What factors have an effect on runs scored at MLB Parks? Part 2

Question:"> What factors have an effect on runs scored at MLB Parks? Part 2

Why I asked the question: I was trying to find why Chase Field had such a high Park Factor over the years and the research expanded to all stadiums from that point.

Analysis: I did some research on effects on all MLB and MiLB stadiums (link to spreadsheet). After it was published, someone brought up that Chase Field had such a high Park Factor and elevation and temperature could not explain the entire difference. Being unable to tell if it was the lower humidity (as some suggested) or park size, I decided to run a multiple regression for the average park factors over the last 3 years (2006 to 2008) against elevation, average temperature, average humidity, park size (RF, RC, CF, LC, LF), average wall height, errors per game, wind direction, surface type and foul territory area.

Explanation of source of data:

Park Factors – I originally used runs scored per game because of the only Park Factors I could find did not go to the decimal point. After my original article ran, I got flooded with many different sets of data and am using Patriot's numbers from his website (htttp://gosu02.tripod.com/id103.html)

Elevation (ft)- Collected from the List of Major League Baseball stadiums on Wikepedia – Elevation is a major factor in determining the distance a ball travels and the time the defense has to react to the ball once it is in play.

Temperature (degrees F)– Collected from the retrosheet database – last 3 years, except only 1 year's worth of data for Washington. The higher the temperature the farther a ball will travel

Relative Humidity (percentage) – Average values from April to September from websites BBC.com and CityRating.com Humidity is not supposed to have much of an effect on the distance a ball travels, but maybe that that small differences will explain some differences.

Dimensions (ft) – Taken from Wikepedia. Only 5 sets used – LF, FC, CF, RC and RF. Originally used total area from ballpark, but I found out that even though these two stadiums that had about the same area the stadium shaped like #1 below had a higher park factor:

Stadium #1 360-380-400-380-360

Stadium #2 380-380-380-380-380

Park Foul Area (ft squared) – Areas were calculated by Mitchel Lichtman. The larger the foul area, more foul balls will be caught, therefore less runs scored

Wind strength and direction (mph) - I used Retrosheet data from the last 3 years (1 year for Washington). The data from Retrosheet comes in the for of 8 different directions. From these different directions, I created the following matrix:

Wind Direction	X component	Y component
To LF	-0.71	0.71
To CF	0	1
To RF	0.71	0.71
LF to RF	1	0
From LF	0.71	-0.71
From CF	0	-1
From RF	-0.71	-0.71
RF to LF	-1	0

I multiplied the X and Y values by the wind speed, added all the wind values up for each component and then divided by the number of games. Y component is a wind blowing out to CF, while the X component is a wind blowing to RF.

Question: When collecting this data, I found there was no wind blowing in form right field and I thought I had made a mistake somewhere. I searched on the games database for hat wind direction and the most recent case was in 2003. Has the wind not once over 5 years blown in from 1 game from RF? Is there some unspoken rule that the scores don't mark it this way?

Opponents Errors per game – I was looking for a way to measure how tough it is to play in a Stadium (i.e. Fly balls in Metrodome). The best metric I could come up with is to average the amount of errors the opposing team has per game.

Playing Surface – The three stadiums with Turf were given a value of 1 and the rest 0. Being that it was the new Field Turf, I wondered if runs scored might go down because the balls hit would be slower than "AstroTurf" and less weird bounces.

Average Wall Height (ft) – Averaged the values ballparks.com Now it is time for a few graphs that show the data collected. *

Note: Data on the Washington Nationals is only from 2008 since they just moved into a new park this last year.

The initial data is for each of the major league parks is location in the following  spreadsheet that can be downloaded.

FactorsForParkFactors

I ran a regression analysis on the data to get an equation that uses the preceding data. The regression equation ended up having an R-squared of 0.714 and the Standard Deviation of the difference of the initial Park Factor and the final Park Factor was 0.0178. There was two problems with that initial equation:

1. The variable for wind blowing to CF was negative, therefore the more the wind was blowing out, less scoring that would be. That just defies all logic, so I threw both the Wind Components out for the next round of analysis

2. The variable for Wall Height was positive, meaning the higher the wall, the more runs that are scored. Home runs score more runs than doubles, so I decided to remove Wall Height also.

