M/L THE MICROLEAGUE PROJECT
← Research overview

SOURCE DOCUMENT · 24 OCTOBER 2026

Defensive sensitivity study

# Defensive strategy sensitivity analysis

Reconstructed 1984 MicroLeague probabilities under specified inputs. **These are not observed MLB probabilities.** No game code, ATR, initial calculator or transition-engine rules were changed. No Altirra/native validation was performed.

## Main results

With the reference Carew/Feller statistics, ratings 2 and third/one-out, the run-prevention ranking reverses between Speed 1 and 2. At Speed 1, infield in allows a run with probability 58.9743%, versus 59.1582% for normal defense. At Speed 2, normal allows 59.3448%, versus 59.7524% for infield in. These comparisons have complete scoring-state distributions, zero unresolved mass and zero continuation tail under the fixed assumptions below.

At the original Speed 3 reference point, normal minimizes runs and batter reach and maximizes inning-ending probability; infield in maximizes lead-runner retirement. These are different objectives, not a single defensive recommendation. Batter speed 1..5 leaves the entire third-only joint baseball-state distribution unchanged, but changes double-play probabilities with first occupied. Catcher/pitcher fielding ratings have no effect in the inspected closed kernels; outfield throw ratings and the relevant infielder gates do. Joint state changes can remain even when headline marginals are unchanged.

## Scope and definitions

The study uses the saved original CAREW/FELLER batter/pitcher/header fixture. Its tail cutpoints are explicitly fixed at243,247,253 across retries; their lifetime across every real runtime path remains unproved. Actions stay offense0 and normal1/corners6/infield7. Material random bytes are IID uniform. No intervening walk-off/game end, AI management or substitutions are modeled. Fielding profiles are controlled effective-rating configurations, not claims about the historical lineup.

Runner-speed scans vary ONLY the original third runner R3; existing R1/R2 stay Speed3. Batter-speed scans replace only the original record speed nibble and the Runner speed, leaving batting statistics unchanged. Incoming geometry is fixed at D7/D8/D9=(2,70,72); empty speed-cache bytes are3, while occupied slots refresh from their actual runners. These are explicit state scenarios, not reconstructed histories of an actual played game.

Generated 388 input scenarios, 2328 alignment/basis evaluations. Dense runner1..5 x batter1..5 x eight fielding profiles applies to third/one-out. All six requested situations also receive one-factor runner, batter and fielding scans; the other situations are not a full factorial. Nine individual positions receive rating0/3 audits with all other positions held2.

**Two time bases are exported.** `selection` is one accepted action; known foul/interruption states are included and may leave the batter active. `pa` follows the same actions through continuations; first-empty situations sum fouls analytically and class7 advances exactly. First-occupied PAs expand up to the recorded horizon and retain both unresolved and nonterminal tail mass. Never compare rows with different bases as though they were the same experiment.

Every metric interval is an unconditional known contribution through a conservative upper bound. PA upper bounds include unknown transitions plus unexpanded tail; selection bounds include only unknown transitions because continuing states are known current-action outcomes. Nothing is normalized to resolved events. `complete_pa_state`/`complete_selection_state` concern scoring/base state; universal air-out fly/line labels can still be unresolved.

The primary five measures are lead runner scoring, lead retirement, remaining third, batter ending at a live base/home, and inning ending. In these third-starting swing-away scenarios the lead retirements are home/return-throw paths. Holding third differs from being stranded at inning end; stranded is exported separately. Batter safe also differs from hit credit: a hit with an inning-ending runner out can leave the batter stranded. `two_outs` counts any two-outs play, including caught-ball/tag-up plays whose official fly/line label remains unknown. `fielders_choice` is the engine event name, including safe no-out home choices.

