A deeper look at what drives a pitcher’s strikeouts.
55% CLW · 25% Fastball Velocity Ceiling · 20% VAA
100 is average. Higher scores indicate a stronger strikeout profile. Starters and relievers are scored separately.
Scores are standardized within each season and role. A PSI+ of 110 is about one standard deviation above that role’s average, and 120 is about two. PSI+ points are standardized distances, not percentages above average. Qualification is based on eligible pitches.
| 1 | 128.8 | 37.8% | 0.188 | 103.2 | -3.98° | |
| 2 | 126.9 | 30.1% | 0.171 | 98.8 | -4.33° | |
| 3 | 125.8 | 29.6% | 0.161 | 100.2 | -4.12° | |
| 4 | 123.4 | 30.0% | 0.169 | 98.6 | -5.01° | |
| 5 | 123.0 | 33.1% | 0.163 | 99.5 | -4.96° | |
| 6 | 121.4 | 30.7% | 0.155 | 98.6 | -4.44° | |
| 7.5 | 120.2 | 27.9% | 0.154 | 100.2 | -4.88° | |
| 7.5 | 120.2 | 28.0% | 0.158 | 96.2 | -3.67° | |
| 9 | 120.0 | 34.7% | 0.155 | 98.9 | -4.81° | |
| 10 | 119.9 | 31.3% | 0.154 | 99.6 | -4.97° |
Rank comes from the v4 release and is calculated within each analytical role; ties can be fractional. Leaderboard K%* uses the component-filtered eligible-pitch denominator and can differ from official full-season SO/BF. The evidence and examples below use official K%.
See how a pitcher’s strikeout profile changes over time, using up to 1,000 eligible pitches before each start.
Rolling scores use a different reference scale from the season leaderboard and aren’t directly comparable.
Rolling PSI+ is calculated for official-start targets using only information available before each start. The current appearance is excluded. Each score uses up to the previous 1,000 eligible pitches and requires at least 200 prior eligible pitches, 30 fastballs, and 20 valid VAA observations. Scores use the frozen 2020–2024 starter reference.
We evaluated year-to-year PSI+ stability and its relationship with next-season strikeout rate.
The 2024→2025 and 2025→2026 target outcomes were held out from final-v4 development and weight selection. Both evaluations use eligible returning pitchers and cover consecutive seasons, so they are not independent replications.
For each season pair, we calculated every metric’s Pearson correlation using the same pitchers who qualified as starters in both seasons.
PSI+ had the highest observed year-to-year correlation among the four metrics in the 2024→2025 and 2025→2026 evaluations.
| Metric | 2024→2025 (n=150) | 2025→2026 (n=155) |
|---|---|---|
| PSI+ | 0.827 | 0.841 |
| SwStr% | 0.756 | 0.745 |
| K% | 0.697 | 0.688 |
| CSW% | 0.638 | 0.595 |
Source-season starters; official target-season K% is regular-season SO/BF.
PSI+ had the highest observed correlation with next-season strikeout rate among the four metrics in the 2024→2025 and 2025→2026 evaluations.
| Metric | 2024→2025 (n=167) | 2025→2026 (n=165) |
|---|---|---|
| Prior K% | 0.696 | 0.648 |
| PSI+ | 0.699 | 0.660 |
| SwStr% | 0.644 | 0.603 |
| CSW% | 0.594 | 0.533 |
Its lead over prior-season K% was small and not statistically conclusive. The paired comparisons supported an advantage over SwStr% and CSW% in each evaluated year pair.
Development evidence came from 2021→2022, 2022→2023, 2023→2024. The later pairs 2024→2025 and 2025→2026 were held out from final-v4 development and weight selection. The results are retrospective and were not externally preregistered. Earlier PSI+ versions were developed with knowledge of some historical outcomes.
Does PSI+ add information when a forecast already includes strikeout results or an established projection?
These evaluations cover 2025 and 2026, with 2026 regular-season results through September 27. They include starters and relievers, using different eligibility rules from the starter comparisons above.
The baseline used actual K%, role, workload, and the gap between published xK% and actual K%. The comparison added the standardized gap between PSI+ and actual K%. Models were fitted on earlier completed season pairs before evaluation on each later pair.
The sample contains 663 pitcher-season transitions from 437 pitchers. Each required at least 500 eligible source-season pitches and 100 batters faced the next season.
| Evaluation | Pitcher-seasons | Baseline RMSE | With PSI+ |
|---|---|---|---|
| 2024→2025 | 327 | 4.031 | 3.939 |
| 2025→2026 | 336 | 4.070 | 3.938 |
| Combined | 663 | 4.051 | 3.939 |
RMSE is root mean squared error, measured in K percentage points. Lower is better.
