Intentional Walk Methodology
Methods and sources for "What the Turang Walk Traded." The study is MLB-01 in the Pascal research repository. It prices the Dodgers' intentional walk of Brice Turang in NLCS Game 2, using only information available before the walk and 2026 regular-season data through Sept. 27, 2026.
- The decision
- Data and information boundary
- League baseline
- Win probability after six innings
- Matchup model
- Registered in advance, and what changed
- Result, uncertainty and sensitivity
- The earlier home run (exploratory)
- Where each number comes from
- Figures
- Replication bundle
- Limitations
The decision
The case is the Dodgers' intentional walk of Brice Turang in the bottom of the sixth inning of NLCS Game 2 at Milwaukee on October 12, 2026. The state was taken from the MLB Stats API live feed for the game. The program that extracts it returns only information known before the walk, and its tests reject any request for the walk's result, for later plays or for the score after the play.
| Item | Value |
|---|---|
| Game | Los Angeles Dodgers at Milwaukee Brewers, NLCS Game 2, October 12, 2026 (MLB game 849812) |
| Series | Milwaukee led 1-0 (verified by the owner) |
| Inning and score | Bottom of the sixth, tied 4-4 |
| Outs and bases | One out, David Hamilton on third |
| Batter walked | Brice Turang, bats left, batting second |
| Pitcher | Brock Stewart, throws right |
| Next batter | William Contreras, bats right, batting third |
| Lineup after Contreras | Jake Bauers (L), Christian Yelich (L), Garrett Mitchell (L), Cooper Pratt (R), Sal Frelick (L), David Hamilton (L), Jackson Chourio (R) |
Earlier in the game, Contreras had singled in the first, made an out in the third and homered in the bottom of the fifth. Those plate appearances are reported as context and are not model inputs.
Data and information boundary
League rates, player rates and models use every final 2026 regular-season game in the research snapshot: 2,426 games from March 25 through September 27, after removing duplicate feeds. Each feed is stored once and identified by SHA-256, with a retrieval receipt. A filter in the code removes any postseason game, and any game dated on or after October 12, from every rate.
Two kinds of information known at the time were left out: 2026 postseason plate appearances before Game 2, which were not acquired, and earlier events in Game 2 itself. The analysis also has no data on defensive positioning, runner speed or bullpen availability. The pre-play base state of every regular-season play was rebuilt from the previous play's base runners, plus any runner newly placed, such as the automatic runner in extra innings. Rebuilt half-inning run totals matched the official linescore in 99.995 percent of 43,152 half-innings, and the rebuilt bases matched an independently processed pitch file in 99.77 percent of 165,769 plate appearances.
League baseline
For each combination of bases and outs, we counted the runs scored from the start of every plate appearance in that situation to the end of its half-inning. Bottom halves of the ninth inning and later were left out, because a walk-off ends them early, as were half-innings without three recorded outs. The ranges in parentheses are 95 percent Wilson intervals: the span where the true rate most likely falls.
| Situation | Plate appearances | Scored at least once | Scored two or more |
|---|---|---|---|
| Runner on third, one out | 1,215 | 65.3% (62.6% to 68.0%) | 16.7% (14.7% to 18.9%) |
| Runners on first and third, one out | 1,960 | 64.2% (62.1% to 66.3%) | 27.9% (26.0% to 29.9%) |
Win probability after six innings
Win probability is the share of games a team in a given situation goes on to win, and one point is one percentage point of that share. Each outcome of the rest of the inning is valued by the home team's win probability at the end of the bottom of the sixth, given its lead. Every remaining half-inning draws its runs from the 2026 distribution of runs in top halves of the seventh through ninth innings (7,274 half-innings, with no runs in 74.1 percent). Top halves stand in for both teams because bottom halves can end early on a walk-off. The home team skips the bottom of the ninth when ahead and wins it by scoring more than its deficit, and a tie after nine innings is settled at the 2026 home win rate in extra innings, 102 of 209 games or 48.8 percent. The calculation is exact, with no simulation, and treats the two teams as evenly matched.
| Home lead after six | Home win probability |
|---|---|
| Down 3 | 10.2% |
| Down 2 | 17.6% |
| Down 1 | 29.6% |
| Tied | 49.7% |
| Up 1 | 70.0% |
| Up 2 | 82.2% |
| Up 3 | 89.7% |
Combining the league baseline with these values gives the league-only estimate: the walk cost the Dodgers about 2.0 points of win probability.