## Runner speed: third, one out

|Situation|R3 speed|Batter speed|Defense ratings|Alignment|Lead runner scores|Lead runner retired (home in these situations)|Lead runner remains third|Batter ends at a live base or home|Inning ends|State status|Unresolved|Nonterminal|
|---|---:|---:|---|---|---:|---:|---:|---:|---:|---|---:|---:|
|third_1|1|4|uniform2|normal|59.158187%|1.285084%|39.556728%|45.742695%|1.285084%|complete_pa_state|0%|0%|
|third_1|1|4|uniform2|corners|61.633329%|1.156716%|37.209955%|50.490743%|1.156716%|complete_pa_state|0%|0%|
|third_1|1|4|uniform2|infield|58.974282%|6.158804%|34.866915%|61.669100%|1.028553%|complete_pa_state|0%|0%|
|third_1|2|4|uniform2|normal|59.344848%|1.098424%|39.556728%|45.742695%|1.098424%|complete_pa_state|0%|0%|
|third_1|2|4|uniform2|corners|61.801344%|0.988702%|37.209955%|50.490743%|0.988702%|complete_pa_state|0%|0%|
|third_1|2|4|uniform2|infield|59.752388%|5.380698%|34.866915%|61.669100%|0.879154%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|normal|59.524329%|0.918943%|39.556728%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|corners|61.962896%|0.827149%|37.209955%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|infield|60.549896%|4.583190%|34.866915%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|4|4|uniform2|normal|59.710989%|0.732283%|39.556728%|45.742695%|0.732283%|complete_pa_state|0%|0%|
|third_1|4|4|uniform2|corners|62.130911%|0.659134%|37.209955%|50.490743%|0.659134%|complete_pa_state|0%|0%|
|third_1|4|4|uniform2|infield|61.328002%|3.805084%|34.866915%|61.669100%|0.586103%|complete_pa_state|0%|0%|
|third_1|5|4|uniform2|normal|59.897649%|0.545622%|39.556728%|45.742695%|0.545622%|complete_pa_state|0%|0%|
|third_1|5|4|uniform2|corners|62.298925%|0.491120%|37.209955%|50.490743%|0.491120%|complete_pa_state|0%|0%|
|third_1|5|4|uniform2|infield|62.131256%|3.001829%|34.866915%|61.669100%|0.436704%|complete_pa_state|0%|0%|

## Batter speed

|Situation|R3 speed|Batter speed|Defense ratings|Alignment|At least one run|Two outs on the play/PA|Engine fielder-choice event|Batter ends at a live base or home|Inning ends|State status|Unresolved|Nonterminal|
|---|---:|---:|---|---|---:|---:|---:|---:|---:|---|---:|---:|
|third_1|3|1|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|1|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|1|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|2|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|2|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|2|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|3|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|3|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|3|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|

Batter speed has no direct term in the third-only scoring kernels. It does enter the ordinary groundball DP gate with first occupied: k=7/8/9 from effective2B+SS ratings, threshold(k-batter_speed)&255 at $5631..$565D. The1B-specific gate instead uses its direct rating. Normal with first occupied short-circuits to $5526; corners and infield take different later routes. Thus a no-effect finding for third-only is not transferable to first+third/loaded states.

Batter-speed ranges for each requested situation (R3 Speed3, ratings2). Values below are endpoint results, with intervals retained; detailed all-five-speed rows are in CSV.

