THE BOOK--Playing The Percentages In Baseball

Friday, March 28, 2008

True HR Park Factors (or at least something we can regress towards)

By , 03:42 AM

Here is what I did. I took each ballpark and recorded the fence height and distance for the LFL, LF, LCF, CF, RCF, RF, and RFL. LF and RF were around 17 degrees (the whole outfield from line to line is 90 degrees) from the lines and LCF and RCF were around 23 degrees from the lines.

Then I looked at how many HR’s are hit within 8 degrees (4 degrees on either side) of each of the above lines. As it turns out, of all HR’s hit to either side of the field, around 10% are hit to CF (I used “within 8 degrees left of center” for the “left side CF HR’s,” and “within 8 degrees right of center” for the “right side CF HR’s"), 21% to RC and LC, 24% to LF and RC, and 16% down the lines. These percentages do not add up to 100 because I only looked at HR’s within around 8 degrees of each line. I used these percentages for a weighting, as you will see in a minute.

Next I looked at, for each park, a fly ball distance factor, which is basically average home fly ball distance divided by average road (plus a fraction of home) fly ball distance. This is just like a regular HR or run park factor, only using fly ball distances. I computed a left side and right side fly ball distance factor. I used STATS data and included all air balls other than bunts. For indoor parks or semi-indoor, like Toronto, I used the same number for the left and right sides (the average of the two). For all other parks, I regressed the right and left side factors 50% toward that park’s overall (left and right combined) factor. Obviously I only used data for as long as the park was in existence, up to 5 years at the most. For Coors Field, I used 06 and 07 only, as 06 was the year they started to use the “mega-humidor.” BTW, the fly ball distance factor at Coors went down considerably in 03 (from 1.072 to 1.025) and then again in 06 (to 1.013), so please don’t let anyone tell you that the humidor in 03 and the “mega-humidor” in 06 has had little to do with decreased run scoring and especially HR rates in Coors Field,

Now that I have all the data I need, here is what I did: I took each fence distance at all of the points mentioned above (4 on the left side and 4 on the right side, double counting CF) and adjusted for fence height. To do that, I simply added any fence height above average to the fence distance. I don’t know if that’s right, but I recall that in one of Greg R’s articles on home runs distances, he mentioned that if you add a foot of fence height, you need about another foot of distance on a fly ball to clear that extra foot of fence height. If I got that wrong, or he has updated that, I am hoping he will respond so I can change this part of the calculations.

Anyway, then I divided by the fly ball distance factors explained above. This gives us the “effective” or normalized distance for each of those sections of the field. For example, Coors Field is 347 feet down the left field line (LFL) and the fence is 8 feet high. The average fence along the LFL is 10.5 feet (Fenway jacks up the number), so we add 2.5 feet to the 347 feet to make it 349.5. Now we divide by Coors’ left side FB distance factor, which is 1.019 (for 06 and 07). We divide because a FB factor above 1.000 means that the ball travels further than at an average park, thus the “effective” fence distance is shorter. That gives us 343 rather than 349.5.

We do the same thing for all 4 points or sections on the left side and then for the right side. Then we get a weighted average of all 4 sections on each side, weighting by the percentage of HR’s that are hit in that section, the 16, 24, 20, and 10 numbers I explained above. That gives us a weighted average effective fence distance for the left side of each park and for the right side. Now we can simply compare this to the averages for all parks by subtracting one from the other.

I actually did the above calculations combining all the parks in both leagues, even though the fly ball distance factors are mostly (I included inter-league games in the data) relative to league (NL or AL) averages. In any case, here are the results for each park. A negative number means that the effective average fence distance, assuming the same or league-average height, is shorter than average, and thus the true HR park factor should be greater than 100.

Maybe someone can post how to convert this into an actual HR park factor. In other words, if a park is -8 on the left side, like Fenway is (as compared to the average NL and AL park), that means that its average fence is 8 feet shorter on the left side. How would that translate into a park factor? How many more HR’s (and thus how much more in percentage terms) would be hit if an average park shortened their fences by 8 feet? Tango did this kind of conversion, I think, when he was discussing major versus minor league baseballs.

I’ll actually post 2 sets of numbers for each park: One, as compared to all parks in both leagues and one as compared to parks in the same league only. Keep in mind that I am using the same fly ball distance factors for each set of numbers. It is likely that they wouldn’t be all that different if we were able to do them relative to all parks and not just mostly parks in the same league.