Adding PSI+ reduced error by 0.112 percentage points, or 2.77%—rounded to 2.8% in the article. The 95% interval for the reduction was 0.048 to 0.177 points. This is a relative reduction in forecast error, not a 2.8-point increase in strikeout rate.
Mike Podhorzer’s published 2022 xK% equation uses swinging, looking, and foul strikes, pitches per plate appearance, and the share of plate appearances reaching a 3–0 count. It estimates the same season’s K%. Here, its gap from actual K% was an input to a model forecasting the following season’s change in K%.
The interval comes from 2,000 bootstrap samples that kept each pitcher’s seasons together and refitted the models. The observed error reduction appeared in both evaluation years and both roles. Repeated pitchers and overlapping seasons mean the 663 transitions are not 663 independent pitchers.
Direction accuracy moved from 67.2% to 67.6%, with an inconclusive difference; shortlist performance did not consistently improve. The result supports information about the size of future K% changes, without establishing a better rule for choosing risers and fallers.
The population is limited to pitchers who returned with sufficient workload. It does not represent pitchers who missed the following season.
For each system, a model using archived projected K% and pitcher role was compared with the same model plus PSI+. Both received the same opportunity to learn a calibration from 2022–2024 outcomes, then were evaluated on the same 663 pitcher-seasons in 2025–2026.
| Forecast model | Baseline RMSE | With PSI+ | Reduction |
|---|---|---|---|
| Calibrated Steamer | 3.972 | 3.899 | 1.83% |
| Calibrated ZiPS | 3.934 | 3.843 | 2.34% |
RMSE is in K percentage points. Reductions use unrounded study values; displayed errors are rounded.
The reductions were 0.073 points for Steamer (95% interval: 0.025 to 0.121) and 0.092 for ZiPS (0.035 to 0.150), using pitcher-cluster bootstrap samples with model refitting.
These results measure PSI+’s contribution to comparably calibrated forecasts. Against the projections as originally published, the adjusted models also had lower error, but the uncertainty intervals crossed zero.
Adding prior K% to both sides of each calibrated comparison retained a positive PSI+ contribution. Comparing an adjusted model with the original published forecast changes both calibration and the addition of PSI+, so it answers a different question.
The archives are designated preseason by FanGraphs; their exact original freeze dates remain unverified. These results describe the available historical archives.
Broader historical checks showed uneven gains, including higher Steamer forecast error after adding PSI+ in 2023 and 2024. Those checks trained on four years and evaluated the fifth, sometimes using later outcomes to estimate an earlier year. They assess historical consistency rather than what could have been forecast at the time. The chronological 2025–2026 comparison above is the main forecasting result.
In a separate historical analysis of 1,668 pitcher-season pairs spanning 2021–2026, adding PSI+ to prior K% increased explained variance (R²) by 0.033. With velocity already in the baseline, the increment was 0.011 (95% interval: 0.005 to 0.020). Component comparisons identified contributions from CLW and VAA. These are fitted historical associations, distinct from the forecast-error evaluations above.
Giving the xK% benchmark velocity first reduced the PSI+ increment to 0.028 RMSE points (95% interval: −0.003 to 0.064). With projected K%, prior K%, and velocity already included, the increment was about 0.030 points for Steamer and 0.015 for ZiPS; the interval remained positive for Steamer and crossed zero for ZiPS. Steamer’s use of velocity is documented.
Rolling PSI+ slightly improved an initial plate-appearance baseline, but a follow-up comparison found no clear added gain after recent K% and velocity were included. Tested batter-specific interactions, in-season updating, and minor-league translation routes have not established an added forecasting benefit. A season-level strikeout profile should not be treated as a proven matchup or prospect-translation model.
The final three-component formula was selected using the 2021→2022, 2022→2023, and 2023→2024 season pairs. The 2024→2025 and 2025→2026 target outcomes were excluded from final-formula development and weight selection. These are retrospective evaluations, not prospectively registered tests or independent external replications; earlier PSI+ versions were developed with knowledge of historical outcomes.
This summary follows the October 24, 2026 article evidence notes and their review of saved study outputs. Preparing the web presentation did not refit the models or rerun the bootstraps. The historical explained-variance and follow-up sensitivity figures come from the corrected research review, not additional confirmatory experiments.
These studies overlap with each other and with earlier evaluations on this page. Their sample sizes should not be added together as independent evidence.
A pitcher’s strikeout rate and PSI+ profile can differ. We tested whether those gaps pointed toward a rise or fall in strikeout rate the following season.
