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 in the following table

Park Factors and Park Characteristics

Team	Park Factors	LF	LC	CF	RC	RF	Average Wall Height	Foul Area	Surface
Arizona Diamondbacks	1.0505	330	376	407	376	335	13.33	26712	0
Atlanta Braves	0.9934	335	380	400	390	330	8.00	23852	0
Baltimore Orioles	0.9946	333	364	410	373	318	13.00	23055	0
Boston Red Sox	1.0313	310	335	390	380	302	19.33	17859	0
Chicago Cubs	1.0257	355	368	400	368	353	14.33	18564	0
Chicago White Sox	1.0285	335	375	400	375	330	8.00	25663	0
Cincinnati Reds	1.0150	328	365	404	365	325	9.33	23376	0
Cleveland Indians	0.9819	325	360	405	375	325	11.67	21664	0
Colorado Rockies	1.1066	347	390	415	382	350	11.00	28269	0
Detroit Tigers	0.9838	345	370	420	388	330	10.00	30227	0
Florida Marlins	0.9667	330	360	434	373	345	8.00	28144	0
Houston Astros	1.0006	315	335	436	365	326	12.33	25139	0
Kansas City Royals	1.0033	330	375	410	375	330	8.00	23528	0
Los Angeles Angels of Anaheim	0.9774	330	382	400	365	330	11.33	22021	0
Los Angeles Dodgers	0.9751	330	368	400	368	330	8.00	18276	0
Milwaukee Brewers	1.0031	344	370	400	374	337	12.00	23047	0
Minnesota Twins	0.9971	343	370	408	352	327	14.33	33578	1
New York Mets	0.9754	338	371	410	371	338	8.00	25665	0
New York Yankees	0.9879	318	399	408	385	314	7.67	18949	0
Oakland Athletics	0.9836	330	362	400	362	330	10.67	40153	0
Philadelphia Phillies	1.0273	329	355	401	357	330	9.53	25107	0
Pittsburgh Pirates	0.9913	325	389	399	364	320	16.00	22914	0
St. Louis Cardinals	0.9816	334	378	396	387	322	9.00	25783	0
San Diego Padres	0.9248	339	368	399	378	309	7.67	21473	0
San Francisco Giants	0.9977	331	375	405	365	326	13.67	23267	0
Seattle Mariners	0.9632	335	375	400	375	335	8.00	26290	0
Tampa Bay Rays	0.9878	315	370	404	370	322	9.50	25590	1
Texas Rangers	1.0497	330	380	400	380	330	10.00	21494	0
Toronto Blue Jays	1.0220	328	375	400	375	328	10.00	30327	1
Washington Nationals	1.0070	336	377	402	370	335	7.00	26400	0

Natural Factors and Errors

Park	Team	Error per Game	% Relative Humidity	Wind Strength to CF	Wind Strength to RF	Elevation	Average Temp
Chase Field	Arizona Diamondbacks	0.58	18.3	-0.60	0.59	1087	80.6
Turner Field	Atlanta Braves	0.66	56.0	0.13	1.68	928	79.8
Oriole Park at Camden Yards	Baltimore Orioles	0.59	52.5	0.71	0.44	30	80.6
Fenway Park	Boston Red Sox	0.62	58.2	1.85	2.16	15	69.1
Wrigley Field	Chicago Cubs	0.72	58.0	-1.20	0.77	600	69.6
U.S. Cellular Field	Chicago White Sox	0.64	58.0	0.05	2.46	595	68.3
Great American Ball Park	Cincinnati Reds	0.55	55.5	0.47	0.42	542	76.2
Progressive Field	Cleveland Indians	0.63	58.2	-0.87	4.23	656	69.1
Coors Field	Colorado Rockies	0.74	35.2	-1.40	0.20	5198	73.7
Comerica Park	Detroit Tigers	0.63	54.7	-0.12	-0.31	600	71.9
Dolphin Stadium	Florida Marlins	0.67	61.8	-5.99	1.30	5	83.2
Minute Maid Park	Houston Astros	0.45	62.3	0.39	-0.46	48	74.5
Kauffman Stadium	Kansas City Royals	0.64	61.5	-0.40	-0.77	877	76.8
Angel Stadium of Anaheim	Los Angeles Angels of Anaheim	0.67	67.2	4.55	1.14	153	75.1
Dodger Stadium	Los Angeles Dodgers	0.69	67.2	5.39	0.46	517	73.4
Miller Park	Milwaukee Brewers	0.66	63.0	-0.78	0.35	598	72.0
Hubert H. Humphrey Metrodome	Minnesota Twins	0.64	57.5	0.00	0.00	992	69.5
Shea Stadium	New York Mets	0.65	54.8	0.59	-0.68	12	72.4
Yankee Stadium	New York Yankees	0.70	54.8	1.84	-0.12	17	72.2
Oakland-Alameda County Coliseum	Oakland Athletics	0.56	59.8	3.47	7.73	7	64.3
Citizens Bank Park	Philadelphia Phillies	0.71	53.7	1.49	3.38	19	74.8
PNC Park	Pittsburgh Pirates	0.64	53.7	1.65	-1.30	726	73.0
Busch Stadium	St. Louis Cardinals	0.57	54.2	2.46	0.39	453	76.9
PETCO Park	San Diego Padres	0.44	65.3	1.89	8.23	21	69.4
AT&T Park	San Francisco Giants	0.66	59.8	8.63	2.85	10	64.4
Safeco Field	Seattle Mariners	0.73	53.5	0.42	1.21	17	64.4
Tropicana Field	Tampa Bay Rays	0.65	59.2	0.00	0.00	38	72.0
Rangers Ballpark in Arlington	Texas Rangers	0.63	56.5	-4.65	4.52	546	81.2
Rogers Centre	Toronto Blue Jays	0.56	57.3	0.17	2.07	290	71.4
Nationals Park	Washington Nationals	0.58	54.2	5.68	-5.68	17	75.9