|Situation|R3 speed|Batter speed|Defense ratings|Alignment|At least one run|Two outs on the play/PA|Engine fielder-choice event|Batter ends at a live base or home|Inning ends|State status|Unresolved|Nonterminal|
|---|---:|---:|---|---|---:|---:|---:|---:|---:|---|---:|---:|
|third_0|3|1|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|1|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|1|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|5|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|5|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|5|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.000000%|complete_pa_state|0%|0%|
|third_1|3|1|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|1|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|1|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|normal|59.524329%|0.918943%|0.000000%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|corners|61.962896%|0.827149%|0.000000%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|5|uniform2|infield|60.549896%|0.735501%|6.437962%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|first_third_0|3|1|uniform2|normal|69.996905%..69.997986% interval|6.979452%..6.980532% interval|8.323837%..8.324917% interval|54.055601%..54.056681% interval|0.000000%..0.001080% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_0|3|1|uniform2|corners|61.961924%..61.962896% interval|5.138864%..5.139836% interval|3.395219%..3.396191% interval|53.876016%..53.876988% interval|0.000000%..0.000972% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_0|3|1|uniform2|infield|57.958758%..57.959622% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|55.223337%..55.224201% interval|0.000000%..0.000864% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|first_third_0|3|5|uniform2|normal|69.996905%..69.997986% interval|4.074823%..4.075903% interval|11.228466%..11.229546% interval|56.960229%..56.961310% interval|0.000000%..0.001080% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_0|3|5|uniform2|corners|61.961924%..61.962896% interval|2.971255%..2.972227% interval|5.562827%..5.563799% interval|56.043624%..56.044596% interval|0.000000%..0.000972% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_0|3|5|uniform2|infield|57.958758%..57.959622% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|55.223337%..55.224201% interval|0.000000%..0.000864% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|first_third_1|3|1|uniform2|normal|64.518172%..64.519252% interval|6.979452%..6.980532% interval|8.323837%..8.324917% interval|54.055601%..54.056681% interval|6.979452%..6.980532% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_1|3|1|uniform2|corners|58.173870%..58.174842% interval|5.138864%..5.139836% interval|3.395219%..3.396191% interval|53.876016%..53.876988% interval|5.138864%..5.139836% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_1|3|1|uniform2|infield|57.958758%..57.959622% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|55.223337%..55.224201% interval|1.201140%..1.202004% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|first_third_1|3|5|uniform2|normal|67.422800%..67.423881% interval|4.074823%..4.075903% interval|11.228466%..11.229546% interval|56.960229%..56.961310% interval|4.074823%..4.075903% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_1|3|5|uniform2|corners|60.341479%..60.342451% interval|2.971255%..2.972227% interval|5.562827%..5.563799% interval|56.043624%..56.044596% interval|2.971255%..2.972227% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_1|3|5|uniform2|infield|57.958758%..57.959622% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|55.223337%..55.224201% interval|1.201140%..1.202004% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_0|3|1|uniform2|normal|80.068626%..80.069707% interval|6.991833%..6.992914% interval|8.323837%..8.324917% interval|54.055601%..54.056681% interval|0.000000%..0.001080% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_0|3|1|uniform2|corners|75.000461%..75.001433% interval|5.688588%..5.689560% interval|10.548493%..10.549465% interval|61.029290%..61.030262% interval|0.000000%..0.000972% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_0|3|1|uniform2|infield|72.617050%..72.617914% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|67.722425%..67.723289% interval|0.000000%..0.000864% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_0|3|5|uniform2|normal|80.068626%..80.069707% interval|4.087205%..4.088285% interval|11.228466%..11.229546% interval|56.960229%..56.961310% interval|0.000000%..0.001080% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_0|3|5|uniform2|corners|75.000461%..75.001433% interval|4.243515%..4.244487% interval|11.993566%..11.994538% interval|62.474363%..62.475335% interval|0.000000%..0.000972% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_0|3|5|uniform2|infield|72.617050%..72.617914% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|67.722425%..67.723289% interval|0.000000%..0.000864% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_1|3|1|uniform2|normal|74.589893%..74.590973% interval|6.991833%..6.992914% interval|8.323837%..8.324917% interval|54.055601%..54.056681% interval|6.991833%..6.992914% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_1|3|1|uniform2|corners|72.475091%..72.476063% interval|5.688588%..5.689560% interval|10.548493%..10.549465% interval|61.029290%..61.030262% interval|5.688588%..5.689560% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_1|3|1|uniform2|infield|72.617050%..72.617914% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|67.722425%..67.723289% interval|3.739790%..3.740654% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_1|3|5|uniform2|normal|77.494521%..77.495602% interval|4.087205%..4.088285% interval|11.228466%..11.229546% interval|56.960229%..56.961310% interval|4.087205%..4.088285% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_1|3|5|uniform2|corners|73.920164%..73.921136% interval|4.243515%..4.244487% interval|11.993566%..11.994538% interval|62.474363%..62.475335% interval|4.243515%..4.244487% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_1|3|5|uniform2|infield|72.617050%..72.617914% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|67.722425%..67.723289% interval|3.739790%..3.740654% interval|partial_pa_state|0.000863859%|1.81281e-13%|

