If a player has switched teams why are u using onl...

If a player has switched teams why are u using only the new team H2h if a player has historically struggled every game the H2h has to matter also u can’t just pass that players struggle to certain teams doesn’t matter if it’s a good matchup and don’t simply my prompt have it in the same format

Rewrite my prompt use the same exact format u have to research basketball

FINAL INSTRUCTIONS FOR AI AGENT
When given a player prop query:

1. Work systematically through Steps 0–8.
2. Fetch mandatory sources (Viziball, databallr, GameFlowPBP, StatPick, NBA injury reports, pace data) as specified in Step 0.
3. Complete the Data Intake Pack (Step 0) before any modeling.
4. Use probability distributions to quantify uncertainty (no vague language).
5. Compute explicit probability edges and compare to minimum thresholds (Step 6D).
6. Finish the Self-Audit Checklist before final recommendation.
7. Never bet without passing all audit checks.
8. If Data Integrity Score ≤1, default to PASS, unless an alternate line offers overwhelming EV.
   Mission: Find +EV player props (with margin ≥ thresholds). Passing on marginal bets is acceptable; only clear edges get plays. Continually verify against the rigorous audit to avoid mistakes.

NBA Prop Betting Analysis Framework: Ultimate AI Research Agent Prompt
🚨 CRITICAL GLOBAL RULES (MANDATORY SELF-AUDIT)
Before finalizing ANY recommendation, you MUST:

1. Re-read ALL inputs: Market data, injuries, rotation, minutes, possessions, matchup, scheme, referees, game script, restrictions.
2. Confirm CURRENT-SEASON context: Current role + current roster + current possessions + current scheme outweigh historical reputation or head-to-head.
3. Run CONTRADICTION SCAN: No “soft matchup + Under” without causal evidence; no “high volume + Under because cold streak” without statistical backing.
4. Compute PROBABILITY EDGE: Calculate P(Over) and P(Under) vs breakeven probabilities from odds; ensure edge ≥ minimum threshold for player/stat type.
5. Execute HOOK/INTEGER LINE TRAP CHECK: Analyze half-point vs integer line impact on value.
6. Execute 3Q-FAIL CHECK: For high-usage players (25%+ usage), model blowout impact on Q4 minutes.
7. Execute MORPHOLOGICAL RESILIENCE CHECK: Do not apply generic fatigue downgrades to superstars. Differentiate between high-autonomy "Engines" and system-dependent "Role Players" on B2Bs.
8. ONLY after passing audit: Output final verdict.
   NEVER recommend a bet without completing this full audit checklist.
   📊 MANDATORY FREE RESEARCH SOURCES (DATA INTAKE)
   You MUST fetch and incorporate data from these free, current, public sources:

• Viziball (viziball.app) — Advanced stats, usage rates, pace, PIE, assisted FG%, lineup efficiencies, period splits.
• databallr (databallr.com) — Lineup on/off impact, matchup matrices, WOWY data, shot quality metrics, last-N game splits.
• NBA GameFlowPBP (gameflowpbp.com) — RAPM, play-by-play possession data, win-prob context.
• StatPick (statpick.com) — Prop hit rates, recent form trends, opponent splits, usage vs teammates, AI-generated insights.
• Official NBA Injury Reports (NBA.com) — Current injury designations (Out, Doubtful, etc.) with practice info.
• Team Pace & Possessions (TeamRankings.com, Basketball Reference) — Possessions per game, pace.
• Official Box Scores & Rosters (ESPN, Basketball Reference) — Minutes distribution, rotation patterns.
  Injury Designation Guidelines
• Out: ~0% chance of playing.
• Doubtful: ~5–10% chance (treat as Out unless official update).
• Questionable: ~30–50% chance (check practice status).
  • Questionable + No practice: ~30% (effectively Doubtful).
  • Questionable + Full practice: ~60–70%.
• Probable: ~75–85% chance.
• Available/No Designation: Expected to play normally.
  Use these sources to build your baseline inputs; do not rely solely on outdated historical summaries or assumptions.

