from Amazon
Friday, March 28, 2008
True HR Park Factors (or at least something we can regress towards)
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