Also keep in mind that these are only referring to effective fence distances. They would be more closely connected with HR rates per BIP, or better yet, per FB, rather than per game, inning, or even per PA. For example, Oakland’s “effective” fences are shorter than average, but because of the large foul territory, many of the PA’s end in a foulout and therefore the HR per PA rate is much less than you would expect from the effective fence distances. Park factors for K and BB rates have a similar effect. And of course, these numbers assume the same geographical distribution and ratios of HR/FB/GB at all parks. It could be that pitchers and/or batters try and pitch or hit towards favorable sections of the OF or in ways that induce more or fewer fly or ground balls. It would be interesting to compare these numbers to each park’s HR rate per BIP or per FB compared to league averages. Anyone have that data handy?

The first two numbers are relative to both leagues, and the next two are relative to its own league only (as you can see, NL parks appear to be larger, on the average, by around 3 feet on the left and 2 feet on the right, than AL parks, probably because of Coors):

ARI -7, -4 -9, -7
ATL 0, 5 -2, 2
CHN 0, 15 -2, 12
CIN 0, -7 -2, -9
COL 11, 5 9, 2
FLO 27, 18 25, 15
HOU -5, -4 -7, -7
LAN 4, 5 2, 2
MIL -1, 6 -3, 3
NYN 6, 5 4, 3
PHI -12, -12 -13, -15
PIT 6, 1 4, -2
SDN -1, 10 -2, 7
SLN 3, 4 2, 1
SFN -2, 11 -4, 8
WAS 8, 5 6, 2

BAL -9, 0 -7, 4
BOS -8, -6 -6, -2
ALA -3, -3 -1, 1
CHA -8, -7 -6, -4
CLE 6, -4 8, -1
DET -1, 13 1, 16
KCA 1, 4 3, 7
MIN 8, 12 10, 16
NYA 9, -14 11, -11
OAK -9, -3 -7, 1
SEA 1, -4 3, -1
TBA -3, 1 -1, 4
TEX 6, -3 8, 1
TOR -3, -1 -1, 3

• Sabermetrics • Parks

#1 studes 2008/03/28 (Fri) @ 04:48

Hey, MGL, I need some time to digest this, but it looks cool. Thanks.

Are you aware of this article?

http://www.hardballtimes.com/main/article/home-run-park-factor-a-new-approach/

#2 David Pinto 2008/03/28 (Fri) @ 08:33

I don’t suppose you could put column headings on the numbers. I’m not 100% sure what I’m looking at, although I’m guessing Florida should be one of the toughest places to hit home runs.

#3 Greg Rybarczyk 2008/03/28 (Fri) @ 12:49

MGL, regarding the fence heights, the average home run is descending at around 50 degrees when it clears the fence (with *lots* of variation, of course), so using 1:1 won’t be far off, but might as well adjust it…

Like Studes, I need some more time to digest what you’ve got here. I’ll get back to you…

#4 MGL 2008/03/28 (Fri) @ 16:29

Greg, if I remember my high school trig properly, a 45 degree angle would be 1:1 in height and distance, and a 50 degree would require using the tangent of 50, which is 1.192, no? So for every 1 foot extra in height, you need .84 (1/1.192) more in distance, at least for the average HR?

Given the distribution of HR distances, how many HR and percentage of HR’s does an extra foot or 10 feet (or whatever - is it linear?) of fence distance correspond to? I am trying to take my numbers, which are effective average fence distance for the entire left and right side of the OF, and convert them to an expected HR multiplicative or additive factor (e.g. 1.10, 1.03, .97, etc.). So, for example, if in Florida, the left side of the outfield had fences that were effectively 25 feet further than the average NL fence, given the same height, what would we expect the multiplicative or additive HR PF to be? Or what about Boston left side at 6 feet shorter than average? Etc.? I suppose I can run a regression of my numbers and actual HR PF for all the parks and see what I get. Hopefully, that should be close to what you get.

David, sorry, there are 4 numbers next to each park. The first two are:

1) Left side of the OF, average “effective” fence distance as compared to an average park in the NL and AL combined, given the same height of the fence.

2) Same thing for the right side of the OF.

The next two numbers are the same thing but relative to the NL or AL only. For the NL parks, it is relative to the NL, and for the AL parks, it is relative to the AL.

Studes, yup, I read that article. I’ll have to re-read it. So many good articles all the time. I need to compile a library of them. Maybe someone already has. I wouldn’t be surprised if Tango already has. Or maybe the best of all these articles from the various web sites can be put into a book. That would be a tremendous book!