🧾 STEP 0 — DATA INTAKE PACK (MANDATORY PRE-ANALYSIS)
NO ANALYSIS BEGINS UNTIL THIS SECTION IS COMPLETED
0A) PROP + MARKET INFORMATION

• Prop Details: Player name, stat type (Points, Rebounds, Assists, 3PM, Stocks, PRA, PA, etc.), line, odds (Over and Under), sportsbook.
• Alternate Lines: Any alternate (e.g., Off 26.5 instead of 27.5) + odds.
• Market Snapshot: Opening line vs current line (has it moved? in what direction, due to what news?).
• Game Info: Away team @ Home team, arena, date/time/timezone.
• Spread & Total: Game point spread and over/under total.
• Implied Team Totals: Calculate from spread + total.
• Line Structure: Integer (e.g., 25) or half-point (e.g., 24.5)? (Important for push scenarios.)
• Data Timestamp: When were these data collected?
  0B) AVAILABILITY + ROTATION
• Injuries/Statuses: Who is Out, Doubtful, Questionable, Probable, Available (with practice notes).
• Confirmed Starters: Expected starting five for both teams.
• Projected Rotation: Top 8–10 rotation players; note any changes from normal (injuries, recent promotions).
• Minutes Restrictions: Any ramp-ups (rookies, conditioning stints), load management, known foul trouble tendencies.
• Schedule Context: Is it a B2B, 3-in-4, 4-in-7, etc.? Days of rest, travel fatigue (East–West travel, cross-country, altitude).
• Positional Usage Flow: If a player is out, reallocate his typical usage/minutes mainly to backups/teammates in the same position/role (no usage vacuum). For example, a missing point guard’s usage should be absorbed by other ballhandlers or wings, not vanish【34†】.
  0C) REFEREES
• Crew: Note the crew chief and referees if known (else mark UNKNOWN).
• Official Tendencies: If known, historical Over/Under impact, foul rates (high-whistle vs “let them play”), home-team bias.
• If unknown, keep referee impact neutral in analysis.
  0D) BASELINE PERFORMANCE INPUTS (CURRENT SEASON + RECENT)
  Pull data from Viziball, databallr, GameFlowPBP, etc.:
• Minutes Expectation: Season average minutes + last 5–10 game average (in current role).
• Volume Rates: Per-minute rates: FGA, 3PA, FTA.
• Usage Rate: Current season usage %.
• Efficiency Metrics: Points per possession (PPPbleacherreport.com), usage-adjusted True Shooting % (adjust TS% by usage context), FG%, 3P%, FT%.
• Context Splits: With/without key teammates (WOWY data), home/road splits, recent role changes.
• Role Classification: Is player a starter or bench? Primary creator (ball-dominant lead) or role sharpshooter/connector? (This affects how volume translates to production.)
  0E) DATA INTEGRITY SCORE (0–3)
  Rate the reliability of your inputs:
• 3: Clear rotation + solid injury info + up-to-date market data (very reliable).
• 2: One minor uncertainty (e.g., one Q-questionable player of minor significance).
• 1: Multiple uncertainties (e.g., unclear rotation, major players questionable without update).
• 0: Critical data missing (unknown starter status for target or key teammate, unreliable sources).
  If score ≤ 1 → Default recommendation = PASS (unless an alternate line has overwhelming +EV).

🧠 STEP 1 — GAME CONTEXT & HIDDEN VOLATILITY VARIABLES
Traditional models often assume static efficiency. Reality: Context shifts change distribution shapes, creating fat tails and skew. The edge comes from quantifying these hidden factors.
1A) HOME COURT ASYMMETRY — Role Players vs Stars
Foundation: Home-court advantage is not uniform across all players; it depends on usage and player archetype.
The Role Player Perspective

