The Punishment Ratio

We need new metrics to capture what we're seeing

Sometimes you need more than just the eye test. Sometimes you need things quantified to better understand what you’re seeing. Especially if you’re a Padres fan. Because the quintessential experience of a Padres fan is seeing flukey and frustrating events over and over again and wondering “Are other fanbases experiencing this?”

While sabermetric mavens Tom Tango, Bill James, and Dan Szymborski have mapped most of the known universe when it comes to player productivity, they’ve done a remarkably terrible job quantifying the frustration a fanbase experiences when flukey events occur. So here are some extremely well thought out advanced metrics, that are definitely not an overreaction to barely 15% of the season and a single bad loss in Coors Field.

Punishment Ratio

If you’ve watched every game the Padres played on the way to their 13-13 record you undoubtedly have the sense that the Padres are committing a lot more errors than you’d expect of a good defensive team. As we’ve covered, they are indeed. But perhaps more importantly it feels like they’re being punished for those errors inordinately harshly. After two more unearned runs were credited Tuesday the Padres have now allowed 19 unearned runs on 17 errors. If we want to understand how harshly the Padres are being punished for their errors on the season we can calculate the Punishment Ratio:

Punishment Ratio (PR) = Unearned Runs / Errors

Here’s how the MLB Punishment Ratio (PR) leaders stack up:

The Padres have been punished to the tune of 1.12 unearned runs for every error they’ve committed this year. You’ll notice that both the Cardinals and Angels have a higher PR but have a lot fewer total errors and unearned runs. Only the unbelievably bad Red Sox (who were ranked the second worst defensive team of all time in 2023 by OAA and are working on a sequel) are truly outpacing the Padres. So yes, the Padres are being punished a lot more harshly than most teams for the errors they’re committing. But we can immediately see above one of the shortcomings of PR: it doesn’t capture the magnitude of the underlying inputs. Additionally, errors and unearned runs aren’t the only source of flukey event frustration. So we need to look further.

Frustration Index

Grounding into a double play is kind of like the “error” of the offense: subject to luck and not necessarily indicative of the player’s underlying skill, flukey and frustrating as hell. If you’ve watched the Padres play this year you might have a sense that they are hitting into double plays, like, all the time. This is essentially true. After another GIDP Tuesday the Padres sit at 26 on the season, just behind the league leading Marlins (28). So if we really want to quantify the magnitude of flukey frustrating events we can add the GIDP to the unearned runs and errors a team has committed to get the Frustration Index:

Frustration Index (FI) = Unearned Runs + Errors + GIDP

Here are the league leaders in Frustration Index (FI):

Putting It All Together

So the Frustration Index tells us the frequency of flukey frustrating events, and the Punishment Ratio tells us whether the baseball Gods are treating these fluke events with inclemency or absolution. But how do you synthesize these findings? How much “Woe is me” is expected? We’ve got you covered: Expected Woe Beyond Anything Conceivable: xWOBACON

Hold on, we’ve just been informed that the name xWOBACON is, against all odds, already taken. Call off your dogs Szymborski we’ll change the name!!

Let’s just call this stat Pythagorean Despair:

Pythagorean Despair = PR * FI

The frequency of total events is adjusted for the absolution granted to defensive miscues that don’t lead to unearned runs. This is roughly how much anguish each team’s fans should expect to feel based on performance in these flukey outcomes that (we desperately hope) don’t have any predictive value.

And for the inevitable critique that this metric contains mathematical incoherencies we’ll remind readers that the canonical example of a trusted baseball metric is OPS, a stat derived by adding two fractions with different denominators together. Also this is a bit.

Here’s the league’s Pythagorean Despair leaderboard:

Again these stats are not predictive (at least we damn well hope they aren’t), but they do square with the eye test. The Padres have both had a lot of errors, and been punished harshly for them on defense, and are grounding into a frustrating amount of double plays on offense. And they’re doing these things more than most every other team.

Good News?

Look the team is still populated by mostly good defenders. The biggest question mark in the preseason seemed to be Jackson Merrill and he has looked highly competent in CF. 3B is a currently an icy abyss but we’re likely to see Manny Machado in the near future. The team leaders in errors are its two best defenders who are on a completely unsustainable error pace:

There is a lot of variance at work and every reason to think that the elusive positive regression is what lies ahead. It remains inconceivable that the Padres would be this bad defensively all year. They should be significantly better on defense going forward.

Big BABIP If True

A strangely encouraging Athletic article was released Monday that had the Padres ranked 16th in their power rankings. But the most interesting part was what Grant Brisbee said about the offense grounding into so many double plays:

That’s actually a very bullish statement, especially if one feels the number of GIDP the Padres have produced is likely to regress downward. It’s honestly pretty hard to believe the Padres have any path to offensive effectiveness in the same tier as the Braves. But it would be big if true!

Nothing Changed

It’s unwise to go searching for answers in baseball’s Bermuda Triangle, and that’s why we haven’t. Nothing fundamentally changed after Tuesday’s loss in the Coors Field torture chamber. But our “metrics” can at least explain the levels frustration many are sensing from watching two unsettling season long trends: the trends are very real. But thankfully those trends both look like small sample size theater, at least to some degree. And despite the Padres struggles their record is exactly league average. Positive regression on both defense and offense can nudge a team from league average to good. We’re nearing the end of April and we haven’t foreclosed on the possibility the team could be good. That’s not nothing!