## Fielding profiles

|Profile|P|C|1B|2B|3B|SS|LF|CF|RF|
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|
|uniform0|0|0|0|0|0|0|0|0|0|
|uniform1|1|1|1|1|1|1|1|1|1|
|uniform2|2|2|2|2|2|2|2|2|2|
|uniform3|3|3|3|3|3|3|3|3|3|
|infield3_outfield0|2|2|3|3|3|3|0|0|0|
|infield0_outfield3|2|2|0|0|0|0|3|3|3|
|catcher3_infield0|2|3|0|0|0|0|2|2|2|
|catcher0_infield3|2|0|3|3|3|3|2|2|2|

|Situation|R3 speed|Batter speed|Defense ratings|Alignment|Lead runner scores|Lead runner retired (home in these situations)|Lead runner remains third|Batter ends at a live base or home|Inning ends|State status|Unresolved|Nonterminal|
|---|---:|---:|---|---|---:|---:|---:|---:|---:|---|---:|---:|
|third_1|3|4|uniform0|normal|60.263791%|0.179481%|39.556728%|45.742695%|0.179481%|complete_pa_state|0%|0%|
|third_1|3|4|uniform0|corners|62.628493%|0.161553%|37.209955%|50.490743%|0.161553%|complete_pa_state|0%|0%|
|third_1|3|4|uniform0|infield|61.141745%|3.991341%|34.866915%|61.669100%|0.143653%|complete_pa_state|0%|0%|
|third_1|3|4|uniform1|normal|59.710989%|0.732283%|39.556728%|45.742695%|0.732283%|complete_pa_state|0%|0%|
|third_1|3|4|uniform1|corners|62.130911%|0.659134%|37.209955%|50.490743%|0.659134%|complete_pa_state|0%|0%|
|third_1|3|4|uniform1|infield|60.699295%|4.433791%|34.866915%|61.669100%|0.586103%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|normal|59.524329%|0.918943%|39.556728%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|corners|61.962896%|0.827149%|37.209955%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|infield|60.549896%|4.583190%|34.866915%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|4|uniform3|normal|59.344848%|1.098424%|39.556728%|45.742695%|1.098424%|complete_pa_state|0%|0%|
|third_1|3|4|uniform3|corners|61.801344%|0.988702%|37.209955%|50.490743%|0.988702%|complete_pa_state|0%|0%|
|third_1|3|4|uniform3|infield|60.406243%|4.726842%|34.866915%|61.669100%|0.879154%|complete_pa_state|0%|0%|
|third_1|3|4|infield3_outfield0|normal|60.263791%|0.179481%|39.556728%|45.742695%|0.179481%|complete_pa_state|0%|0%|
|third_1|3|4|infield3_outfield0|corners|62.628493%|0.161553%|37.209955%|50.490743%|0.161553%|complete_pa_state|0%|0%|
|third_1|3|4|infield3_outfield0|infield|61.141745%|3.991341%|34.866915%|61.669100%|0.143653%|complete_pa_state|0%|0%|
|third_1|3|4|infield0_outfield3|normal|59.344848%|1.098424%|39.556728%|45.742695%|1.098424%|complete_pa_state|0%|0%|
|third_1|3|4|infield0_outfield3|corners|61.801344%|0.988702%|37.209955%|50.490743%|0.988702%|complete_pa_state|0%|0%|
|third_1|3|4|infield0_outfield3|infield|60.406243%|4.726842%|34.866915%|61.669100%|0.879154%|complete_pa_state|0%|0%|
|third_1|3|4|catcher3_infield0|normal|59.524329%|0.918943%|39.556728%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|4|catcher3_infield0|corners|61.962896%|0.827149%|37.209955%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|4|catcher3_infield0|infield|60.549896%|4.583190%|34.866915%|61.669100%|0.735501%|complete_pa_state|0%|0%|
|third_1|3|4|catcher0_infield3|normal|59.524329%|0.918943%|39.556728%|45.742695%|0.918943%|complete_pa_state|0%|0%|
|third_1|3|4|catcher0_infield3|corners|61.962896%|0.827149%|37.209955%|50.490743%|0.827149%|complete_pa_state|0%|0%|
|third_1|3|4|catcher0_infield3|infield|60.549896%|4.583190%|34.866915%|61.669100%|0.735501%|complete_pa_state|0%|0%|