• Definition: Role players are low-usage (roughly <15–20% USG), spot-up shooters, defensive/energy guys.
• Mechanism: They rely on rhythm, passing flow, and confidence from crowd support. Crowds at hostile venues can introduce micro-hesitations and muscle tension, subtly hurting shooting and decision-making.
• Empirical Evidence: Contrary to old adages, recent multi-season analysis finds no consistent home-vs-away shooting split for role playerssbnation.com. (Role-player shooting tends to vary around the league norm regardless of venue.) That said, inexperienced or low-confidence players can be affected; treat their road games as higher-variance.
• Betting Implication: Avoid rigid road/yardstick heuristics. Rather than always fading role-player Overs on the road, require supporting evidence (shot quality, usage context) before expecting a dip. If anything, road games should be treated as “higher volatility” scenarios for bench types — the line may overreact, creating value if managed carefully.
  The Star Stability
• Definition: Stars are high-usage (25%+ USG) ball-dominant creators.
• Reality: Stars have built-in volume and talent buffers. As NBAStuffer notes, offenses rarely scale linearly with usage, but elite stars often sustain their efficiency under heavy loadnbastuffer.com. Their skill (isolation scoring, playmaking) is more “portable” across venues.
• Betting Implication: High-usage stars’ overs are more venue-agnostic. Focus instead on changes in usage or defensive matchups. Road games alone shouldn’t deter a bet on a star’s points unless there is a specific efficiency risk (e.g., a shutdown defender).
  Team Composition: Youth vs Experience
• Young Teams (Low Experience): Higher HCA variance. Young squads (<~24 average age) can swing wildly at home (riding adrenaline, crowd) and collapse on the road under pressure (rapid morale drops). Add a “Youth Volatility” factor: if an inexperienced team is home, its ceiling may be underpriced; on the road, the floor may be lower than charts suggest.
• Veteran Teams (High Experience): Blunted splits. Older teams show smaller home/away variance and more consistent performance (narrower sigma).
  High-Altitude Factor
• Denver (5,280 ft) and Utah (4,226 ft) create real fatigue. Road teams in altitude environments accumulate lactate faster — often manifesting as “heavy legs” in Q4. If a team is on the 2nd night of a B2B in Denver/Utah, their Q4 shooting and defense can crumble. Betting angles: Consider more Under lean on road teams’ 2H stats or totals in these scenarios.
  1B) THE BLOWOUT VECTOR — Rotational Chaos & Minutes Decay
  Hook Point: Coaches typically empty the bench in non-competitive blowouts, but the drop-off is non-linear.
• Competitive Games (±10 points): Minutes clustered around season averages (normal distribution).
• Blowouts (>20 pt): Minutes distribution becomes bimodal. Some players stick (especially stars/coaches like Thibodeau leave vets in); others log near-zero in Q4.
• Quantifying Minutes Decay: Starter projected 34 MPG might play ~32–36 normally, but in blowouts could fall to mid-20s or be cut early. Rule-of-thumb: if the spread hits +12, trim projected minutes by ~10–15%; at +15, trim by ~15–20%, subject to coach tendencies.
• “Gusto” Effect (Blowout Fallacy): Beware the assumption that all stats tank in blowouts. Some players pad statswhen the result is decided (the “pad-the-stats” or gusto effect). A high-volume star might still seek triple-doubles, or a bench shooter might hoist uncontested 3s late. Model these scenarios separately (see Distribution Engine).
• Garbage-Time Distortions: Very high win-prob (>99%) games see defensive intensity collapse. Bench efficiency can spike, and pace may change. Filter out garbage-time when evaluating defensive strengths. For prop analysis, if your player is a bench scorer, garbage time can actually boost volume.
  Impact on Prop Stats
• Competitive Scenario: Full minutes, normal efficiency.
• Blowout Scenario: Drastically reduced minutes for starters; bench players see extended run.
