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t was double that or 2 sd assuming no park effects whitey was double counted by about 10 runs by raw babip and a little more than that by the dwar calculation now dwar does remove popups and line drives from consideration that will reduce the luck sd i m not sure how much compared to raw babip but even if the sd drops from 0 5 to 0 4 or something that s still pretty big we could just adjust dwar for this the babip home road numbers are readily available on b r but i think the adjustments for fielding and park are exaggerated in other ways as i wrote about in previous sets of posts a different algorithm for adjusting pitcher war where we regress both fielding and park to the mean by significant amounts might reduce the double count enough that we won t really need to make a correction for it it will probably adjust both whitey ford and jack kralick enough that whitey winds up on top although i haven t checked that in detail yet i ll work on that for the next post posted by phil birnbaum 3 18 2023 04 00 00 pm 3 comments wednesday november 16 2022 home field advantage is naturally higher in a hitter s park the rockies have always had a huge home field advantage hfa at coors from 1993 to 2001 colorado has played 545 at home but only 395 on the road that s the equivalent of the difference between going 89 73 and 64 98 why such a big difference i have some ideas i m working on but the most obvious one although it s not that big as we will see is that higher scoring naturally mathematically leads to a bigger hfa when teams play better at home than on the road for whatever reason the manifestation of better is in physical performance not winning percentage as such the translation from performance to winning percentage depends on the characteristics of the game in mlb historically the home team plays around 540 but if the commissioner decreed that now games were going to be 36 innings long instead of 9 the home advantage would roughly double with the home team now winning at a 580 pace why with the game four times as long the sd of the score difference by luck would double but the home team s run advantage would quadruple so the run differential by talent would double compared to luck since the normal distribution is almost linear at such small differences roughly from 0 1 sd to 0 2 sd hfa would approximately double but it s not always that a higher score number increases hfa if it was decided that all runs now count as 2 points like in basketball scoring would double but obviously hfa would stay the same roughly speaking increased scoring increases the home advantage only if it also increases the signal to noise ratio of performance to luck increasing the length of the game does that doubling all the scores does not in 2000 coors field increased scoring by about 40 if that forty percent was obtained by increasing games from 9 innings to 13 innings hfa would be around 20 higher if the forty percent was obtained by making every run count as 1 4 runs hfa would be 0 higher in reality the increase could be anywhere between 0 and 20 or beyond we probably have the tools available to get a pretty good estimate of the true increase let s start with the overall average hfa my subscription to baseball reference allowed me to obtain home and road batting records all teams combined for the 1980 2022 seasons ab h 2b 3b hr bb so home 3209469 846723 161290 19928 95790 321178 612545 road 3363640 859813 163954 17203 96043 308047 668363 what s the run differential between those two batting lines we can look at actual runs or even the difference in run statistics like runs created or extrapolated runs but for better accuracy i used tom tango s on line markov calculator the version modified by bill skelton found here it turns out the home batting line leads to 4 79 runs per nine innings and the road batting line works out to 4 36 r 9 ab h 2b 3b hr bb so r 9 home 3209469 846723 161290 19928 95790 321178 612545 4 79 road 3363640 859813 163954 17203 96043 308047 668363 4 36 difference 0 43 that s a difference of 0 43 runs per game using the rule of thumb that 10 runs equals one win a rough estimate is that the home team should have a win advantage of 0 043 wins per game for a winning percentage of 543 that s a pretty good estimate home teams actually went 539 in that span 51832 44409 but we ll actually need to be more accurate than that because the 10 runs per win figure will change significantly for higher scoring environments such as coors so let s calculate an estimate of the actual runs per win for this scoring environment the tango skelton markov calculator includes a feature where given the batting line it will show the probability of a team scoring any particular number of runs in a nine inning game here s part of that output home road 2 runs 1201 1342 3 runs 1315 1404 4 runs 1282 1309 from this table which actually extends from 0 to 30 runs we can calculate how many runs it would take for the road team to turn a loss into a win case 1 if the road team is tied after 9 innings it has about a 50 chance of winning with one additional run it turns that into 100 so an additional run in a tie game is worth half a win how often is the game tied well the chance of a 2 2 tie is 1202 1342 or about 1 6 the chance of a 3 3 tie is 1315 1404 or 1 8 adding up the 2 2 and the 3 3 and the 0 0 and the 1 1 and the 4 4 and the 5 5 and so on all the way down the line the overall chance is 9 7 case 2 if the road team is down a run after 9 innings it loses which is a 0 chance of winning with one additional run it s tied and turns that into a 50 chance so an additional run there is also worth half a win how often is the road team down a run well the chance of a 3 2 result is 1315 1342 or about 1 8 the chance of 4 3 is 1282 1404 another 1 8 and so on the total a 9 54 chance the road team winds up losing by one run what s the chance that the additional run will give the home team the extra half win we can repeat the calculation but instead of 3 2 we ll calculate 2 3 instead of 4 3 we ll calculate 3 4 and so on the total only 8 54 it makes sense that it s smaller because the better team is less likely to be behind by a run than ahead by a run we ll average the home and road numbers to get 9 04 so we have 9 7 chance of a tie 9 0 chance of behind one run 18 7 chance that a run will create half a win converting that 18 7 chance to r w 0 187 half wins per run 5 35 runs per half win 10 7 runs per win so we ll use 10 7 runs per win for our calculation why by the way do we get 10 7 runs per win instead of the rule of thumb that it should be 10 0 flat i think it s becuase the markov simulation always plays the bottom of the ninth even when the home team is already up it therefore includes a bunch of meaningless runs that don t occur in reality when some of the run currency is randomly useless it pushes the price of a win higher we d expect that roughly 1 18 of all runs scored are in the bottom of the ninth with the home team having already won if we discount those by multiplying 10 7 by 17 18 we get 10 1 runs per win bingo we saw earlier that the home team had an advantage of 0 43 runs per game dividing that by 10 3 runs per win gives us predicted hfa of 42 wins per game 542 actual hfa of 39 wins per game 539 we re off a bit the difference is about 2 sd my guess is that the markov calculation which is necessarily simplified is very slightly off and we only notice because of the huge sample size of almost 100 000 actual games ok now let s do the same thing but this time for coors field only i could do the same thing i did for mlb as a whole split the combined coors batting line into home and road and calculate those individually the problem with that is well if i do that i ll be getting the rockies actual hfa at coors which is huge because it includes all kinds of factors that we re not concerned with like altitude acclimatization tailoring 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 ump...