Effective rating0 has a special throw table, not the continuation of a straight line: Speed1..5 thresholds8,8,9,10,10. For r>0, threshold=(speed+4-r)&255. In third-only play, outfield ratings control tag-up risk; the home-safe gate uses third speed and geometry, not an infielder rating. Infield ratings can still change the joint error-family batter-base distribution even when these five marginals do not change.

Physical2B and SS enter the summed DP gate;1B has a separate direct gate. Loaded failed home plays can query physical1B/2B/3B/SS for a second out. Pitcher home follow-up uses a sign bit instead of a pitcher rating. Shared advancement maps some infield contexts to LF/CF/RF throw ratings through $657D. Error rejection samples positions3..9 and weights acceptance by their effective rating. P/C are unused in these closed gates. Individual-position audits distinguish their absence from the confounded mixed-profile comparisons; this is not a proof about unresolved nonstandard roster lookups or other offensive actions.

## Six game situations at the reference speeds/ratings

|Situation|R3 speed|Batter speed|Defense ratings|Alignment|At least one run|Lead runner retired (home in these situations)|Lead runner remains third|Lead runner stranded at inning end|Batter ends at a live base or home|Inning ends|Two outs on the play/PA|Engine fielder-choice event|State status|Unresolved|Nonterminal|
|---|---:|---:|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---|---:|---:|
|third_0|3|4|uniform2|normal|59.524329%|0.918943%|39.556728%|0.000000%|45.742695%|0.000000%|0.918943%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|4|uniform2|corners|61.962896%|0.827149%|37.209955%|0.000000%|50.490743%|0.000000%|0.827149%|0.000000%|complete_pa_state|0%|0%|
|third_0|3|4|uniform2|infield|60.549896%|4.583190%|34.866915%|0.000000%|61.669100%|0.000000%|0.735501%|6.437962%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|normal|59.524329%|0.918943%|39.556728%|0.000000%|45.742695%|0.918943%|0.918943%|0.000000%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|corners|61.962896%|0.827149%|37.209955%|0.000000%|50.490743%|0.827149%|0.827149%|0.000000%|complete_pa_state|0%|0%|
|third_1|3|4|uniform2|infield|60.549896%|4.583190%|34.866915%|0.000000%|61.669100%|0.735501%|0.735501%|6.437962%|complete_pa_state|0%|0%|
|first_third_0|3|4|uniform2|normal|69.996905%..69.997986% interval|0.918943%..0.920023% interval|29.083071%..29.084152% interval|0.000000%..0.001080% interval|56.227022%..56.228103% interval|0.000000%..0.001080% interval|4.808030%..4.809111% interval|10.495258%..10.496339% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_0|3|4|uniform2|corners|61.961924%..61.962896% interval|0.827149%..0.828121% interval|37.209955%..37.210927% interval|0.000000%..0.000972% interval|55.496461%..55.497433% interval|0.000000%..0.000972% interval|3.518419%..3.519390% interval|5.015664%..5.016636% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_0|3|4|uniform2|infield|57.958758%..57.959622% interval|0.735501%..0.736365% interval|41.304877%..41.305740% interval|0.000000%..0.000864% interval|55.223337%..55.224201% interval|0.000000%..0.000864% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|first_third_1|3|4|uniform2|normal|66.689593%..66.690673% interval|0.918943%..0.920023% interval|28.501463%..28.502544% interval|3.888920%..3.890001% interval|56.227022%..56.228103% interval|4.808030%..4.809111% interval|4.808030%..4.809111% interval|10.495258%..10.496339% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|first_third_1|3|4|uniform2|corners|59.794316%..59.795287% interval|0.827149%..0.828121% interval|36.686444%..36.687416% interval|2.691119%..2.692091% interval|55.496461%..55.497433% interval|3.518419%..3.519390% interval|3.518419%..3.519390% interval|5.015664%..5.016636% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|first_third_1|3|4|uniform2|infield|57.958758%..57.959622% interval|0.735501%..0.736365% interval|40.839371%..40.840234% interval|0.465506%..0.466370% interval|55.223337%..55.224201% interval|1.201140%..1.202004% interval|1.201140%..1.202004% interval|0.001165%..0.002029% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_0|3|4|uniform2|normal|80.068626%..80.069707% interval|0.918943%..0.920023% interval|19.011350%..19.012431% interval|0.000000%..0.001080% interval|56.