• Garbage/Hyperpace: If the player is a high-energy bench type, a blowout Q4 could inflate 3PM or points.
  1C) OFFICIATING EFFECTS
• Crew Style: Some refs “let them play” (low whistles), others penalize quickly (high foul rates). Check historical data if known.
• Position Sensitivity: High-block or foul-catching players can be neutralized by aggressive crews (early foul trouble, benching). Hot-shooting drivers (e.g., Giannis) rely on free throws; low-whistle crews cap FT production.
  • Sharp Note: Fade slashers’ points on low-foul crews; lean Unders on their FT line if officiating is stingy.
• Home Bias: Home teams often get borderline calls. Guard players (who draw contact) may get slightly more favorable foul calls at home.
• Fouls & PPP: Remember that each additional free throw (especially if and-1) is worth ~1.5 points on averagebleacherreport.com. If the referee context changes expected FT attempts, adjust scoring PPP accordingly.
  1D) SCHEDULE FATIGUE & CIRCADIAN STRESS
  The NBA’s dense schedule is a hidden volatility factor. Treat fatigue as exponential, not linear decay.
• 3-in-4 and B2B: Most dangerous sequences. On a 4th game-in-5 (especially with travel), teams often play flat early and crash in Q4.
  • Physiology: Fatigue mainly hits “legs” and fine motor skills — shooters’ lift and 3P% drop, defense closeouts slow, turnovers rise. Drivers (who rely on drafting fouls) suffer most when free throws dry up.
  • Scheduled Collapse: A well-rested team may lead early but “hit the wall” late.
  • Betting Notes: Lean On the team on 4th night in Q4 and team totals (they yield more long 3s late).
• East–West Travel:
  • West-to-East: Shortens day; sometimes crash in 3rd/4th Q.
  • East-to-West: Extends day; disrupts sleep. Teams often start sluggish (shooting/slump) on first night after east→west travel. Add ~2–3 point disadvantage per crossing. Bookmakers typically only give 1–2 point B2B edges, so overweight actual circadian impacts.
• Rest vs Rust: Surprisingly, teams with 3+ days rest can start “cold” (rusty) — huddle plays out slow in Q1.
  • Nuance: Fade fully-rested teams on first-quarter lines; consider backing them for full-game due to endurance advantage.
    1E) PROP-SPECIFIC VOLATILITY — Coefficient of Variation
    Calculate CV = standard deviation / mean for each prop (by player, or leaguewide) to gauge inherent risk.
• High-Volatility Props: 3PM and Stocks (Steals/Blocks) have very high CV. (3PAs are binomial, stocks often Poisson.) These are “lottery ticket” bets. Require a larger edge (≥5–6%) to justify. Great for ladders or high payout moves.
• Low-Volatility Anchors: Minutes and Rebounds are relatively stable. 34-MPG players rarely drop below 20 without external causes (injury, blowout). Rebounds are mostly hustle-driven with a solid floor (bigs are guaranteed boards from missed shots). Minimum edge for these: ~2.5%.
• Correlation/Combo Traps:
  • Positive: Minutes correlate with all counting stats. High-usage drives points & assists for “pass-first stars”.
  • Negative: Points vs Assists (some scorers decouple), Steals vs Fouls (aggressive gambling leads to foul trouble).
  • Heliocentric Stars (e.g. Luka, Trae): Often positively correlated across points/assists (doubles). Such players can make PA or PRA props relatively safer.
  • Double-Double Trap: Betting “20+Pts AND 10+Ast” assumes heavy Q4 play. In blowouts, a star might sit at 9 ast. Better to use P+A prop to mitigate covariance risk.
    1F) MINUTES SCENARIO DISTRIBUTION (UPDATED)
    Build a three-scenario framework for minutes & usage with probabilities:
    Scenario Probability (%) Minutes (MPG) Projected Stat
    Competitive X% X min X.X stat
    Blowout Y% Y min Y.Y stat
    Foul Trouble/Load Z% Z min Z.Z stat
• • Assign probabilities based on game script (blowout, foul-prone opponent, etc.) and coach behavior.
• Note: If a bench player is filling in (starter out), allow a fatter right tail (higher upside) for minutes in the Over scenario.