In both evaluated season pairs, most pitchers’ strikeout rates moved in the direction indicated by PSI+.
| Size of the gap | 2024→2025 | 2025→2026 |
|---|---|---|
| > 0.5 standard deviations | 66.2%43 of 65 | 78.8%52 of 66 |
| > 1 standard deviation | 78.6%11 of 14 | 81.3%13 of 16 |
Percentages show how often strikeout rate moved in the indicated direction the following season.
PSI+ had a higher hit rate than the K%-based baseline in all four comparisons. The uncertainty intervals did not establish a conclusive advantage over that baseline.
Disagreement compares each measure’s position relative to its source-season analytical-role group. SD means standard deviation, a way to express how far a value sits above or below that group’s average. Positive disagreement means PSI+ is relatively stronger than official K%; negative disagreement means it is relatively weaker. This is a standardized comparison, not a direct subtraction of PSI+ points and K%.
The evaluation uses eligible returning pitchers from 2024→2025 and 2025→2026. Source and target seasons each require at least 500 component-eligible pitches. Source PSI+ and official K% are standardized within the complete eligible source-season analytical-role population before target-season eligibility is applied.
D = z(final raw composite) − z(source official K%), using sample SD within that population. Success requires D × (target official K% − source official K%) > 0; zero movement does not count as success.
Frozen Calibrated Mean Reversion (RTM): clip(0.06640644066937201 + 0.6811693423468024 × prior_K, 0, 1). The plus sign is part of the frozen rule; prior_K uses fraction units. The comparator was kept fixed, and no new model was fit for this comparison.
| Pair | Threshold | n | PSI rate | RTM rate | Lift, pp | Paired 95% interval, pp |
|---|---|---|---|---|---|---|
| 2024→2025 | >0.5 SD | 65 | 66.15% | 56.92% | +9.23 | [-5.80, 23.08] |
| 2024→2025 | >1 SD | 14 | 78.57% | 64.29% | +14.29 | [0.00, 38.47] |
| 2025→2026 | >0.5 SD | 66 | 78.79% | 66.67% | +12.12 | [-4.35, 24.05] |
| 2025→2026 | >1 SD | 16 | 81.25% | 56.25% | +25.00 | [0.00, 50.00] |
Across the two pair-observation sets, descriptive totals were 95/131 (72.5%) above 0.5 SD and 24/30 (80.0%) above 1 SD. The totals combine overlapping seasons and repeated pitchers, so they should not be treated as independent pooled evidence.
These four pitchers had gaps between their PSI+ profiles and strikeout rates. Each card shows the next season’s strikeout rate.
These examples were selected retrospectively, after the following season’s results were known.
These examples were selected retrospectively to show differences between PSI+ and strikeout rate from the same season. They illustrate the metric and should not be treated as an unbiased validation sample or evidence that PSI+ caused the later change.
Strikeout rate is official regular-season SO/BF. Component percentiles compare pitchers within the same source season and analytical role.
Duran’s 2025 PSI+ of 120.1 reflected strength across CLW, velocity, and VAA. His profile stood further above the reliever average than his already-strong strikeout rate.
Component percentiles compare pitchers in the same season and role.
Context: Workload: 287→236 BF. His target season included an oblique injured-list interruption, and 236 BF is a modest relief sample.
Official source: 80 SO / 287 BF; target: 84 SO / 236 BF. The target workload falls below the stricter 250-BF relief sensitivity cutoff but still meets this illustration’s eligibility rule.
Teams: MIN/PHI → PHI
Standardized gap: +1.244 SD. The sign shows whether PSI+ was relatively stronger or weaker than official K% within the source-season role group.
Component definitions: Fastball velocity is pooled FF/SI/FC release-speed p95. Pooled raw VAA is signed FF/SI/FC VAA at the front of home plate (y = 17/12 ft), without location adjustment, height adjustment, or pitch-type standardization.
Source score contributions: CLW +12.13, velocity +5.88, VAA +2.12 PSI points. These contributions describe the source score; they do not sum to disagreement or later K% movement.
Woo’s 2024 PSI+ was 108.5, led by VAA in the 95.9th percentile among starters.
Component percentiles compare pitchers in the same season and role.
Context: Workload: 472→731 BF.
Official source: 101 SO / 472 BF; target: 198 SO / 731 BF. The workload expanded. The movement toward the source cohort mean is compatible with mean reversion. This example alone does not establish whether PSI+ adds predictive information beyond mean reversion.
Teams: SEA → SEA
Standardized gap: +0.888 SD. The sign shows whether PSI+ was relatively stronger or weaker than official K% within the source-season role group.
Component definitions: Fastball velocity is pooled FF/SI/FC release-speed p95. Pooled raw VAA is signed FF/SI/FC VAA at the front of home plate (y = 17/12 ft), without location adjustment, height adjustment, or pitch-type standardization.
