Required knowledge: DRC+ and park factors

TL;DR read the title above, the rant 3 paragraphs down, and the very bottom

DRC+ is supposed to be a fully park-adjusted metric, but from the initial article, I couldn’t understand how that could be consistent with the reported results without either an exceptional amount of overfitting or extremely good luck. Team DRC+ was reported to be more reliable than team wRC+ at describing the SAME SEASON’s team runs/PA. Since wRC+ is based off of wOBA, team wOBA basically is team scoring offense (r=0.94), and DRC+ regresses certain components of wOBA back towards the mean quite significantly (which is why DRC+ is structurally unfit for use in WAR), it made no sense to me that a metric that took away actual hits that created actual runs from teams with good BABIPs and invented hits in place of actual outs for teams with bad BABIPs could possibly correlate better to actual runs scored than a metric that used what happened on the field. It’s not quite logically impossible for that to be true, but it’s pretty damn close.

It turns out the simple explanation for how a park-adjusted significantly regressed metric beat a park-adjusted unregressed metric is the correct one. It didn’t. DRC+ keeps in a bunch of park factor and calls itself a park-adjusted metric when it’s simply not one, and not even close to one. The park factor table near the bottom of the DRC+article should have given anybody who knows anything about baseball serious pause, and of course it fits right in with DRC+’s “great descriptiveness”.

# RANT

How in the hell does a park factor of 104 for Coors get published without explanation by any person or institution trying to be serious? The observed park factors (halved) the last few years, in reverse order: 114 (2018), 115, 116, 117, 120, 109, 123… You can’t throw out a number like Coors 104 like it’s nothing. If Jonathan Judge could actually justify it somehow- maybe last year we got a fantastic confluence of garbage pitchers and great situational hitting at Coors and the reverse on the road while still somehow only putting up a 114, where you could at least handwave an attempt at a justification, then he should have made that case when he was asked about it, but instead he gave an answer indicative of never having taken a serious look at it. Spitting out a 104 for Coors should have been like a tornado siren going off in his ear to do basic quality control checks on park effects for the entire model, but it evidently wasn’t, so here I am doing it instead.

# /RANT

The basic questions are “how correlated is team DRC+ to home park factor?” and “how correlated should team DRC+ be to home park factor?”. The naive answer to the second question is “not correlated at all since it’s park adjusted, duh”, but it’s possible that the talented hitters skew towards hitters’ parks, which would cause a legitimate positive correlation, or that they skew towards pitchers’ parks, which would cause a legitimate negative correlation. As it turns out, over the 2003-2017 timeframe, hitting talent doesn’t skew at all, but that’s an assertion that has to be demonstrated instead of just assumed true, so let’s get to it.

We need a way to make (offensive talent, home park factor) team-season pairs that can measure both components separately without being causally correlated to each other. Seasonal team road wOBA is a basically unbiased way to measure offensive quality independent of home park factor because the opposing parks played in have to average out pretty similarly for every team in the same league (AL/NL)**. If we use that, then we need a way to make a park factor for those seasons that can’t include that year’s data, because everything else being equal, an increase in a team’s road wOBA would decrease its home park factor****, and we’re explicitly trying to avoid nonsense like that. Using the observed park factors from *surrounding years*, not the current year, to estimate the current year’s park factor solves that problem, assuming those estimates don’t suck.

** there’s a tiny bias from not playing road games in a stadium with your park factor, but correcting that by adding a hypothetical 5 road games at estimated home park factor doesn’t change conclusions)

**** some increase will be skill that will, on average, increase home wOBA as well and mostly cancel out, and some increase will be luck that won’t cancel out and would screw the analysis up

# Methodology

I used all eligible team-batting-seasons, pitchers included, from 2003-2017. To estimate park factors, I used the surrounding 2 years (T-2, T-1, T+1, T+2) of observed park factors (for runs) if they were available, the surrounding 1 year (T-1, T+1) otherwise, and threw out the season if I didn’t have those. That means I threw out all 2018s as well as the first and last years in each park. I ignored other changes (moved fences, etc).

Because I have no idea what DRC+ is doing with pitcher-batters, how good its AL-NL benchmarking is, and the assumption of nearly equivalent aggregate road parks is only guaranteed to hold between same-league teams, I did the DRC+ analysis separately for AL and NL teams.

To control for changing leaguewide wOBA in the 2003-2017 time period, I used the same wOBA/LgAvGwOBA wOBA% method I used in DRC+ really isn’t any good at predicting next year’s wOBA for team switchers for wOBA and DRC+, just for AL teams and NL teams separately for the reasons above. After this step, I did analyses with and without Coors because it’s an extreme outlier. We already know with near certainty that their treatment of Coors is ~~kind of questionable~~ batshit crazy and keeps way too much park effect in DRC+, so I wanted to see how they did everywhere else.

# Results

The park factor estimation worked pretty well. 2 surrounding year PF correlated to the observed PF for the year in question at r=0.54 (0.65 with Coors) and the 1 surrounding year at r=0.52 (0.61 with Coors). The 5-year FanGraphs PF, WHICH USES THE YEAR IN QUESTION, only correlates at r=0.7 (0.77 with Coors) and the 1 and 2 year park factors correlate to the Fangraphs PF at 0.87 and 0.96 respectively. This is plenty to work with given the effect sizes later.

Team road wOBA% (squared or linear) correlates to the estimated home park factor at r = -0.03, literally nothing, and with the 5 extra hypothetical games as mentioned in the footnote above, r=0.02, also literally nothing. It didn’t have to be this way, but it’s convenient that it is. Just to show that road wOBA isn’t all noise, it correlates to that season’s home wOBA% at r=0.32 (0.35 with the adjustment) even though we’re dealing with half seasons and home wOBA% contains the entire park factor. Road wOBA% correlates to home wOBA%/sqrt(estimated park factor) at r=0.56 (and wOBA%/park factor at r=0.54). That’s estimated park factor from surrounding years, not using the home and road wOBA data in question.

Home wOBA% is obviously hugely correlated to estimated park factor (r=0.46 for home wOBA%^2 vs estimated PF), but park adjusting it by correlating

(home wOBA%)^2/estimated park factor TO estimated park factor

has r= -0.00017. Completely uncorrelated to estimated PF (it’s pure luck that it’s THAT low).

So we’ve established that road wOBA really does contain a lot of information on a team’s offensive talent (that’s a legitimate naive “duh”), that it’s virtually uncorrelated to true home park factor, and that park-adjusted home wOBA% (using PF estimates from other seasons only) is also uncorrelated to true home park factor. If DRC+ is a correctly park-adjusted metric that measures offensive talent, DRC+% should also have to be virtually uncorrelated to true home park factor.

And… the correlation of DRC+% to estimated park factor is r= 0.38 for AL teams, r=0.29 for NL teams excluding Colorado, r=0.31 including Colorado. Well then. That certainly explains how it can be more descriptive than an actually park-adjusted metric.