After rerunning the regression after removing Wall Height and Wind, I got the following equation Standard Deviation of 0.0.0184 and R-squared of 0.692:

Park Factors = Away Teams Errors per game * (0.016) + % Relative Humidity * (-0.0012) + Foul Area * (-0.00000061) + Elevation * (0.000021) + Average Temperature * (0.00077) + Left Field * (-0.0010) + Left Center Field * (-0.00063) + Center Field * (-0.0010) + Right Center Field * (-0.00020) + Right Field * (0.0011) + 0.0090 (if Surface is turf) + 1.7056

Here is a simple chart of the factors for easy comparison of the factor and how much effects the park factor and run scoring environment. 

The amount each factor has on Park Factors and Runs Scored (9.54 runs per game was the average runs scored by both teams over the past 3 years

Factor	Change in Park Factor	Change Runs Scored per game (9.54 runs per game)
10 degree F increase	0.0077	0.073
Increase in RH by 10%	0.0120	-0.115
10,000 sq ft increase in foul area	-0.0061	-0.058
Surface is Turf	0.0090	0.085
1000 ft increase in elevation	0.0206	0.196
1 Errors for Away Team	0.0160	0.150
10 ft increase in LF	-0.0100	-0.095
10 ft increase in LC	-0.0063	-0.060
10 ft increase in CF	-0.0101	-0.096
10 ft increase in RC	-0.0020	-0.019
10 ft increase in RF	0.0106	0.101

As it can be seen, each factor can significantly effect the runs scored.

The following table is the original and final numbers for each of the ballparks. I also have added a column of combined stadium attributes (Dimensions, Foul Area and Surface Type) added to the equation's constant value to help to show which stadium designs lead to more runs.

Team	Park	Original Value	Dimen plus constant	Projected Value	Diference	Original Value	Dimen plus constant	Projected Value	Difference
Arizona Diamondbacks	Chase Field	1.0505	0.9930	1.0642	-0.0136	10.0214	9.4725	10.1512	-0.1298
Atlanta Braves	Turner Field	0.9934	0.9862	1.0090	-0.0157	9.4758	9.4076	9.6254	-0.1495
Baltimore Orioles	Oriole Park at Camden Yards	0.9946	0.9794	0.9875	0.0070	9.4874	9.3425	9.4202	0.0672
Boston Red Sox	Fenway Park	1.0313	1.0256	1.0183	0.0130	9.8382	9.7836	9.7137	0.1245
Chicago Cubs	Wrigley Field	1.0257	1.0059	1.0127	0.0130	9.7841	9.5951	9.6603	0.1238
Chicago White Sox	U.S. Cellular Field	1.0285	0.9912	0.9958	0.0328	9.8115	9.4557	9.4987	0.3128
Cincinnati Reds	Great American Ball Park	1.0150	0.9986	1.0096	0.0054	9.6825	9.5258	9.6307	0.0518
Cleveland Indians	Progressive Field	0.9819	1.0028	1.0087	-0.0268	9.3667	9.5659	9.6227	-0.2560
Colorado Rockies	Coors Field	1.1066	0.9729	1.1056	0.0010	10.5559	9.2808	10.5461	0.0098
Detroit Tigers	Comerica Park	0.9838	0.9589	0.9702	0.0136	9.3846	9.1474	9.2551	0.1295
Florida Marlins	Dolphin Stadium	0.9667	0.9863	0.9859	-0.0192	9.2217	9.4083	9.4045	-0.1828
Houston Astros	Minute Maid Park	1.0006	0.9983	0.9881	0.0125	9.5452	9.5230	9.4258	0.1194
Kansas City Royals	Kauffman Stadium	1.0033	0.9874	1.0001	0.0033	9.5710	9.4195	9.5399	0.0312
Los Angeles Angels of Anaheim	Angel Stadium of Anaheim	0.9774	0.9960	0.9860	-0.0086	9.3238	9.5010	9.4059	-0.0821
Los Angeles Dodgers	Dodger Stadium	0.9751	1.0065	1.0030	-0.0278	9.3021	9.6016	9.5677	-0.2655
Milwaukee Brewers	Miller Park	1.0031	0.9947	0.9963	0.0068	9.5688	9.4882	9.5039	0.0649
Minnesota Twins	Hubert H. Humphrey Metrodome	0.9971	0.9839	0.9981	-0.0011	9.5111	9.3856	9.5214	-0.0103
New York Mets	Shea Stadium	0.9754	0.9900	0.9896	-0.0142	9.3046	9.4437	9.4396	-0.1350
New York Yankees	Yankee Stadium	0.9879	0.9700	0.9704	0.0176	9.4243	9.2535	9.2568	0.1675
Oakland Athletics	Oakland-Alameda County Coliseum	0.9836	0.9982	0.9840	-0.0004	9.3831	9.5223	9.3865	-0.0034
Philadelphia Phillies	Citizens Bank Park	1.0273	1.0128	1.0167	0.0105	9.7994	9.6613	9.6989	0.1006
Pittsburgh Pirates	PNC Park	0.9913	0.9866	1.0026	-0.0113	9.4561	9.4113	9.5641	-0.1080
St. Louis Cardinals	Busch Stadium	0.9816	0.9834	0.9951	-0.0135	9.3637	9.3811	9.4929	-0.1292
San Diego Padres	PETCO Park	0.9248	0.9724	0.9539	-0.0291	8.8215	9.2756	9.0992	-0.2777
San Francisco Giants	AT&T Park	0.9977	0.9894	0.9769	0.0208	9.5172	9.4380	9.3189	0.1983
Seattle Mariners	Safeco Field	0.9632	0.9962	0.9925	-0.0293	9.1884	9.5027	9.4680	-0.2797
Tampa Bay Rays	Tropicana Field	0.9878	1.0118	1.0063	-0.0186	9.4225	9.6519	9.5997	-0.1772
Texas Rangers	Rangers Ballpark in Arlington	1.0497	0.9946	1.0096	0.0401	10.0137	9.4877	9.6312	0.3825
Toronto Blue Jays	Rogers Centre	1.0220	1.0022	1.0023	0.0197	9.7490	9.5604	9.5615	0.1875
Washington Nationals	Nationals Park	1.0070	0.9928	0.9949	0.0120	9.6058	9.4707	9.4910	0.1148