227022%..56.228103% interval|0.000000%..0.001080% interval|4.820412%..4.821492% interval|10.495258%..10.496339% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_0|3|4|uniform2|corners|75.000461%..75.001433% interval|7.339997%..7.340968% interval|17.658571%..17.659543% interval|0.000000%..0.000972% interval|62.109587%..62.110559% interval|0.000000%..0.000972% interval|4.608291%..4.609263% interval|11.628790%..11.629762% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_0|3|4|uniform2|infield|72.617050%..72.617914% interval|11.074143%..11.075007% interval|16.307943%..16.308807% interval|0.000000%..0.000864% interval|67.722425%..67.723289% interval|0.000000%..0.000864% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|partial_pa_state|0.000863859%|1.81281e-13%|
|loaded_1|3|4|uniform2|normal|76.761314%..76.762394% interval|0.918943%..0.920023% interval|18.429742%..18.430823% interval|3.888920%..3.890001% interval|56.227022%..56.228103% interval|4.820412%..4.821492% interval|4.820412%..4.821492% interval|10.495258%..10.496339% interval|partial_pa_state|0.00108035%|5.81557e-13%|
|loaded_1|3|4|uniform2|corners|73.555388%..73.556360% interval|7.339997%..7.340968% interval|17.135060%..17.136032% interval|1.968583%..1.969555% interval|62.109587%..62.110559% interval|4.608291%..4.609263% interval|4.608291%..4.609263% interval|11.628790%..11.629762% interval|partial_pa_state|0.000971964%|3.34742e-13%|
|loaded_1|3|4|uniform2|infield|72.617050%..72.617914% interval|11.074143%..11.075007% interval|15.842437%..15.843301% interval|0.465506%..0.466370% interval|67.722425%..67.723289% interval|3.739790%..3.740654% interval|3.739790%..3.740654% interval|12.500253%..12.501117% interval|partial_pa_state|0.000863859%|1.81281e-13%|

First-occupied PA results remain partial: missed fouls can remap geometry to a nonstandard lineup lookup, and finite expansion leaves a small tail. Complete one-selection distributions, plus all known terminal and unresolved PA rows, are retained in the joint CSV. This prevents a near-complete approximation being mislabeled exact.

## Four separate defensive objectives

Rankings use exact Fraction intervals. A certified minimum has upper bound no greater than every rival lower bound; a certified maximum uses the reverse comparison. Strict comparisons require disjoint intervals. Possible-best sets retain candidates when intervals overlap. Exact ties are preserved. There is no combined utility, run expectancy, win probability, equilibrium or global dominance claim.

|Situation|Objective|Certified best|Possible best|Comparison|Max unknown|Max nonterminal|
|---|---|---|---|---|---:|---:|
|third_1|min any_run|normal|normal|exact|0%|0%|
|third_1|max lead_retired|infield|infield|exact|0%|0%|
|third_1|min batter_safe|normal|normal|exact|0%|0%|
|third_1|max inning_ends|normal|normal|exact|0%|0%|
|third_0|min any_run|normal|normal|exact|0%|0%|
|third_0|max lead_retired|infield|infield|exact|0%|0%|
|third_0|min batter_safe|normal|normal|exact|0%|0%|
|third_0|max inning_ends|normal|corners|infield|normal|corners|infield|exact|0%|0%|
|first_third_0|min any_run|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_0|max lead_retired|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_0|min batter_safe|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_0|max inning_ends|not certified|normal|corners|infield|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_1|min any_run|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_1|max lead_retired|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_1|min batter_safe|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|first_third_1|max inning_ends|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_0|min any_run|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_0|max lead_retired|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_0|min batter_safe|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_0|max inning_ends|not certified|normal|corners|infield|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_1|min any_run|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_1|max lead_retired|infield|infield|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_1|min batter_safe|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|
|loaded_1|max inning_ends|normal|normal|interval_bounds|0.00108035%|5.81557e-13%|