Matchup model
Plate-appearance outcomes. Each 2026 plate appearance was classified as a strikeout, a walk or hit-by-pitch, a single, double, triple or home run, or an out or error on a ground ball or on a ball in the air. Intentional walks were left out of every rate.
Player rates. Each Brewers hitter's 2026 rates against right-handed pitchers were pulled toward the league rates for hitters of his handedness against right-handers, by adding the equivalent of 250 plate appearances at the league rate. Stewart's 2026 rates against all batters were pulled toward league rates by adding 400 plate appearances. Stewart had 101 regular-season plate appearances in the sample, so his rates are close to league average. Hitter and pitcher rates were combined with the odds-ratio method, a standard way to blend a hitter's and a pitcher's rates relative to the league, and then rescaled to add to one.
What happens after each outcome. For each starting situation and outcome, the model uses the league's actual mix of resulting situations and runs scored. Situations with fewer than 20 examples (18 of 192) were pooled across out counts.
The inning. An exact calculation follows Milwaukee's lineup one plate appearance at a time until the third out. It assumes Stewart pitches the rest of the inning and Milwaukee uses no pinch hitters. One branch starts with a runner on third, one out and Turang batting, and the other with runners on first and third, one out and Contreras batting.
Registered in advance, and what changed
The question, data, model, checks and verdict labels were written down and fingerprinted with a SHA-256 hash before the Game 2 data was requested. The preregistration's SHA-256 is 4e26d58c3da28961fd37f81ffe26c0dda38fc02a5fc13749cb8b3ffe9ad7e3b9. Every later change is a dated amendment that says whether results had been seen.
- The calibration check failed. Run with league-average hitters, the preregistered model had to reproduce the league chance of scoring from each of the two situations within 2 points. With a runner on third and one out it came in 2.8 points low. That triggered a preregistered stop, and the model's direct output is reported only as exploratory.
- Amendment 001. It fixed an error in rebuilding the bases that double-counted runners who moved during a plate appearance. It was written after first results were seen, and the calibration check still failed after the fix.
- Amendment 002 (post-hoc). Each branch is anchored to the measured league distribution for its situation, and the model supplies only the difference between Milwaukee's lineup against Stewart and a league-average lineup. That removes the model's level error by construction. It was chosen after results were known, so every estimate that depends on it is labeled post-hoc.
- A held-out check of the anchored model. Rates and anchors were fitted on games through July 31 and then used to predict the chance of scoring for 994 plate appearances from August 1 onward that began in either situation. The anchored model did slightly better than league rates alone, with a Brier score (the average squared error of the predicted chance, where lower is better) of 0.2198 against 0.2206, but the 95 percent range of the difference included zero. The adjustment for these particular players adds little, and most of the estimate comes from the league baseline.
Result, uncertainty and sensitivity
Under the anchored model, Milwaukee's win probability was 65.9 percent if Stewart pitched to Turang and 68.1 percent after the walk, a cost to the Dodgers of 2.2 points. The labels were fixed in advance: disfavored, clear (a cost of at least one point) and stable (the same direction under every alternative assumption).
| Assumption | Cost of the walk to the Dodgers, points |
|---|---|
| Main estimate (anchored) | 2.22 |
| Player rates pulled half as far toward league average | 2.26 |
| Player rates pulled twice as far toward league average | 2.16 |
| Stewart's rates against the batter's hand only | 2.21 |
| A league-average pitcher instead of Stewart | 2.28 |
| Remaining innings drawn from all top halves, innings 1 to 9 | 2.27 |
| Home win rate in extra innings set to 50% | 2.21 |
| Outcome effects taken from innings 6 to 9 only | 2.19 |
| Combined: rates pulled twice as far and innings 6 to 9 only | 2.14 |
We also reran the whole analysis on 500 reshuffled versions of the season, drawing whole games at random and recomputing every rate, outcome effect and anchor. The cost stayed between 1.10 and 3.32 points in the middle 95 percent of those reruns, and every rerun showed a cost. That range reflects the luck of which games were played, not the choice of model.