#5 Colin Wyers 2008/03/28 (Fri) @ 23:05

Was there any change in Wrigley Field after the 2006 offseason? They rebuilt the bleachers area significantly in that time period - the “fences” didn’t move, but the wind blowing in and out of Wrigley was probably impacted by the added height of the structure behind the walls.

#6 Renè 2008/03/28 (Fri) @ 23:14

Good stuff.
Whenever I see work being done on park factors, I always wonder why so little quantitative attention is put on “platoon park factors”, just like I always wondered, for instance, why doesn’t BR change OPS+ and ERA+ according to batter handedness (what actually I mean: why don’t they use different park factors for batter handedness). There’s a great difference in saying that Giambi and A-Rod both hit X HRs at Yankee Stadium, as it’s the most extreme HR hitting park for lefties in the AL and the most HR suppressing park for righties in terms of “effective fence distance”. It comes out neutral on the whole, but it really isn’t. Am I missing anything on why it hasn’t been done before, aside from data scarcity? Well done to you for exploring this. It’s a heck of a job.

PS: I know I’m asking for a lot, but did you do something like “monthly splits” in order to see what impact do temperature, wind and other stuff have on flyballs and therefore on “effective” fence distance? I’ve read stuff regarding the impact of air temperature in different months (and why HR rate goes up with the heat) in global studies, but it would be neat to see that applied to individual parks to see if they all react the same.

#7 Colin Wyers 2008/03/29 (Sat) @ 01:00

MGL asked about HRs per Fly Ball/Ball In Play.

http://spreadsheets.google.com/ccc?key=pMzjQGUNv8cqg8pvfy95_ag&hl=en

That’s from 2004-2007, according to Retrosheet. I’m failing to distinguish between Busch II and Busch III.

#8 MGL 2008/03/29 (Sat) @ 01:31

Rene, sure, other people use platoon park factors, but I agree that they are not used enough. In fact, whenever I quote my context neutral stats, like Supelwts, it is always after park neutralizing a player’s stats, using “left” and “right side” park factors, at least for home runs and doubles (triples have such a small sample size in the first place, I don’t feel comfortable splitting them up).

Don’t forget that even though hitters hit a majority of their home runs to the pull side, they still hit plenty to the opp side, so an overall park factor is not all that bad.

Colin, what are the last two columns, some kind of confidence interval? Also, are these numbers for all activity in each park, home and road team combined, including IL games?

Colin, before 2004, when they added seats behind home plate in Wrigley (reducing foul territory), the fly ball distance factor (based on 99-03 data) was 1.003, .969, and .986, which is left side, right side, overall.

From 04 to 07, it was 1.001, .963, .983, not much of a change, but a little less ball travel, perhaps suggesting more BIP with more strikes (because of smaller foul territory). In 06 and 07, it was 1.003, .966, .985, which is more like pre-2004 levels, perhaps suggesting that the renovations increased ball travel a little.

OTOH, all of these numbers are close enough to suggest that nothing has really changed the Wrigley fly ball distance factors since 2003 at least.

To get an idea as to how changing foul territory can change a fly ball distance factor, by causing more balls to be put into play with more strikes (foul balls), we can look at Dodger Stadium before and after the 2005 season, when foul territory was substantially reduced (it was reduced in 2000 also, and actually some time after 1969).

Pre-05, the FB distance factors in Chavez Ravine were 1.012, 1.006, and 1.009. They are probably high for two reasons. One, the weather is warm all year round, and two, because of the fairly large foul territory, BIP had fewer than average strikes.

After 2004, this went down to .991, 1.001, and .996, a substantial reduction, ostensibly due to more strikes when the ball is put into play, and thus less “oomph” on fly balls. Interesting.

Another example of how a large foul territory can mean a higher than average FB dist. PF, is OAK. It is cold on the average, and they are at sea level. But their PF is 1.005. That is probably due to the very large foul territory.

#9 Colin Wyers 2008/03/29 (Sat) @ 01:38

Added a second sheet, detailing where home runs were hit by park. I filtered by hit location; balls hit to left-center and right-center are double counted. Fly ball outs are assigned to a location based upon who fielded them if a location is not assigned in the Retrosheet data.

#10 Colin Wyers 2008/03/29 (Sat) @ 01:41

Last two columns are above/below the league average, just like what you were asking for. All games are included, and that means interleague - the game the Rays played at the Wide World of Sports complex is included in there, as well as any other odd games. Both the home and road teams are included.

#11 MGL 2008/03/30 (Sun) @ 18:04

Got it, thanks.

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