Revisiting the DRC+ team switcher claim

The algorithm has changed a fair bit since I investigated that claim- at the least, it’s gotten rid of most of its park factor and regresses (effectively) less than it used to.  It’s not impossible that it could grade out differently now than it did before, and I told somebody on twitter that I’d check it out again, so here we are.  First of all, let’s remind everybody what their claim is.  From, Jonathan Judge says:

Table 2: Reliability of Team-Switchers, Year 1 to Year 2 (2010-2018); Normal Pearson Correlations[3]

Metric Reliability Error Variance Accounted For
DRC+ 0.73 0.001 53%
wOBA 0.35 0.001 12%
wRC+ 0.35 0.001 12%
OPS+ 0.34 0.001 12%
OPS 0.33 0.002 11%
True Average 0.30 0.002 9%
AVG 0.30 0.002 9%
OBP 0.30 0.002 9%

With this comparison, DRC+ pulls far ahead of all other batting metrics, park-adjusted and unadjusted. There are essentially three tiers of performance: (1) the group at the bottom, ranging from correlations of .3 to .33; (2) the middle group of wOBA and wRC+, which are a clear level up from the other metrics; and finally (3) DRC+, which has almost double the reliability of the other metrics.

You should pay attention to the “Variance Accounted For” column, more commonly known as r-squared. DRC+ accounts for over three times as much variance between batters than the next-best batting metric. In fact, one season of DRC+ explains over half of the expected differences in plate appearance quality between hitters who have switched teams; wRC+ checks in at a mere 16 percent.  The difference is not only clear: it is not even close.

Let’s look at Predictiveness.  It’s a very good sign that DRC+ correlates well with itself, but games are won by actual runs, not deserved runs. Using wOBA as a surrogate for run-scoring, how predictive is DRC+ for a hitter’s performance in the following season?

Table 3: Reliability of Team-Switchers, Year 1 to Year 2 wOBA (2010-2018); Normal Pearson Correlations

Metric Predictiveness Error
DRC+ 0.50 0.001
wOBA 0.37 0.001
wRC+ 0.37 0.002
OPS+ 0.37 0.001
OPS 0.35 0.002
True Average 0.34 0.002
OBP 0.30 0.002
AVG 0.25 0.002

If we may, let’s take a moment to reflect on the differences in performance we see in Table 3. It took baseball decades to reach consensus on the importance of OBP over AVG (worth five points of predictiveness), not to mention OPS (another five points), and finally to reach the existing standard metric, wOBA, in 2006. Over slightly more than a century, that represents an improvement of 12 points of predictiveness. Just over 10 years later, DRC+ now offers 13 points of improvement over wOBA alone.


Reading that, you’re pretty much expecting a DIPS-level revelation.  So let’s see how good DRC+ really is at predicting team switchers.  I put DRC+ on the wOBA scale, normalized each performance to the league-average wOBA that season (it ranged from .315 to .326), and measured the mean absolute error (MAE) of wOBA projections for the next season, weighted by the harmonic mean of the PAs in each season.  DRC+ had a MAE of 34.2 points of wOBA for team-switching position players.  Projecting every team-switching position player to be exactly league average had a MAE of 33.1 points of wOBA.  That’s not a mistake.  After all that build-up, DRC+ is literally worse at projecting team-switching position players than assuming that they’re all league average.

If you want to say something about pitchers at the plate…





Even though Jonathan Judge felt like calling me a total asshole incompetent troll last night, I’m going to show how his metric could be not totally awful at this task if it were designed and quality-tested better.  As I noted yesterday, DRC+’s weightings are *way* too aggressive on small numbers of PAs.  DRC+ shouldn’t *need* to be regressed after the fact- the whole idea of the metric is that players should only be getting credit for what they’ve shown they deserve (in the given season), and after a few PAs, they barely deserve anything, but DRC+ doesn’t grasp that at all and its creator doesn’t seem to realize or care that it’s a problem.

If we regress DRC+ after the fact to see what happens in an attempt to correct that flaw, it’s actually not a dumpster fire.  All weightings are harmonic means of the PAs.  Every position player pair of consecutive 2010-18 seasons with at least 1 PA in each is eligible.  All tables are MAEs in points of wOBA trying to project year T+1 wOBA..

First off, I determined the regression amounts for DRC+ and wOBA to minimize the weighted MAE for all position players, and that came out to adding 416 league average PAs for wOBA and 273 league average PAs for DRC+.  wOBA assigns 100% credit to the batter.  DRC+ *still* needs to be regressed 65% as much as wOBA.  DRC+ is ridiculously overaggressive assigning “deserved” credit.