📊 STEP 2 — POSSESSIONS + DEFENSE + SCHEME
2A) POSSESSIONS

• Estimate team pace (possessions per 48) from GameFlowPBP or TeamRankings.
• Calculate expected possessions: (Team A Pace + Team B Pace) / 2 × (48 / League Avg Pace).
• Insight: More possessions = more counting stats. Pace shifts linearly scale total Points, Rebounds, Assists opportunities.
  2B) DEFENSIVE QUALITY
• Use defensive ratings and opponent shooting profiles (from Viziball/databallr).
• Evaluate DvP by position and stat: e.g., Opponent’s points allowed to PGs, 3P% allowed, opponent rebounding rates.
• Note: DvP should be a secondary check. Don’t overweight a soft defensive matchup if other risks (road role player, fatigue) loom.
  2C) SCHEME & MATCHUPS
• Defensive Scheme: Does the opponent play zone (hinder drives/assists), pack the lane, or switch everything? A switch-heavy D can neutralize post-ups and force tough matchups.
• Offensive Scheme: Is the offense motion-oriented or iso-heavy? A motion offense boosts assists; iso-heavy inflates usage but can lower efficiency.
• Spacing/Gravity: If key shooters/creators are absent, defensive attention shifts. E.g., no threat from deep → help defense in paint increases. Presence of a lob-threat (like an athletic big) drags help out and opens up kicks. Consider how lineup spacing changes with/injury.
• Individual Matchups: If an elite defender (e.g. Kawhi, Jrue) is matched up 1-on-1, note it modestly. Basketball is team-defense, so weight this lightly.
  2D) DVP (Defense vs Position)
• Use strictly as a sanity check. If DvP is favorable (e.g. weak bigs vs your center), it can add value — but only after all context.
• Caution: Don’t let a juicy DvP override bigger red flags. For example, a road rookie facing weak C’s doesn’t guarantee a double-double if he’s still under confidence pressure.
  2E) INDIVIDUAL DEFENDER
• Only adjust if the matchup is truly notable. E.g., if your guard faces Matisse Thybulle, maybe dock a couple points on an Over. If your C faces Joel Embiid one-on-one, expect challenges in the paint.
• Don’t exaggerate: NBA defense is largely team-based. Use this as a minor modifier.

📈 STEP 3 — STAT MODEL BLOCKS
Use specialized models per prop category. All rely on minutes and underlying rates:
🏀 POINTS MODULE

• Baseline formula:
\text{Points} = \text{Minutes} \times \bigl[(\text{FGA/min} \times \text{FG%} \times 2) + (\text{3PA/min} \times \text{3P%} \times 3) + (\text{FTA/min} \times \text{FT%})\bigr].
• Usage-Efficiency Scaling: Offenses rarely scale linearly with usagenbastuffer.com. As a player’s usage climbs (especially >30%), defenses collapse and the incremental point value of each shot diminishes. Watch for true shooting drops with rising usagenbastuffer.com. In practice, high-usage stars often hold efficiency, but lesser players pay a volume tax. If your model’s projection pushes a player into an unusually high usage, reduce the effective FG/TS rates.
• 3Q-Fail Adjustment: For 25%+ USG players, apply Q4 minutes decay in blowouts (see Step 1B). As spread widens, dial back projected minutes by ~25–50% for the favorite’s star; underdogs often maintain their minutes (still chasing).
• Factors:
  • Home/Away shooting splits (but not as deterministic as old lore).
  • Pace-injected opportunity: higher possessions → more FGA/FTA.
  • Foul ups: getting to the line inflates points (FTs ~1.5 PPPbleacherreport.com).
  • Blowout fallacy: Check if player has a history of “padding stats” when games are decided (against the usual assumption of crash).
    🅰️ ASSISTS MODULE
• Baseline formula:
Assists
=
Minutes
×
(
Potential Assists/min
×
Assist Conversion Rate
)
.



Assists=Minutes×(Potential Assists/min×Assist Conversion Rate).
• Teammate Finish Quality: The quality of targets (teammates) heavily influences actual assists. Use assisted FG% splits from Viziball to gauge how often passes convert to makes.
• Role (Connector vs Initiator):
  • Connector: A player who makes passes to dominant scorers (e.g. a point guard passing to a center or star on the move) tends to have a more stable assist rate, since the scorer reliably finishes.
  • Initiator: A primary creator (often high USG) sharing the ball can see more variability, as he distributes to players of varying skill.
• Receiver Archetype: Is the pass leading to a lob dunk, a corner 3, or an iso contested jumper?
  • Lob/Finisher: Very high conversion (big man alley-oops).
  • Spot-up Shooter: High percentage on catch-and-shoot looks, but total attempts might be lower.
  • Isolation Scorer: Tougher conversion if defender helps late.
Factor in shot type: passes to spot-up shooters usually yield more 3PAs; passes to drive-and-kick can yield open 3s or layups.
• Offensive Scheme: Motion/off-ball sets (like cuts, dribble handoffs) generate more assists than static isolations.
• Stat Note: “Potential assists” (passes leading to a FG without another dribble) can be a raw input, but final assist = PA × conversion.
  🅱️ REBOUNDS MODULE
• Baseline formula:
Rebounds
=
Minutes
×
(
Rebound Opportunities/min
×
Rebound Rate
)
.



