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oring of personnel to field etc so i m going to try to convert the coors line into an approximation of what the split would look like if it were similar to mlb as a whole here s that 1980 2022 mlb split from above except i ve added the percentage difference between home and road on a per ab basis below ab h 2b 3b hr bb so home 3209469 846723 161290 19928 95790 321178 612545 road 3363640 859813 163954 17203 96043 308047 668363 diff 3 2 3 5 21 4 4 5 9 3 3 9 i ll try to create something similar for 2000 coors the overall batting line for both teams looked like this ab h 2b 3b hr bb so r 9 coors 5843 1860 359 56 245 633 933 7 43 here s my arbitrary split into rockies vs road team in such a way to keep roughly the same percentage differences as in mlb overall while also keeping the r 9 roughly 7 43 here s what i came up with ab h 2b 3b hr bb so home 5843 1884 362 66 249 672 936 road 5843 1826 350 54 238 615 974 diff 3 2 3 4 22 2 4 6 9 3 3 9 i ran those through tango s calculator to get runs per 9 innings ab h 2b 3b hr bb so r 9 home 5843 1884 362 66 249 672 936 7 783 road 5843 1826 350 54 238 615 974 7 071 avg 7 427 diff 712 next i ran the runs per game distribution calculation to get a runs per win estimate i won t go through the details here but it s the same thing as before calculate the probability of a tie then a one run home win then a one run road win etc the result 14 37 runs per win as expected that s significantly higher than the 10 7 we calculated for mlb overall adjusting 14 37 for the superfluous bottom of the ninth gives about 13 6 so if you prefer you can compare 13 6 coors to 10 1 overall the difference of 712 runs per game divided by 14 43 runs per win gives an hfa of 0 0495 wins per game which translates to a home winning percentage of 5495 comparing the two results 542 home field winning percentage normal 549 home field winning percentage coors 007 difference the difference of 007 is worth only about half a win per home season sure half a win is half a win but i m a little disappointed that s all we wind up with after all this work it s certainly not as much of an effect as i thought there would be before i started even if you deducted this inherent 007 it would barely make a dent in the rockies 150 percentage point difference between coors and road the rockies would still be in first place on the fangraphs chart by a sizeable margin 42 points instead of 49 looked at another way an additional 007 would move an average team from the middle of the 29 year standings to about halfway to the top so maybe it s not that small after all still our conclusion has to be that the rockies huge hfa over the years is maybe 10 percent a mathematical inevitability of all those extra runs and 90 percent other causes labels baseball home field advantage markov mlb runs per win posted by phil birnbaum 11 16 2022 04 59 00 pm 8 comments tuesday september 07 2021 are umpires racially biased a 2021 study part ii part i is here 20 percent of drivers own diesel cars and the other 80 percent own regular gasoline cars diesels are on average less reliable than regular cars the average diesel costs 2 000 a year in service while the average regular car only costs 1 000 researchers wonder if there s a way to reduce costs maybe diesels cost more partly because mechanics don t like them or are unfamiliar with them they create a regression that controls for the model age and mileage of the car as well as driver age and habits but they also include a variable for whether the mechanic owns the same type of car diesel or gasoline as the owner they call that variable utm or user technician match they run the regression and the utm coefficient turns out negative and significant it turns out that when the mechanic owns the same type of car as the user maintenance costs are more than 13 percent lower the researchers conclude that finding a mechanic who owns the same kind of car as you will substantially reduce your maintenance costs but that s not correct the mechanic makes no difference at all that 13 percent from the regression is showing something completely different if you want to solve this as a puzzle you can stop reading and try there s enough information here to figure it out the overall average maintenance cost combining gasoline and diesel is 1200 that s the sum of 80 percent of 1000 plus 20 percent of 2000 so what s the average cost for only those cars that match the mechanic s car my first thought was it s the same 1200 because if the mechanic s car makes no difference how can that number change but it does change the reason is when the user s car matches the mechanic s it s much less likely to be a diesel the gasoline owners are over represented when it comes to matching each has an 80 chance of being included in the utm sample while the diesel owner has only a 20 chance in the overall population the ratio of gasoline to diesel is 4 1 but the ratio of gasoline gasoline to diesel diesel is 16 1 so instead