The earlier home run (exploratory)
This check asked whether hitters do better later in a game after homering earlier. Each later plate appearance was compared with the same hitter's rates in his other games, against a control group of later plate appearances without an earlier home run. The design was fixed before the check ran, but it was not preregistered, so the result is labeled exploratory. It describes the league and says nothing about Contreras in particular.
| Outcome | After an earlier home run (8,953 plate appearances) relative to the control group (119,228) |
|---|---|
| Home runs | 1.05 times (95% range 0.93 to 1.16) |
| Hits | 1.01 times (0.97 to 1.05) |
| Strikeouts | 0.99 times (0.95 to 1.03) |
Where each number comes from
All paths are in research/mlb01/ in the private pascal-abs-research repository and are included in the replication bundle. The claim ledger, CLAIM_LEDGER.md, maps each article statement to its source, type and approval, and the publishing ledger is content/pieces/turang-intentional-walk/ledger.md in the pascal-site repository.
| Article statement | Value | Source |
|---|---|---|
| Decision state | As above | output/decision_state.json |
| Contreras's earlier plate appearances | Single, out, home run | prior_context.py |
| League chance of scoring at least once | 65.3% vs. 64.2% | output/league_run_distributions.json |
| League chance of two or more runs | 16.7% vs. 27.9% | output/league_run_distributions.json |
| Home win probability, tied, up 1, up 2 | 49.7%, 70.0%, 82.2% | output/w_function.json |
| League-only cost of the walk | about 2 points | output/e2_generic.json |
| Modeled strikeout chance, Contreras and Turang | about 18% and 24% | output/e3_matchup.json |
| Dodgers' chances, pitch or walk | about 34% and 32% | output/e3_matchup.json |
| Cost range across assumptions | 2.1 to 2.3 points | output/sensitivity.json |
| Range from reshuffled seasons | 1.1 to 3.3 points | output/bootstrap.json |
| Modeled two or more runs | 18% vs. 28% | output/e3_matchup.json |
| Calibration miss | 2.8 points | output/validation.json |
| Held-out check | 994 plate appearances | output/validation.json |
| Stewart's sample | 101 plate appearances | output/player_rates.json |
| Earlier home run check | 1.05 (0.93 to 1.16) | output/x1.json |
Figures
The three figures are generated by research/mlb01/figures/build_figures.py from the outputs above, and no figure value is typed by hand. The exact plotted values are in figures/source/, and the figures were copied into this page after checking each file's SHA-256 against the research figure manifest. Figure 1 shows the league baseline, Figure 2 the win probability by lead, and Figure 3 the modeled runs in the rest of the inning for each choice, from the post-hoc model.
Replication bundle
The research repository is private, so the material behind this page is published as a replication bundle (82 KB). It contains the charter, the frozen preregistration and both amendments with their SHA-256 values, the validation plan, provenance, claim ledger and results, the build and figure code with its tests, the exploratory home-run check, the figure source tables and the aggregate outputs. MANIFEST.txt lists the SHA-256 of every file, and README.txt names the source commit. Raw MLB Stats API feeds and row-level data are not redistributed.
Limitations
The matchup estimate is post-hoc: the preregistered version failed its calibration check, and the anchored version was chosen after results were known. The held-out check could not separate the adjustment for these players from league rates, so most of the estimate is the league-wide trade. Stewart's sample is small, and the model treats him as close to league average. Runner speed, infield positioning, bullpen plans, pinch hitters and postseason scoring conditions are not modeled, regular-season rates are applied to a postseason game, and both teams are treated as evenly matched over the remaining innings. The earlier-home-run check is exploratory and league-wide. The result of the plate appearance after the walk is deliberately left out of every calculation, and the study makes no causal or psychological claims.