Calculating park factors - Collin Erickson

I’ve been thinking a bit about park factors recently. A lot of stats are pretty meaningless without context. 40 home runs for a Rockies player is not as good as 40 home runs for a Dodgers player because Coors is much more hitter-friendly. Park factors are used to determine how many runs are scored at any given stadium compared to the rest of the league. +/- stats like OPS+ and ERA- adjust for the stadium, making comparisons for players across teams more fair.

I’m just going to see if I can do park factor calculations simply. I’ll start by just finding the ratio of runs scored at home divided by runs scored away for each team.

library(magrittr)
library(ggplot2)

## Registered S3 methods overwritten by 'ggplot2':
##   method         from 
##   [.quosures     rlang
##   c.quosures     rlang
##   print.quosures rlang

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Load the data as d.

d <- readRDS("MLB2018.rds")

game_scores <- d %>% group_by(home_team, away_team, game_pk) %>%
  summarise(home_score=max(home_score), away_score=max(away_score))

team_scores <- with(game_scores,
                   rbind(data.frame(team=home_team, score=home_score, home=1),
                         data.frame(team=away_team, score=away_score, home=-1))
)

parkfactors <- team_scores %>% group_by(team, home) %>% summarize(totalruns=sum(score)) %>% 
  group_by(team) %>% summarize(ParkFactor=totalruns[which(home>.5)] / totalruns[which(home<(-.5))]) %>% 
  arrange(desc(ParkFactor))
parkfactors %>% print(n=30)

## # A tibble: 30 x 2
##    team  ParkFactor
##    <fct>      <dbl>
##  1 TEX        1.40 
##  2 COL        1.29 
##  3 CIN        1.21 
##  4 BAL        1.19 
##  5 PHI        1.17 
##  6 CLE        1.15 
##  7 MIN        1.13 
##  8 BOS        1.12 
##  9 WSH        1.11 
## 10 NYY        1.11 
## 11 SF         1.09 
## 12 DET        1.07 
## 13 KC         1.06 
## 14 ARI        1.06 
## 15 TB         1.03 
## 16 ATL        1.03 
## 17 TOR        1.01 
## 18 MIL        1.01 
## 19 SD         0.993
## 20 CHC        0.987
## 21 LAA        0.948
## 22 CWS        0.940
## 23 MIA        0.871
## 24 PIT        0.869
## 25 HOU        0.858
## 26 STL        0.819
## 27 LAD        0.817
## 28 OAK        0.806
## 29 SEA        0.765
## 30 NYM        0.649

These park factors aren’t correct, but they are neighborhood estimates.

Using runs allowed

I didn’t use runs scored by opponents in the above calculation. By using the total runs scored in home games divided by total runs scored in away games, it should reduce the error by a bit.

team_scores2 <- with(game_scores,
                   rbind(data.frame(team=home_team, score=home_score+away_score, home=1),
                         data.frame(team=away_team, score=away_score+home_score, home=-1))
)

parkfactors2 <- team_scores2 %>% group_by(team, home) %>% summarize(totalruns=sum(score)) %>% 
  group_by(team) %>% summarize(ParkFactor=totalruns[which(home>.5)] / totalruns[which(home<(-.5))]) %>% 
  arrange(desc(ParkFactor))
parkfactors2 %>% print(n=30)

## # A tibble: 30 x 2
##    team  ParkFactor
##    <fct>      <dbl>
##  1 TEX        1.36 
##  2 COL        1.26 
##  3 WSH        1.14 
##  4 CLE        1.14 
##  5 CIN        1.12 
##  6 NYY        1.11 
##  7 ATL        1.11 
##  8 CHC        1.09 
##  9 BOS        1.07 
## 10 ARI        1.07 
## 11 KC         1.06 
## 12 PHI        1.05 
## 13 SD         1.03 
## 14 MIN        1.02 
## 15 SF         1.00 
## 16 MIL        0.994
## 17 BAL        0.993
## 18 HOU        0.983
## 19 LAA        0.966
## 20 TOR        0.954
## 21 CWS        0.946
## 22 DET        0.943
## 23 TB         0.926
## 24 STL        0.916
## 25 LAD        0.890
## 26 PIT        0.868
## 27 SEA        0.838
## 28 OAK        0.834
## 29 MIA        0.760
## 30 NYM        0.724

These are decent results, and are basically what ESPN gives for 2018 park factors.

Factors not considered

There are still a ton of things that affect the park factor that this simple calculation doesn’t consider.

Quality of teams/pitchers. If a team plays more bad teams at home than away, it could affect the result. In general this should average out.
Number of outs. I just treated all games equally, but games that go to extra innings, or if the bottom of the ninth isn’t played, should be accounted for.
Not only did I not account for the number of outs, I didn’t account for the number of home and away games. Usually they are equal, but not with game 163s, or rain outs that never get made up. This would be a simple fix.
Interleague games. Having a DH in home games but not all away (or vice versa for NL teams) boosts the park factor (decrease for NL).
Park factors may be different for right/left handed hitters
I only used the data for a single year, but I could reduce the uncertainty by using data from multiple years.
There are different factors for different events. Each park could have a factor for home runs, and a different one for doubles.

Best formula

I tried to find what the best formula is for calculating park factors. The calculations become very difficult, despite seeming simple from the calculations I made. Baseball Reference gives details on how to calculate Park Adjustments, and it’s not easy to follow.