effect of any one park. The factors then allow us to estimate how these players would perform in a neutral environment.

As of this writing on May 20, the Yankees have played 19 games at home, which have seen a total of 71 homeruns, 37 by Yankees hitters, 34 by their opposition. They've played 21 games on the road, with 49 homeruns, 27 by Yankees hitters and 22 by their opposition. 71 homers at Yankee Stadium divided by 49 in the Yankees road games gives a factor of 1.45-indicating the new Yankee Stadium inflates homerun rates 45%. The Yankees have played two more games on the road than at home, so let's instead find the ratio of the home HR% (hr/(ab-so)) of .064 to their road game rate of .043, which is 1.48-slightly higher, but basically the same.

Is 20 games, a quarter of a season, enough of a sample size to get a reliable factor? After two exhibitions and three regular season games, Olney calculates an increase of 250%. After 19 regular season home games, I calculate an increase of 45%. What is it likely to be by the end of the season?

From 1985 to 1991, a period of seven seasons, there were no changes in the National League in either ballparks or schedule. I ran a series of one year, two year and three year factors to find out how much each varied from the seven year 'true' value at each park. The chart below shows the standard deviation of the results for each category at each sample size. After one year all categories are fairly close to 2 decimal point accuracy, except homeruns which take three years and triples which take even longer.

If Yankee Stadium still has a homerun factor of 1.45 at the end of the year, with a SD of .149, that means there's a 70% chance the 'true' value is between 1.30 and 1.60, and a 95% chance of it being between 1.15 and 1.75. After 19 games it is still possible that Yankee Stadium could turn out to be an average park.


       SDT   XBH    SI    DO    TR    HR    BB    SO
1 Yr  .039  .083  .044  .091  .292  .149  .069  .044
2 Yr  .023  .057  .025  .060  .207  .085  .054  .030
3 Yr  .018  .046  .020  .045  .161  .060  .041  .023

A stadium having a factor of 1.45 tells us that plays in that park will be increased by 45% over normal rates. We can use this number to normalize the performance of batters and pitchers to what they would have done in a 'neutral' park. Each team is scheduled to play half their games at home, the other half at the various road parks. If we assume that the road parks average out to 1.00, then the 'team' factor which is applied to the seasons stats would be (home+road)/2, or in this case (1.45+1.00)/2, which is 1.22. Yankees hitters would be normalized by having their homerun percentage reduced by 22%, and the pitchers increased by 22%. However, with interleague play and unbalanced schedules, we can not assume the a team's road parks average 1.00. The Pirates play division games in Great American Ballpark, Miller Field, Wrigley Field and Minute Maid Park, all of which are among the easiest to homer in. The Rockies play division games in Petco Park, Dodger Stadium and AT&T Park, which are among the hardest. After the initial calculation of each park's factors, use those to normalize each team's road statistics and rerun to generate a new version of factors. A third time is even better, but more than that doesn't add any meaningful accuracy.

The chart shows that it takes at least three years to get a fairly accurate set of factors, but before that time has gone by a new stadium has likely been constructed-the road parks have changed. Assuming Yankee Stadium's HR factor reamains higher than the park it replaced, the factor for Fenway Park will go down because Red Sox hitters can be expected to hit more homers on the road. In 1978, Fenway was the fourth easiest park in the AL to homer in, but in 1999, Fenway had dropped to the ninth-Fenway hadn't changed, it was all the other parks that changed. Can we legitimately say "It used to be a hitter's park, but now it's a pitcher's park." It would make sense for each park's factors to remain constant as long as there had not been any changes in that park. To find each team's factors, multiply how many times they play in each park by each park's factors, then divide the sum by the total number of games. The team factor can change each year with a different mix of road parks for each team, while the factors for each park do not change as long as the park hasn't changed. When play by play data is available, team factors to adjust a season total are not needed. Instead, how each player performed in each ballpark can be normalized with that park's factors, and then summed into an adjusted season total.

1978   American League               1999   American League
ParkID Name                  HRpf   ParkID Name                  HRpf
SEA02  Kingdome              1.55   DET04  Tiger Stadium         1.21
DET04  Tiger Stadium         1.21   BAL12  Camden Yards          1.13
TOR01  Exhibition Stadium    1.06   STP01  Tropicana Field       1.12
BOS07  Fenway Park           1.02   TOR02  Skydome               1.10
MIN02  Metropolitan Stadium  1.00   ARL02  Ballpark at Arlington 1.10
CLE07  Cleveland Stadium     1.00   SEA02  Kingdome              1.09
ARL01  Arlington Stadium     0.94   NYC16  Yankee Stadium        1.07
OAK01  Oakland Coliseum      0.93   KAN06  Kaufman Stadium       1.05
NYC16  Yankee Stadium        0.92   BOS07  Fenway Park           1.02
ANA01  Anaheim Stadium       0.86   ANA01  Anaheim Stadium       1.01
MIL05  County Stadium        0.85   MIN03  Metrodome             0.98
CHI10  Comiskey Park         0.79   CHI12  Comiskey Park II      0.98
KAN06  Kaufman Stadium       0.77   OAK01  Oakland Coliseum      0.97
BAL11  Memorial Stadium      0.76   CLE08  Jacobs Field          0.95

In calculating long term park factors, I first made a list of ballpark 'versions'. Three Rivers Stadium opened in Pittsburgh in 1970, so that's version 1. In 1975, an inner wooden fence was constructed, about 6 feet shorter, creating version 2 which lasted until it's closing after the 2000 season. Version 2 of Veteran's Stadium in Philadelphia existed from 1972 to 2003. Three River v2 and Veteran's v2 both existed from 1975 to 2000. For those 26 seasons, compare the Pirates and Phillies stats in Pittsburgh with the same two teams stats in Philadelphia. Repeat for every combination of ballpark versions, then compare the total home to road stats for the entire range of years.

