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

Question: What factors have an effect on runs scored at MLB Parks?

Why I asked the question: I was trying to find why Chase Field had such a high Park Factor over the years and study just exploded from there.

Analysis: Originally I did some research on effects on all MLB and MiLB stadiums (link to spreadsheet). After it was available someone brought up that Chase Field had such a high Park Factor and elevation and temperature could not explain the entire effect. Trying to able to tell if it was the lower humidity (as some suggested) or park size, I decided to run a multiple regression for the average total runs scored per game (home and away team scores averaged) against elevation, average temperature, average humidity, park size and foul territory area.

I plan to use park factors at some point in the analysis, but I can only find park factors in single digits (e.g. 102 vice 102.45). Using these leads to a very low r-squared do to too much rounding. Once I find the data, I will run the data against them to predict park factors.

Sources of data:

Runs Scored – Collect from retrosheet database – average values from last three years

Elevation - List of Major League Baseball stadiums on Wikepedia

Temperature – Collected from the retrosheet database – last 3 years

Humidity – Average values from April to September from websites BBC.com and CityRating.com

Park Fair Area – Calculated using the equations discussed on The Book blog

Park Foul Area – Areas were calculated by Mitchel Lichtman

The data is for each of the major league parks is in the following table

Table 1

Team	Park	Original Runs scored (league adjusted)	Fair Area	Foul Area	Humidity %	Elevation (ft)	Average Temp (F)
Arizona Diamondbacks	Chase Field	9.67	109999	26712	18.3	1087	80.6
Atlanta Braves	Turner Field	9.58	113031	23852	56.0	928	79.8
Baltimore Orioles	Oriole Park at Camden Yards	9.99	106745	23055	52.5	30	80.6
Boston Red Sox	Fenway Park	9.68	99147	17859	58.2	15	69.1
Chicago Cubs	Wrigley Field	9.77	107892	18564	58.0	600	69.6
Chicago White Sox	U.S. Cellular Field	9.69	108913	25663	58.0	595	68.3
Cincinnati Reds	Great American Ball Park	10.13	104830	23376	55.5	542	76.2
Cleveland Indians	Progressive Field	9.41	105817	21664	58.2	656	69.1
Colorado Rockies	Coors Field	10.55	116260	28269	35.2	5198	73.7
Detroit Tigers	Comerica Park	9.75	112983	30227	54.7	600	71.9
Florida Marlins	Dolphin Stadium	9.66	109542	28144	61.8	5	83.2
Houston Astros	Minute Maid Park	9.13	102328	25139	62.3	48	74.5
Kansas City Royals	Kauffman Stadium	9.39	109689	23528	61.5	877	76.8
Los Angeles Angels of Anaheim	Angel Stadium of Anaheim	8.86	108130	22021	67.2	153	75.1
Los Angeles Dodgers	Dodger Stadium	8.93	105899	18276	67.2	517	73.4
Milwaukee Brewers	Miller Park	9.32	108367	23047	63.0	598	72.0
Minnesota Twins	Hubert H. Humphrey Metrodome	8.35	104404	33578	57.5	992	69.5
New York Mets	Shea Stadium	9.14	112137	25665	54.8	12	72.4
New York Yankees	Yankee Stadium	9.77	115349	18949	54.8	17	72.2
Oakland Athletics	Oakland-Alameda County Coliseum	7.98	103539	40153	59.8	7	64.3
Philadelphia Phillies	Citizens Bank Park	10.23	101280	25107	53.7	19	74.8
Pittsburgh Pirates	PNC Park	9.37	108670	22914	53.7	726	73.0
St. Louis Cardinals	Busch Stadium	9.20	111239	25783	54.2	453	76.9
San Diego Padres	PETCO Park	7.71	107331	21473	65.3	21	69.4
San Francisco Giants	AT&T Park	8.98	107077	23267	59.8	10	64.4
Seattle Mariners	Safeco Field	8.72	109120	26290	53.5	17	64.4
Tampa Bay Rays	Tropicana Field	9.03	106163	25590	59.2	38	72.0
Texas Rangers	Rangers Ballpark in Arlington	10.51	110743	21494	56.5	546	81.2
Toronto Blue Jays	Rogers Centre	8.46	108540	30327	57.3	290	71.4
Washington Nationals	Nationals Park	9.04	108752	26400	54.2	17	76.1

I ran a regression on the data to get an equation that uses the data to create a best fit line. I originally ran fence height as part of the regression and the final regression equation was even less accurate. The equation to predict the runs scored after running the regression is:

Runs Scored = 0.0513 * Degrees F +0.000212 * Elevation in feet – 0.0176 * % Relative Humidity – 0.0000543 * Foul Area in square feet – 0.00000982 * Fair Area in square feet + 8.874 [+0.4267 runs for AL Park]

Standard Deviation of 0.47 and R-squared of 0.526

Here is a simple chart of the factors for easy comparison.

Table 2

Factor	Change in Total Runs Scored per Game
10 degree F increase	+0.51
Increase in RH by 10%	-0.18
10,000 sq ft increase in foul area	-0.54
10,000 sq ft increase in playing area	-0.098
1000 ft increase in elevation	+0.21

As it can be seen, each factor can significantly effect the runs scored. The following table is the original and final number for each of the ballparks.

