PSI+: A New Way to Measure Strikeout Skill

In 2025, with a job search underway and the baseball season approaching, I decided to build a pitcher strikeout model. Part of it was staying busy. Part of it was keeping my data analysis skills sharp for future jobs. Mostly it was baseball, which has always been my favorite sport.

The model worked. I kept refining it and tracking it. Somewhere in that process a few questions kept coming up. The model used strikeout rate, or K%, as one of its core pitcher-side inputs. K% works, but it doesn't always tell you why it works, or whether it's going to continue. The model was occasionally wrong in ways that felt predictable in hindsight, and the suspicion was that another way to describe that part of a pitcher had to exist somewhere in the data.

That suspicion is what led to PSI+.

What K% Doesn't Show

Two pitchers can post identical strikeout rates while getting there in very different ways. One gets his misses with a 98 mph riding fastball that crosses the plate on a flat angle. The other leans on a slider or changeup once he reaches two strikes. Their K% tells us how often they finished the job. It leaves plenty to explore about the pitches that got them there.

Pitcher Strikeout Index, or PSI+ for short, is what came out of that suspicion. I built it to describe a pitcher's underlying strikeout profile through count-weighted whiffs and fastball traits. Instead of starting with strikeouts after the fact, it starts with some of the pitch-level pieces underneath them.

How PSI+ Works

PSI+ takes its name from the unit of pressure measurement. Counts matter, and Count-Leveraged Whiff Rate (CLW) gives whiffs different weights depending on where they happen in the count. The fastball components add velocity and trajectory to that picture.

Count-Leveraged Whiff Rate makes up 55% of the formula. A two-strike whiff can finish the hitter; a first-pitch whiff only opens the plate appearance. CLW measures the rate of swinging strikes across the whole arsenal, counting two-strike pitches double, first pitches half, and other pitches at their usual weight. Misses against sliders, changeups, and other secondary pitches count here, too.

Fastball Velocity Ceiling makes up 25%. This uses the 95th percentile of four-seamer, sinker, and cutter velocity. Think of it as the speed near the top of a pitcher's fastball range, without letting one unusually hot reading define the number.

Vertical Approach Angle makes up 20%. VAA describes how flat or steep a fastball is traveling when it reaches home plate. PSI+ gives more credit to flatter average angles across those same fastball types. The measurement also reflects pitch location, which PSI+ does not adjust for. A flatter angle isn't automatically better in every situation.

Starters and relievers are scored separately, with 100 representing the average for that role in that season. Higher scores describe stronger profiles. A 120 is well above average on the PSI+ scale; it doesn't mean 20% more strikeouts. The methodology explains the full calculation.

Does It Hold Up?

In comparisons from 2024 to 2025 and from 2025 to 2026, PSI+ was more consistent from season to season than K%, swinging-strike rate, or called-strike-plus-whiff rate among pitchers who qualified as starters in both years. A pitcher's strikeout rate could move around while more of his pitch profile remained recognizable.

For the next-season K% comparisons, pitchers needed to qualify as starters in the earlier season, but not necessarily the following season. PSI+ also had the strongest relationship with next-season K% of those four measures in both evaluations. Its advantages over the two strike-based measures held up statistically. Its small lead over prior K% wasn't conclusive. That gives PSI+ a useful combination: greater repeatability, with a relationship to future strikeouts similar to strikeout rate itself.

These are historical tests. The final formula was selected using earlier seasons, with 2025 and 2026 outcomes excluded from that selection. The evidence section has the comparisons and sample sizes.

When the Numbers Disagree

The pitchers who drew my interest were the ones whose strikeout rate and pitch profile told different stories. Bryan Woo and Caleb Ferguson show what that looks like.

Woo struck out 21.4% of the batters he faced in 2024, but his PSI+ was 108.5. All three ingredients were above average, led by a VAA in the 95.9th percentile among starters. His K% rose to 27.1% in 2025 as his workload grew from 472 to 731 batters faced.

Caleb Ferguson struck out 26.9% of the batters he faced in 2024, but his PSI+ was 94.2. All three components were below the reliever average, pointing to a weaker profile than his strikeout rate suggested. In 2025, his K% fell to 18.9% over a similar workload.

The broader tests focused on starters with larger gaps between the two measures. K% moved in the direction PSI+ indicated for 43 of 65 pitchers in the first comparison and 52 of 66 in the second. The test compared each measure with its own group average, putting the two on a common scale.

Strikeout rates also tend to move back toward the average. PSI+ pointed in the right direction more often than a forecast based on that tendency, but the tests didn’t establish a conclusive advantage. A disagreement gives us a reason to inspect the pitcher more closely, with the components and context helping explain what we're looking at.

Adding to a Forecast

The next question was whether a forecast could improve by using PSI+ alongside strikeout rate.

These forecast tests included starters and relievers, with results through the end of the 2026 regular season.

One test started with actual K%, role, workload, and Mike Podhorzer's published expected-strikeout-rate equation, or xK%. That equation uses the strikes and counts a pitcher accumulated to estimate his same-season strikeout rate. Adding PSI+ reduced forecast error in both 2025 and 2026, with an overall reduction of 2.8% across 663 pitcher-season transitions. The error measure was root mean squared error (RMSE), which gives greater weight to larger misses.

Historical tests using archived Steamer and ZiPS projections also found gains. Each projection received an adjustment learned from earlier seasons, with and without PSI+. Adding PSI+ to those adjusted forecasts reduced forecast error by 1.8% for Steamer and 2.3% for ZiPS across 2025 and 2026.

Fastball velocity accounts for much of the added information. A larger historical analysis also found a smaller contribution from VAA and count-weighted whiffs after accounting for velocity. That analysis measured how well models fit the data they were built on. The forecast tests above evaluated predictions on later seasons excluded from model fitting. The complete metric brings those pieces together in one score that can be inspected. The strongest results so far concern the season-level strikeout profile and its contribution to next-season forecasts.

Reading a Pitcher's Profile

I'd start with a pitcher you know. Find him on the StatPacks leaderboard and click his name to see “What drives this score?” The bars show how many points each component adds above or below the average. Two pitchers with the same total can look quite different underneath it. For a comparison with strikeout rate, use official season K%; the table's K%* uses a restricted pitch sample.

The rolling view follows the profile before each start using up to the previous 1,000 eligible pitches. Select a start to see its breakdown, or use “What changed?” to compare it with the preceding start. A flat total can hide an improvement in one component and a decline in another. The rolling chart uses the same reference group across seasons, while the leaderboard compares a pitcher with others in his role that year.

Baseball's best public numbers rarely make the old ones disappear. They give us another angle on the same pitcher. PSI+ is meant to keep that angle close to the pitches themselves. That means looking at the two-strike miss, the extra gear on a fastball, and the path that pitch takes to the plate.