of 20 the proportion of double diesels in the both cars match population is only 1 in 17 or 5 9 that means the average cost of utm repairs is only 1059 that s 94 1 percent of 1000 plus 5 9 of 2000 that works out to 13 3 percent less than the overall 1200 here s a chart that maybe makes it clearer here s how the raw numbers of utm pairings break down per 1000 population technician gasoline diesel total user gasoline 640 160 800 user diesel 160 40 200 total 800 200 1000 the highlighted diagonal is where the user matches the mechanic there are 680 cars on that diagonal but only 40 1 in 17 are diesel in short the utm coefficient is significant not because matching the mechanic selects better mechanics but because it selectively samples for more reliable gasoline cars in the umpire race study i talked about last post they had a regression like that where they put all the umpires and batters together into one regression and looked at the ubm variable where the umpire s race matches the batter s race from last post here s the table the author included the numbers are umpire errors per 1000 outside of zone pitches negative favors the batter umpire black hispanic white black batter 5 3 0 3 hispanic batter 7 8 5 9 white batter 5 6 4 4 i had adjusted that to equalize the baseline umpire black hispanic white black batter 5 6 0 9 0 3 hispanic batter 2 2 4 4 5 9 white batter i think i m able to estimate from the original study that the batter population was almost exactly in the 2 3 4 range 22 percent black 34 percent hispanic and 44 percent white using those numbers i m going to adjust the chart one more time to show approximately what it would look like if the umpires were exactly alike no bias and each column added to zero umpire black hispanic white black batter 2 2 2 2 2 2 hispanic batter 3 8 3 8 3 8 white batter 1 7 1 7 1 7 i chose those numbers so the average ubm average of diagonals in ratio 22 34 44 is zero and also to closely fit the actual numbers the study found that is suppose you ran a regression using the author s data but controlling for batter and umpire race and suppose there was no racial bias in that case you d get that table which represents our null hypothesis of no racial bias if the null hypothesis is true what will a regression spit out for ubm if the batters were represented in their actual ratio 22 34 44 you d get zero diagonal effect weight product black ubm 2 2 22 0 5 hispanic ubm 3 8 34 1 5 white ubm 1 7 44 0 8 overall ubm 100 0 0 per 1000 however in the actual population in the mlb study the diagonals do not appear in the 22 34 44 ratio that s because the umpires were overwhelmingly white 88 percent white there were only 5 percent black umpires and 7 percent hispanic umpires so the white batters matched their umpire much more often than the hispanic or black batters using 5 7 88 for umpires and 22 34 44 for batters the relative frequency of each combination looks like this here s the breakdown per 1000 pitches batter umpire black hispanic white total black batter 11 15 194 220 hispanic batter 17 24 300 341 white batter 22 31 387 439 umpire total 50 70 881 1000 because there are so few minority umpires there are only 24 hispanic hispanic pairs out of 422 total matches on the ubm diagonal that s only 5 7 hispanic batters rather than 34 percent diagonal frequency percent black ubm 11 2 6 hispanic ubm 24 5 7 white ubm 387 91 7 overall ubm 422 100 if we calculate the observed average of the diagonal with this 11 24 387 breakdown we get this effect weight product black ubm 2 2 2 6 0 06 per 1000 hispanic ubm 3 8 5 7 0 22 per 1000 white ubm 1 7 91 7 1 56 per 1000 overall ubm 100 1 40 per 1000 hispanic batters receive more bad calls for reasons other than racial bias by restricting the sample of hispanic batters to only those who see a hispanic umpire we selectively sample fewer hispanic batters in the ubm pool and so we get fewer bad calls under the null hypothesis of no bias ubm plate appearances still see 1 40 fewer bad calls per 100 pitches because of selective sampling that 1 40 figure is compared to the overall average the regression coefficient however compares it to the non ubm case what s the average of the non ubm case well if a ubm happens 422 times out of 1000 and results in 1 40 pitches fewer than average and the average is zero then the other 578 times out of 1000 there must have been 1 02 pitches more than average effect weight product ubm 1 40 42 2 0 59 per 1000 non ubm 1 02 57 8 0 59 per 1000 full sample 100 0 00 per 1000 so the coefficient the regression produces ubm compared to non ubm will be 2 42 what did the actual study find 2 81 that leaves only 0 39 as the estimate of potential umpire bias 2 81 selective sampling plus possible bias 2 42 effect of selective sampling only 0 39 revised estimate of possible bias the study found 2 81 fewer bad calls per 1000 when the umpire matched the pitcher but 2 42 of that is selective sampling leaving only 0 39 that could be umpire bias is that 0 39 statistically significant i