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.

Table 3. 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 in Runs Scored per game (9.54 runs per game)
10 degree F increase	0.008	0.07
Increase in RH by 10%	0.012	-0.12
10,000 sq ft increase in foul area	-0.006	-0.06
Surface is Turf	0.009	0.09
1000 ft increase in elevation	0.021	0.20
1 Errors for Away Team	0.016	0.15
10 ft increase in LF	-0.010	-0.10
10 ft increase in LC	-0.006	-0.06
10 ft increase in CF	-0.010	-0.10
10 ft increase in RC	-0.002	-0.02
10 ft increase in RF	0.011	0.10

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.

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.

Team	Park	Original Value	Dimensions plus constant	Projected Value	Difference
Los Angeles Angels of Anaheim	Angel Stadium of Anaheim	0.9774	0.9960	0.9860	-0.0086
Minnesota Twins	Hubert H. Humphrey Metrodome	0.9971	0.9839	0.9981	-0.0011
Oakland Athletics	Oakland-Alameda County Coliseum	0.9836	0.9982	0.9840	-0.0004
Colorado Rockies	Coors Field	1.1066	0.9729	1.1056	0.0010
Kansas City Royals	Kauffman Stadium	1.0033	0.9874	1.0001	0.0033
Cincinnati Reds	Great American Ball Park	1.0150	0.9986	1.0096	0.0054
Milwaukee Brewers	Miller Park	1.0031	0.9947	0.9963	0.0068
Baltimore Orioles	Oriole Park at Camden Yards	0.9946	0.9794	0.9875	0.0070

I grouped the parks that exceeded the Standard Deviation of 0.0184 These are the stadiums that the factors I am using can't explain the runs scored at that stadium.

Team	Park	Original Value	Dimensions plus constant	Projected Value	Difference
Seattle Mariners	Safeco Field	0.9632	0.9962	0.9925	-0.0293
San Diego Padres	PETCO Park	0.9248	0.9724	0.9539	-0.0291
Los Angeles Dodgers	Dodger Stadium	0.9751	1.0065	1.0030	-0.0278
Cleveland Indians	Progressive Field	0.9819	1.0028	1.0087	-0.0268
Toronto Blue Jays	Rogers Centre	1.0220	1.0022	1.0023	0.0197
San Francisco Giants	AT&T Park	0.9977	0.9894	0.9769	0.0208
Chicago White Sox	U.S. Cellular Field	1.0285	0.9912	0.9958	0.0328
Texas Rangers	Rangers Ballpark in Arlington	1.0497	0.9946	1.0096	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	0.01
LC	371	-0.24	379	-0.24	0
CF	410	-0.41	408	-0.41	0
RC	371	-0.07	383	-0.08	-0.01
RF	338	0.36	330	0.35	-0.01
Foul Area	25665	-0.02	20900	-0.01	0
				Total =	-0.01

The new Mets stadium looks to allow less runs per game than the previous one. If you used the 9.54 runs per game environment, 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.


Extra information for those that want to do their own regression analysis.

You could run your own regression using LINEST() in OpenOffice by using the data I have collected. I have the spreadsheet for download and by inserting your own park factors into the spreadsheet, it will calculate the values for you.

Note: LINEST() puts the equation values in the opposite order they occur in the table and the 3rd value down on the left is the r-squared value.

Instructions:

1. Open the spreadsheet in OpenOffice Calc. I use OpenOffice because it's free for everyone and creates the variables simply.
2. Inset your values for the various teams into Table 1, 2, 3 and 4 under Park Factor columns. The cells for LINEST() will automatically update using the numbers.
3. Copy all the LINEST() values and paste them into the area after Table 2. The upper left hand corner of the original data should be pasted on the cell that has a border. See following image.



4. All the values will be automatically updated in Table 2
5. Do the same with Tables 3 and 4, but they don't contain Wall Height and Wind factors.