I've spoken mainly of homeruns in this article, as that category is the one that varies the most between ballparks, ranging from 1.65 for the Polo Grounds 1954-1963 to 0.48 for the Astrodome 1977-1984. Other than the mile high Coors Field with it's BABIP factor of 1.15, base hits range from Kansas City's Municipal Stadium at 1.08 to Milwaukee's County Stadium at 0.92. Candlestick Park in San Francisco had the highest SO factor at 1.11, while Coors Field is the hardest place to fan at 0.85. The bottom of the SO factor list is populated by the various incarnations of fields in Denver, Kansas City, Atlanta, Pittsburgh, Chicago and St. Louis-almost all of the major league cities away from the coasts and a thousand or more feet above sea level. The theory is that breaking pitches don't move as much at higher altitudes, where the air is thinner, resulting in higher contact rates, but that's another article.

In summary

  • Don't expect more than two decimal places of accuracy
  • It takes three seasons to get a good homerun factor.
  • Park Factors should not change if the park does not change.
  • Team factors are the weighted mean of park factors which can be applied to individual players statistics.
NAME                         ParkID Ver Since Games  SDT  XBH   SI   DO   TR   HR   BB   SO   
Angel Stadium of Anaheim      ANA01   4  1997   812 1.00 0.96 1.02 0.99 0.76 1.01 1.00 0.99
Rangers Ballpark in Arlington ARL02   1  1994  1027 1.03 1.02 1.02 1.02 1.35 1.10 1.00 0.95
Turner Field                  ATL02   1  1997   810 1.01 0.94 1.03 0.95 1.03 0.96 1.00 0.99
Oriole Park at Camden Yards   BAL12   1  2002  1100 0.98 0.89 1.01 0.89 0.70 1.13 1.02 0.97
Fenway Park                   BOS07   7  1956  3965 1.07 1.15 1.03 1.27 1.01 1.02 1.00 0.98
Wrigley Field                 CHI11   7  1956  4006 1.02 0.98 1.02 1.01 0.98 1.19 1.02 0.99
U.S. Cellular Field           CHI12   2  2001   569 0.99 0.96 1.00 0.97 0.80 1.26 1.02 0.97
Great American Ballpark       CIN09   1  2003   406 0.97 0.99 0.97 1.01 0.50 1.24 0.97 0.99
Progressive Field             CLE08   1  1994  1008 1.01 1.02 1.00 1.05 0.78 0.95 1.03 1.00
Coors Field                   DEN02   2  2005   244 1.10 0.97 1.11 1.03 1.24 1.09 0.98 0.85
Comerica Park                 DET05   2  2003   324 1.00 0.93 1.02 0.86 1.56 0.87 0.95 0.94
Minute Maid Park              HOU03   1  2000   648 1.02 1.00 1.02 0.98 1.39 1.18 0.96 1.00
Kauffman Stadium              KAN06   4  2004  7323 1.04 1.08 1.01 1.11 1.21 0.83 1.04 0.92
Dodger Stadium                LOS03   6  2001  7567 0.99 0.89 1.03 0.91 0.61 1.08 1.03 1.03
Land Shark Stadium            MIA01   2  1994  1017 1.00 0.99 1.01 0.95 1.36 0.92 1.06 1.05
Miller Park                   MIL06   1  2001   570 0.98 1.03 0.97 1.02 0.92 1.13 1.04 1.01
Hubert H. Humphrey Metrodome  MIN03   2  1983  1836 1.03 1.09 1.00 1.11 1.28 0.98 1.00 1.04
Shea Stadium                  NYC17   3  1985  1744 0.98 0.95 1.00 0.94 0.90 0.93 0.97 1.02
Yankee Stadium                NYC16   7  1988  1420 0.99 0.94 1.01 0.95 0.73 1.07 0.96 0.99
Oakland Coliseum              OAK01   6  1996   885 0.96 1.01 0.96 0.98 0.89 0.97 0.97 0.96
Citizens Bank Park            PHI13   1  2004   324 1.01 0.96 1.03 0.97 0.96 1.23 0.89 0.97
Chase Field                   PHO01   1  1998   729 1.05 1.06 1.03 1.07 1.60 1.11 1.03 0.92
PNC Park                      PIT08   1  2001   565 1.03 1.01 1.03 1.08 0.77 0.89 0.95 0.92
PetCo Park                    SAN02   2  2006   162 0.94 0.86 0.99 0.77 1.07 0.90 1.00 1.08
AT&T Park                     SFO03   2  2004   325 1.05 0.98 1.05 1.00 1.24 0.87 0.96 0.94
Safeco Field                  SEA03   1  1999   650 0.96 0.96 0.97 0.94 0.76 0.93 1.09 1.07
Busch Stadium III             STL10   1  2006   161 1.01 0.90 1.05 0.91 0.82 0.82 0.97 0.90
Tropicana Field               STP01   2  2001   561 0.99 1.01 0.99 0.97 1.29 0.98 0.98 1.02
SkyDome                       TOR02   1  1989  1320 1.00 1.10 0.96 1.10 1.11 1.10 1.02 1.01
Robert F. Kennedy Stadium     WAS10   3  1971   324 0.97 0.94 0.99 0.90 0.98 0.77 0.88 1.01

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