Table 1.  MAEs for all players

lgavg raw DRC+ raw wOBA reg wOBA reg DRC+
33.21 31.00 33.71 29.04 28.89

Table 2. MAEs for all players broken down by year T PAs

Year T PA lgavg raw DRC+ raw wOBA reg wOBA reg DRC+ T+1 wOBA
1-99 PAs 51.76 48.84 71.82 49.32 48.91 0.284
100-399 PA 36.66 36.64 40.16 34.12 33.44 0.304
400+ PA 30.77 27.65 28.97 25.81 25.91 0.328

Didn’t I just say DRC+ had a problem with being too aggressive in small samples?  Well, this is one area where that mistake pays off- because the group of hitters who have 1-99 PA over a full season are terrible, being overaggressive crediting their suckiness pays off, but if you’re in a situation like now, where the real players instead of just the scrubs and callups have 1-99 PAs, being overaggressive is terribly inaccurate.  Once the population mean approaches league-average quality, the need for- and benefit of- regression is clear. If we cheat and regress each bucket to its population mean, it’s clear that DRC+ wasn’t actually doing anything special in the low-PA bucket, it’s just that regression to 36 points of wOBA higher than the mean wasn’t a great corrector.

Table 3. (CHEATING) MAEs for all players broken down by year T PAs, regressed to their group means (same regression amounts as above).

Year T PA lgavg raw DRC+ raw wOBA reg wOBA reg DRC+ T+1 wOBA
1-99 PAs 51.76 48.84 71.82 46.17 46.30 0.284
100-399 PA 36.66 36.64 40.16 33.07 33.03 0.304
400+ PA 30.77 27.65 28.97 26.00 25.98 0.328

There’s very little difference between regressed wOBA and regressed DRC+ here.  DRC+ “wins” over wOBA by 0.00015 wOBA MAE over all position players, clearly justifying the massive amount of hype Jonathan Judge pumped us up with.  If we completely ignore the trash position players and only optimize over players who had 100+PA in year T, then the regression amounts increase slightly- 437 PA for wOBA and 286 for DRC+, and we get this chart:

Table 4. MAEs for all players broken down by year T PAs, optimized on 100+ PA players

Year T PA lgavg raw DRC+ raw wOBA reg wOBA reg DRC+ T+1 wOBA
100+ PA 32.55 30.37 32.36 28.32 28.19 0.321
100-399 PA 36.66 36.64 40.16 34.12 33.45 0.304
400+ PA 30.77 27.65 28.97 25.81 25.91 0.328

Nothing to see here either, DRC+ with a 0.00013 MAE advantage again.  Using only 400+PA players to optimize over only changes the DRC+ entry to 25.90, so regressed wOBA wins a 0.00009 MAE victory here.

In conclusion, regressed wOBA and regressed DRC+ are so close that there’s no meaningful difference, and I’d grade DRC+ a microscopic winner.  Raw DRC+ is completely awful in comparison, even though DRC+ shouldn’t need anywhere near this amount of extra regression if it were working correctly to begin with.

I’ve slowrolled the rest of the team-switcher nonsense.  It’s not very exciting either.  I defined 3 classes of players, Stay = played both years entirely for the same team, Switch = played year T entirely for 1 team and year T+1 entirely for 1 other team, Midseason = switched midseason in at least one of the years.

Table 5. MAEs for all players broken down by stay/switch, any number of year T PAs



lgavg raw DRC+ raw wOBA reg wOBA reg DRC+ T+1 wOBA
stay 33.21 29.86 32.19 27.91 27.86 0.325
switch 33.12 34.20 37.89 31.57 31.53 0.312
mid 33.29 33.01 36.47 31.67 31.00 0.305
sw+mid 33.21 33.60 37.17 31.62 31.26 0.309

It’s the same story as before.  Raw DRC+ sucks balls at projecting T+1 wOBA and is actually worse than “everybody’s league average” for switchers, regressed DRC+ wins a microscopic victory over regressed wOBA for stayers and switchers.  THERE’S (STILL) LITERALLY NOTHING TO THE CLAIM THAT DRC+, REGRESSED OR OTHERWISE, IS ANYTHING SPECIAL WITH RESPECT TO PROJECTING TEAM SWITCHERS.  These are the same conclusions I found the first time I looked, and they still hold for the current version of the DRC+ algorithm.


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