### Certified ranking reversals

The reversal CSV tests pairwise strict reversals while changing only the named input axis, holding the others fixed. Only disjoint exact/bounded intervals count. A few reversals do not establish global domination or a universal defensive prescription.

|Axis|Basis|Objective metric|Pair A / B|A lower-probability scenario|A higher-probability scenario|
|---|---|---|---|---|---|
|batter_speed|pa|any_run|corners / infield|loaded_1_r3_b1_uniform2|loaded_1_r3_b2_uniform2|
|runner_speed|pa|any_run|normal / infield|third_1_r2_b1_uniform0|third_1_r1_b1_uniform0|
|situation|pa|any_run|normal / corners|third_1_r1_b4_uniform2|first_third_0_r1_b4_uniform2|
|batter_speed|pa|batter_safe|normal / infield|first_third_0_r3_b1_uniform2|first_third_0_r3_b4_uniform2|
|batter_speed|pa|inning_ends|normal / corners|loaded_1_r3_b5_uniform2|loaded_1_r3_b1_uniform2|
|profile|pa|batter_safe|corners / infield|first_third_0_r3_b4_uniform3|first_third_0_r3_b4_uniform2|
|runner_speed|pa|inning_ends|normal / corners|loaded_1_r1_b4_uniform2|loaded_1_r3_b4_uniform2|
|situation|pa|lead_retired|normal / corners|loaded_0_r1_b4_uniform2|third_1_r1_b4_uniform2|
|situation|pa|batter_safe|normal / corners|third_1_r1_b4_uniform2|first_third_0_r1_b4_uniform2|
|situation|pa|inning_ends|normal / corners|loaded_1_r1_b4_uniform2|third_1_r1_b4_uniform2|
|batter_speed|selection|any_run|corners / infield|loaded_1_r3_b1_uniform2|loaded_1_r3_b2_uniform2|
|runner_speed|selection|any_run|normal / infield|third_1_r2_b1_uniform0|third_1_r1_b1_uniform0|

Every witness uses certified strict interval separation; endpoint status, unknown mass and nonterminal mass are included in the reversal CSV and join to the full metric rows. Lower probability is favorable for the two minimization objectives and unfavorable for the two maximization objectives.

## Integer thresholds and arithmetic

|t|Raw byte count with floor(10R/256)<t|
|---:|---:|
|0|0|
|1|26|
|2|52|
|3|77|
|4|103|
|5|128|
|6|154|
|7|180|
|8|205|
|9|231|
|10|256|

These25/26-byte bucket changes are real rounding discontinuities. Rating0 creates plateaus; the shared single helper also has an automatic Speed>=5 branch. Changing R3 speed can affect another runner on a double because $5054 sets C5=3 and reads original third cache. Initial batting weights/cutpoints are identical across batter-speed1..5; only later state gates differ. All15 initial speed/alignment cases have monotone cutpoints and no byte-addition overflow in this fixture. The threshold CSV records every case. No floating arithmetic selects branches or ranks defenses. Original byte-wrap behavior remains in the unchanged engine, including the separate runner regression s=255,r=2 -> threshold1.