Source score contributions: CLW +2.05, velocity +1.89, VAA +4.59 PSI points. These contributions describe the source score; they do not sum to disagreement or later K% movement.
Eflin’s above-average CLW was offset by lower velocity and VAA, producing a 97.1 PSI+ in 2023 despite his 26.46% strikeout rate.
Component percentiles compare pitchers in the same season and role.
Context: Workload: 703→684 BF. The target season included back and shoulder injury interruptions and a trade from Tampa Bay to Baltimore.
Official source: 186 SO / 703 BF; target: 134 SO / 684 BF. The similar BF totals include injury interruptions. This example comes from the development period rather than a third held-out evaluation pair. The movement is also compatible with ordinary mean reversion.
Teams: TBR → TBR/BAL
Standardized gap: −1.348 SD. The sign shows whether PSI+ was relatively stronger or weaker than official K% within the source-season role group.
Component definitions: Fastball velocity is pooled FF/SI/FC release-speed p95. Pooled raw VAA is signed FF/SI/FC VAA at the front of home plate (y = 17/12 ft), without location adjustment, height adjustment, or pitch-type standardization.
Source score contributions: CLW +3.14, velocity −1.65, VAA −4.39 PSI points. These contributions describe the source score; they do not sum to disagreement or later K% movement.
Ferguson’s 2024 strikeout rate was 26.91%, while his 94.2 PSI+ reflected below-average values across all three components.
Component percentiles compare pitchers in the same season and role.
Context: Workload: 249→270 BF, with multiple teams in both seasons. The observed decline is also compatible with mean reversion.
Official source: 67 SO / 249 BF; target: 51 SO / 270 BF.
Teams: NYY/HOU → PIT/SEA
Standardized gap: −1.040 SD. The sign shows whether PSI+ was relatively stronger or weaker than official K% within the source-season role group.
Component definitions: Fastball velocity is pooled FF/SI/FC release-speed p95. Pooled raw VAA is signed FF/SI/FC VAA at the front of home plate (y = 17/12 ft), without location adjustment, height adjustment, or pitch-type standardization.
Source score contributions: CLW −3.10, velocity −1.54, VAA −1.15 PSI points. These contributions describe the source score; they do not sum to disagreement or later K% movement.
PSI+ underwent rigorous testing and validation as part of a comprehensive methodology review. The review re-evaluated the components and their weights, retired SLWR, and corrected the VAA calculation to use the standard signed convention and front-of-plate endpoint. Historical and current scores were rebuilt using the resulting three-component formula: 55% CLW, 25% Fastball Velocity Ceiling, and 20% VAA. The rebuilt outputs were independently reproduced and checked within the project; this was not an external scientific replication.
An earlier version of PSI+ included Secondary Leverage Whiff Rate to represent secondary-pitch whiffs directly. Later testing found substantial overlap with CLW and too little independent value to keep SLWR as a separate component. Removing SLWR did not make PSI+ materially more dependent on fastball traits, so the current formula excludes it.
PSI+ combines CLW, Fastball Velocity Ceiling, and VAA using weights of 55%, 25%, and 20%. Season scores are scaled separately for starters and relievers in each year, with 100 representing the group average.
A score of 100 is the mean for the relevant season and role population. A 110 is about one standard deviation above that mean, and a 120 is about two. PSI+ points are standardized distances, not percentages above average.
Rolling scores use the frozen 2020–2024 starter reference, while season scores are standardized within that season and analytical role. The two scales aren’t directly comparable.
Metric psi_plus_v4_m3_55_25_20_20260925; final data cutoff September 27, 2026. Frozen role-specific 2020–2024 component reference bounds use clipped q02–q98 normalization with inherited epsilon 1e-10, followed by weighted sum and sample-SD season-role standardization.
Analytical starter means at least 45 eligible pitches per tracked appearance, separate from official games started. Publication requires 200 eligible pitches, 30 pooled fastballs for velocity, and 30 valid fastball VAA observations. Missing core components are unscored without imputation or weight redistribution.
VAA is pooled raw FF/SI/FC vertical approach angle at the front of home plate (y = 17/12 ft). Less-negative is flatter and receives more PSI+ credit; more-negative is steeper. It is not location-adjusted, height-adjusted, or pitch-type standardized.
Rolling targets are official games started. Each score uses up to 1,000 strictly prior eligible pitches, requires 200 prior pitches, at least 30 fastballs, and at least 20 valid VAA observations. The current appearance is excluded and the scale uses the frozen 2020–2024 starter reference. Historical/evidence cohorts separately require 500 eligible pitches and official SO/BF outcomes.
Season scores and rolling scores use different reference populations and are not directly comparable.