Table 3

Team	Park	Original Runs scored (league adjusted)	Projected Runs scored (league adjusted)	Original Runs Scored (not league adjusted)	Projected Runs Scored (not league adjusted)	Difference (Original – Projected)
Arizona Diamondbacks	Chase Field	9.67	10.38	9.67	10.38	-0.71
Atlanta Braves	Turner Field	9.58	9.77	9.58	9.77	-0.18
Baltimore Orioles	Oriole Park at Camden Yards	9.99	9.79	10.42	10.21	0.21
Boston Red Sox	Fenway Park	9.68	9.45	10.11	9.88	0.23
Chicago Cubs	Wrigley Field	9.77	9.48	9.77	9.48	0.29
Chicago White Sox	U.S. Cellular Field	9.69	9.02	10.12	9.44	0.68
Cincinnati Reds	Great American Ball Park	10.13	9.62	10.13	9.62	0.52
Cleveland Indians	Progressive Field	9.41	9.31	9.84	9.74	0.10
Colorado Rockies	Coors Field	10.55	10.46	10.55	10.46	0.09
Detroit Tigers	Comerica Park	9.75	8.97	10.18	9.40	0.78
Florida Marlins	Dolphin Stadium	9.66	9.45	9.66	9.45	0.21
Houston Astros	Minute Maid Park	9.13	9.23	9.13	9.23	-0.10
Kansas City Royals	Kauffman Stadium	9.39	9.56	9.82	9.98	-0.17
Los Angeles Angels of Anaheim	Angel Stadium of Anaheim	8.86	9.31	9.29	9.74	-0.45
Los Angeles Dodgers	Dodger Stadium	8.93	9.53	8.93	9.53	-0.60
Milwaukee Brewers	Miller Park	9.32	9.26	9.32	9.26	0.06
Minnesota Twins	Hubert H. Humphrey Metrodome	8.35	8.78	8.78	9.21	-0.43
New York Mets	Shea Stadium	9.14	9.13	9.14	9.13	0.01
New York Yankees	Yankee Stadium	9.77	9.45	10.20	9.88	0.32
Oakland Athletics	Oakland-Alameda County Coliseum	7.98	7.92	8.40	8.34	0.06
Philadelphia Phillies	Citizens Bank Park	10.23	9.41	10.23	9.41	0.82
Pittsburgh Pirates	PNC Park	9.37	9.51	9.37	9.51	-0.15
St. Louis Cardinals	Busch Stadium	9.20	9.46	9.20	9.46	-0.26
San Diego Padres	PETCO Park	7.71	9.06	7.71	9.06	-1.35
San Francisco Giants	AT&T Park	8.98	8.81	8.98	8.81	0.17
Seattle Mariners	Safeco Field	8.72	8.73	9.15	9.16	-0.01
Tampa Bay Rays	Tropicana Field	9.03	9.10	9.46	9.52	-0.06
Texas Rangers	Rangers Ballpark in Arlington	10.51	9.90	10.94	10.32	0.61
Toronto Blue Jays	Rogers Centre	8.46	8.87	8.89	9.30	-0.41
Washington Nationals	Nationals Park	9.04	9.32	9.04	9.32	-0.28

The equation is able to predict some stadiums run production very accurately. Here is a table where the regression equation was able to predict the runs scored (within 0.1 runs).

Table 4

Team	Park	Original Runs scored (league adjusted)	Projected Runs scored (league adjusted)	Difference (Original – Projected)
Houston Astros	Minute Maid Park	9.13	9.23	-0.10
Tampa Bay Rays	Tropicana Field	9.03	9.10	-0.06
Seattle Mariners	Safeco Field	8.72	8.73	-0.01
New York Mets	Shea Stadium	9.14	9.13	0.01
Milwaukee Brewers	Miller Park	9.32	9.26	0.06
Oakland Athletics	Oakland-Alameda County Coliseum	7.98	7.92	0.06
Colorado Rockies	Coors Field	10.55	10.46	0.09
Cleveland Indians	Progressive Field	9.41	9.31	0.10

I grouped the parks that exceeded the Standard Deviation of 0.47. These are the parks that through the factors that run scoring environment can't be explained as well.

Team	Park	Original Runs scored (league adjusted)	Projected Runs scored (league adjusted)	Difference (Original – Projected)
San Diego Padres	PETCO Park	7.71	9.06	-1.35
Arizona Diamondbacks	Chase Field	9.67	10.38	-0.71
Los Angeles Dodgers	Dodger Stadium	8.93	9.53	-0.60
Cincinnati Reds	Great American Ball Park	10.13	9.62	0.52
Texas Rangers	Rangers Ballpark in Arlington	10.51	9.90	0.61
Chicago White Sox	U.S. Cellular Field	9.69	9.02	0.68
Detroit Tigers	Comerica Park	9.75	8.97	0.78
Philadelphia Phillies	Citizens Bank Park	10.23	9.41	0.82

For future analysis, I will look into park factors and also any other factors related to the parks. If you have another set of data (e.g. hits or home runs) feel free to send them and I will run them against the data. Also, you could run your own regression using LINEST() in Excel or OpenOffice (for us cheap people).

I would like to use wind as a measurement, but haven't found a good way to convert wind speed and direction into one variable. Again, if anyone has any idea, please let me know. If any one can think of other factors to consider, please let me know.