## Files and rebuild commands

Run from the project root. The default study includes the dense main grid, all six one-factor scans and individual-position audits. It takes several minutes. The Python module remains importable; importing does not generate files.

```powershell
python -B reverse_engineering/DEFENSIVE_STRATEGY.py
python -B -m unittest discover -s reverse_engineering -p 'test_defensive_strategy.py' -v
```

Use `--output-dir <new-directory>` for an independent export, `--max-selections 8` to set the first-occupied PA horizon, or `--quick` for a clearly marked reference-only smoke export. A quick export is not the full requested study. No external Python packages or network services are needed.

- DEFENSIVE_STRATEGY_METRICS.csv: long exact lower/upper probabilities, percentage columns, scenario inputs, status and remaining mass.
- DEFENSIVE_STRATEGY_JOINT.csv: identity-level destinations, runs/outs, occupied bases, ended inning, active batter, event/hit credit and unknown reason; rows sum1 per case. Unknown fields are blank, not0.
- DEFENSIVE_STRATEGY_RANKINGS.csv: four independent interval-certified/possible-best objectives.
- DEFENSIVE_STRATEGY_REVERSALS.csv: matched-input pairwise reversal witnesses, exact endpoint intervals and completeness.
- DEFENSIVE_STRATEGY_POSITION_EFFECTS.csv: one-position changes, metric delta bounds and joint total-variation bounds.
- DEFENSIVE_STRATEGY_THRESHOLDS.csv: starting/adjusted weights, cutpoints, byte counts and warnings.
- DEFENSIVE_STRATEGY_MANIFEST.json: assumptions, experimental design, profiles and exact source hashes.
- DEFENSIVE_STRATEGY.html: offline heatmaps, scenario controls, completeness legend and joint-state inspector.

The HTML heatmaps use one probability scale across alignments. Incomplete cells are hatched and display bounds; unrun factorial cells are marked not run. Exact fractions remain in CSV and cell tooltips. Blue encodes probability, not goodness; green outlines apply only to interval-certified best alignments for the selected objective.

## Evidence and validation

Primary mechanics: RUNNER_ADVANCEMENT_ANALYSIS.md sections1..5; $64BB/$6587 speed/throw gates, $5613 DP gate, $6636 home play, $5D30 early normal-defense branch, $5298 tag-up and $50F8 error rejection. Initial fixed-point math stays in MATCHUP_CALCULATOR.py and MICROLEAGUE_ALGORITHMS.py; original-byte references remain in MICROLEAGUE_DISASSEMBLY.asm and the saved fixture.

Automated tests reproduce the previously reported Carew/Feller fractions and percentages, check complete versus partial scopes, exact interval rankings/ties/reversals, joint mass conservation and CSV fields, catcher/pitcher isolation, batter-speed invariance in third-only states, and the strict U10 bucket counts. These are static/model tests, not independent native validation. The historical frozen research-index checksum failure, if encountered during full-suite discovery, is an existing preservation-test exception documented in prior reports.

Status counts: `{"complete_pa_state": 756, "complete_selection_state": 1164, "partial_pa_state": 408}`. Input and source hashes are in the manifest; original applications and the ATR are preserved.

## Recorded validation for this research run

All 19 new sensitivity tests passed. Full discovery ran 118 tests: 117 passed; the sole failure is the historical frozen RESEARCH_INDEX.md hash assertion, already documented before this work. No existing probability-engine test was changed.

All 30,264 exported metric rows satisfy0<=lower<=upper<=1. All 69,580 joint rows were re-read from CSV; their exact probabilities sum1 for each of 2,328 cases, with runner identities, scored/retired separation and out/inning flags checked. All 350 exported reversal witnesses have strict disjoint intervals in both opposite directions. All recorded source hashes match the files used.

The generated JavaScript passed Node syntax checking, and the embedded HTML dataset was parsed and reconciled with the source manifest. Browser preview was blocked by the app browser URL policy; no successful visual or interactive browser check is claimed. The local preview server was stopped. This validation record is a dated session audit; rebuilding reports does not automatically rerun tests or UI checks.

Pre/post SHA-256 fingerprints covered all 63 pre-existing source/report/reference/data artifacts in the research scope. Only the research-index roadmap changed. The ATR, original applications, both probability modules, existing tests and historical reports are byte-identical to their pre-task versions.