The regression equation is able to predict some stadiums run production quite well. Here is a table where the regression was able to predict the Park Factor within 0.01.

The regression equation is able to predict some stadiums run production quite well. Here is a list of stadiums where the regression was able to predict the Park Factor within 0.01.

Angel Stadium of Anaheim    -0.0086

Hubert H. Humphrey Metrodome    -0.0011

Oakland-Alameda County Coliseum    -0.0004

Coors Field    0.0010

Kauffman Stadium    0.0033

Great American Ball Park    0.0054

Miller Park    0.0068

Oriole Park at Camden Yards    0.0070

Seattle Mariners    -0.0293

San Diego Padres    -0.0291

Los Angeles Dodgers    -0.0278

Cleveland Indians    -0.0268

Toronto Blue Jays    0.0197

San Francisco Giants    0.0208

Chicago White Sox    0.0328

Texas Rangers    0.0401

Using the preceding data we can do analysis on future parks. I will pick the Met's new stadium, Citi Field. Most of the natural effects will be the same and the errors aren't know yet, but we can look at the dimensions and foul area to come to some conclusion.

Feature	Shea Stadium	Change in PF	Citi Field	Change in PF	Difference (Citi-Shea)
LF	338	-0.34	335	-0.33	0.010
LC	371	-0.24	379	-0.24	0.000
CF	410	-0.41	408	-0.41	0.000
RC	371	-0.07	383	-0.08	-0.010
RF	338	0.36	330	0.35	-0.010
Foul Area	25665	-0.02	20900	-0.01	-0.003
				Total	-0.013

The new Mets stadium looks to allow less runs per game than the previous one.  If  the 9.54 runs per game environment is used, it would allow 0.12 runs less per game or about 10 less runs over the entire 81 home games.

I have had a lot of help putting this study together and special thanks to Mitchel Lichtman and Patriot for providing and data and to Sky Kalkman for his many suggestions. I hope the data gives people more of an insight to various variables that go into a stadium and how much of an effect each variable has on the run scored environment.