doubt it for what it s worth the original estimate had an sd of 0 44 so adjusting for selective sampling we re less than 1 sd from zero so the conclusion the study s finding of a 0 28 ubm effect cannot be attributed to umpire bias it s mostly a natural mathematical artifact resulting from the fact that a hispanic batters see more incorrect calls for reasons other than bias b hispanic umpires are rare and c the regression didn t control for the race of batter and umpire separately because of that almost the entire effect the study attributes to racial bias is just selective sampling labels baseball bias race referee bias umpires posted by phil birnbaum 9 07 2021 01 21 00 pm 2 comments monday august 30 2021 are umpires racially biased a 2021 study part i are mlb umpires racially biased there s a recent new study that claims they are the author who wrote it as an undergrad thesis mentioned it on twitter and when i checked a week or so later there were lots of articles and links to it here for instance is a baseball prospectus post reporting on it and here s a yahoo report the study tried to figure whether umpires make more bad calls against batters of a race other than theirs where there is no umpire batter match or ubm as the literature calls it it ran regressions on called pitches from 2008 to 2020 to figure out how best to predict the probability of the home plate umpire calling a pitch incorrectly based on mlb gameday pitch location the author controlled for many different factors and found a statistically significant coefficient for ubm concluding that the pitcher gains an advantage when the umpire is of the same race it also argues that white umpires in particular could be the driving force behind discrimination in mlb i don t think any of that is right i think the results point to something different and benign imagine a baseball league where some teams are comprised of dentists while the others are jockeys the league didn t hire any umpires so the players take turns and promise to call pitches fairly they play a bunch of games and it turns out that the umpires call more strikes against the dentists than against the jockeys nobody is surprised jockeys are short and thus have small strike zones it s true that the data shows that if you look at the jockey umpires you ll see that they call a lot fewer strikes against batters of their own group than against batters of the other group their ubm coefficient is high and statistically significant does that mean the jockey umps are racist against dentists no of course not it s just that the dentists have bigger strike zones it s the same but in reverse for the dentist umpires they call more strikes against their fellow dentists again not because of pro jockey reverse racism but because of the different strike zones later teams of nba players enter the league these guys are tall with huge strike zones so they get a lot of called strikes even from their own umpires let s put some numbers on this we ll say there are 10 teams of dentists 1 team of jockeys and 2 teams of nba players the jockeys are 10 in called strikes compared to average and the nba players are 10 that leaves the dentists at 1 in order for the average to be zero here s a chart that shows every umpire is completely fair and unbiased umpire jockey nba dentist jockey batter 10 10 10 nba batter 10 10 10 dentist batter 1 1 1 i ve highlighted the ubm cells where the umpire matches the batter if you look only at those cells and don t think too much about what s going on you could think the umpires are horribly biased the jockey batters get 10 fewer strikes than average from jockey umpires that s awful but then when you look closer you see the horizontal row is all 10 that means all the umpires called the jockeys the same way 10 so it s probably something about the jockey batters that made that happen in this case it s that they re short i think this is what s going on in the actual study but it s harder to see because the chart isn t set up with the raw numbers the author ran different regressions for the three different umpire races and set a different set of batters as the zero level for each since they re calibrated to a different standard of player the results make the umpires look very different if i had done here what the author did there the chart above would have looked like this umpire jockey nba dentist jockey batter 0 20 9 nba batter 20 0 11 dentist batter 9 11 0 if you just look at this chart without knowing you can t compare the columns to each other because they re based on a different zero baseline it s easy to think there s evidence of bias you d look at the chart and say hey it looks like jockey umpires are racist against nba batters and dentists also dentist umpires are racist against nba players but favor jockeys somewhat but look nba umpires actually favor other races that s probably because nba umpires are new to the tournament and are going out of their way to app...
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