An Iota of xwOBA: Does Overperformance Improve Confidence?

Paul Goldschmidt’s 2022 was a year for the ages, literally: the Cardinals’ first baseman defied senescence to post a 7.1 WAR and 177 wRC+, numbers which respectively tied for the 25th-best season among hitters 34 and older and the 15th-highest among those same elders with at least 500 plate appearances since 1920. This year, the slugger has largely picked up where he left off, with a 164 wRC+ through his first 186 trips to the plate. And according to xwOBA, he’s been significantly better than last year.

In case you’re not familiar, Weighted On-Base Average (wOBA) evaluates overall offensive performance in one stat, using linear weights to measure the relative value of each offensive outcome and then putting that number on the same scale as OBP. xwOBA, a product of Baseball Savant, combines a hitter’s walk and strikeout numbers with a prediction for how they should have faired on balls in play based on launch angle and exit velocity.

Last year, Goldschmidt put up a career-best wRC+, but xwOBA was telling us that some of that was smoke and mirrors: his .367 mark was well shy of his actual wOBA of .419. That 52-point divergence was the fifth-highest overperformance among hitters with at least 500 plate appearances in a single season since the introduction of xwOBA in 2015. Entering his age-35 season and due for some regression, I dismissed the idea of another big year from the first baseman.

Yet not only is Goldschmidt’s wOBA above .400 again, but his xwOBA has soared. In fact, prior to Monday’s tilt, he was under-performing it by 21 points. Most of this is due to more frequent hard contact: he’s raised his hard-hit rate nearly 10 points to 55.2% and his barrel rate a few ticks up to 15.2%, both Statcast-era highs for him. But a cursory look at his batted-ball profile (again, prior to Monday) indicates that it’s unlikely a swing change is behind his mashing:

It’s interesting that he’s chosen this year, shift ban and all, to post his lowest pull rate since 2015. Yet this is still a minor change; if anything, it speaks to his remarkable bat control that his pull rate range has only just exceeded 5% over the past nine seasons, including this campaign.

Meanwhile, Goldschmidt’s average launch angle has dropped half a degree, which explains the fall in popup rate and increase in line drives. But a glance at his launch angle distributions tells you how minimal this change really is (with 2022 in red):

Perhaps he’s just becoming more familiar with his new custom bat as he enters his second season with it. Or maybe the smartest player Nolan Arenado has ever seen has continued tinkering in ways imperceptible to me. I wouldn’t be surprised if Goldschmidt saw his xwOBA numbers from last year and got to work this offseason like he didn’t just win an MVP. After all, he ditched the bat model he’d used after 11 excellent big league seasons because a biomechanics lab told him to. In other words, he continues to evolve with the game.

But a lot of hitters probably would have had a season like his and figured, why fix what ain’t broke, advanced metrics be damned? Even for the anti-Goldschmidt, I wondered if a wOBA overperformance — relative to xwOBA — portended a future xwOBA increase simply because improved confidence brought about stronger underlying skills.

While the discourse on overperformance relative to peripherals is ongoing, this got me interested in another question: do said overperformers tend to improve upon their peripherals over time? Whether due to a skepticism of their overperformance (and subsequent desire for continued adjustment) or simply more confidence, this was seemingly the case for hitters last season. I split the regular season into two halves, one comprising April through June and the other July through October. For the 218 hitters who had at least 150 plate appearances in each half, a first-half wOBA overperformance correlated significantly with better second-half wOBAs:

Or put another way, players who overperformed their xwOBA by at least 20 points in the first half posted about the same xwOBA on average, better than those who underperformed in the first half by at least 20 points or those who were roughly on par with expectations:

These are pretty small differences despite their statistical significance, and sure enough, when I ran the same analysis on 2021, there were no significant gaps. I also tried doing a year-over-year analysis, replacing first half and second half with the entire 2021 season compared to the entire ’22 season, also to no avail.

Then I tried the same analysis with pitchers who had at least 30 innings in both halves of the 2022 and ’21 seasons. There, I had the advantage of being able to use not only xwOBA but also other performance evaluators and estimators like FIP, xFIP, and SIERA. In SIERA’s case, for example, this meant that I could look at ERA overperformances relative to SIERA in the first half compared to SIERA improvements in the second half. In 2021 at least, first-half SIERA overperformers significantly lowered their SIERA in the second half, as did xFIP overperformers, but when I did the year-over-year analysis, ’21 SIERA and xFIP overperformers had significantly worse marks in ’22.

Strangely, while the offensive environment in 2022 was somewhat impoverished relative to ’21, peripheral-overperforming pitchers posted even worse peripherals in the former year. In this case, perhaps any increase in confidence or renewed effort to improve upon underlying traits came crashing down once regression hit. But what about players who achieve a more sustained confidence boost by overperforming their peripherals time and again?

Consider Goldschmidt’s friend and teammate, Arenado. Since the advent of xwOBA, his wOBA has outperformed the x-stat by at least 20 points each season until this one. At the start of this season, it seemed like his secret sauce had evaporated: in April, he posted a paltry .263 wOBA that actually lagged behind his .268 xwOBA. Of 46 Arenado months on record (min. 50 plate appearances), this represented one of just eight in which he underperformed. But thus far in May, he’s rebounded in a big way by posting a .409 wOBA and a .403 xwOBA, moving back into the positive of wOBA/xwOBA differential and vastly improving upon his stats (both peripheral and otherwise). Perhaps an even better example of what I’m trying to get at is Arenado’s 2022 season, in which he posted a .359/.319 wOBA/xwOBA through June and then worked up to a .403/.359 wOBA/xwOBA for the home stretch. This came on the heels of a 25-point overperformance in 2021.

So I ran one more test to unearth Arenado-like players, this time going back to hitters and the split-in-half 2022 season. Consider the following (where “OP” stands for “Overperformer”):

These are mostly small samples, and I had to lower the threshold for overperformance to just 10 points in order to get them even this large. But they indicate that most of the reason why overperformers improved upon their xwOBAs in the second half in 2022 was due to improvements among the subset of players who also overperformed their xwOBA in ’21. In other words: repeat customers like Arenado, whose sustained overperformance outweighed any impending regression and in fact seemed to fuel somewhat of an improvement.

Regardless of whether overperformance actually leads to more confidence or not (and the evidence is certainly mixed), all of this is to say that what Goldschmidt is doing this season is extremely impressive. He didn’t get complacent like some may have after a career year, perhaps even realizing that he wasn’t the kind of hitter who could continue to outpace his quality of contact. And this time around, his gains in that area are for real. At 35 years old, he probably won’t continue to post career-best numbers going forward, but his propensity for adjustments has him poised to remain productive for the foreseeable future.