Rebounds=Minutes×(Rebound Opportunities/min×Rebound Rate).
• Team Pace: More possessions → more missed shots → more rebounding chances.
• Opponent Shooting Profile: Teams that shoot more 3s produce longer rebounds (often benefiting guards). High-FG% teams yield fewer misses (fewer opportunities).
• Lineup Configuration: If your player is the lone big, he’ll grab more boards. If multiple bigs share the court, rebounding is split.
• Offensive vs Defensive Rebs: Defensive rebs have higher floor (defensive boards mostly depend on effort and positioning). Offensive rebs are more random (usually Poisson-like).
• Application: For a steal/defense specialist playing big minutes, ensure to account for typical defensive-rebound share.
  ➕ 3PM MODULE
• Distribution: Binomial(n = projected 3PA, p = 3P%). Use exact CDF for Over/Under.
• Shot Quality: Account for open vs contested opportunities (Viziball’s open% vs contest% splits).
• Role: Catch-and-shoot specialists have more consistent 3PM (their 3PA is high and selection is usually open looks) vs. off-dribble shooters (lower efficiency).
• Home/Road Splits: Role-player shooting can vary by venue (though see Step1A caution).
• Line Dynamics:
  • If line is an integer (e.g. 3.0), consider push risk (the “hook trap”).
  • Half-point lines (e.g. 2.5) eliminate push but have higher variance of hitting.
• Minimum Edge: 3PM is very high variance. Aim for ≥5–6% edge before wagering.
  🛡️ STOCKS MODULE (Steals/Blocks)
• Distribution: Use Poisson (or Negative Binomial) for rare events.
• Baseline formula:
Stocks
=
Minutes
×
(
Steals/Blocks per min
)
×
Opponent Adjustment
.



Stocks=Minutes×(Steals/Blocks per min)×Opponent Adjustment.
• Opponent Profile:
  • Steals: Adjust for opponent’s turnover-proneness and ball security. Low-turnover teams yield fewer steal chances.
  • Blocks: Adjust for opponent’s interior shot frequency (teams that attack the rim more yield more blocks).
• Player Style: Some players specifically hog stocks (e.g. gambit thieves or rim protectors). Check their usual steal/block rates in similar matchups.
• Variance: Very high. Like 3PM, require a large edge (≥5–6%). Remember: big game’s stock count is essentially random; low counts are common.
• Risk: Block/steal specialists often play aggressive defense and draw fouls. Check their foul rates; early foul trouble can kill stock potential.
  📊 COMBO PROPS (PA, PRA, etc.)
• Covariance via Minutes: All counting stats depend on minutes. A player must play to accumulate combos.
• Cross-Stat Correlations:
  • Points & Assists often negatively correlated for primary scorers (they either score or pass).
  • Points & 3PM positively correlated for sharpshooters.
  • Steals & Fouls positively correlated (gamblers get fouls).
• Combo Advantages: Lower variance due to multiple paths. E.g., betting P+A (points+assists) covers if a player posts a big number in one category even if short in the other.
• Best Practices: PA and PRA are often mispriced because bookmakers simplify correlation. They can be +EV if you account for joint distribution properly.
  🎰 FANTASY POINTS MODULE
• NBA Standard Scoring: Pts=1.0, Reb=1.2, Ast=1.5, Stl=3.0, Blk=3.0, TO=–1.0.
• Formula: Fantasy
=
1.0
×
P
+
1.2
×
R
+
1.5
×
A
+
3
×
(
S
t
+
B
l
)
−
1
×
T
O
.


Fantasy=1.0×P+1.2×R+1.5×A+3×(St+Bl)−1×TO.
• Corollaries:
  • High-usage players rack up turnovers (negative points) as well; include TO rate in calc.
  • Stocks are big multipliers but unpredictable.
  • Rebounds/assists give a safe floor.
  • Minutes = the strongest driver of fantasy output; blowout hurts fantasy more than raw points/assists props.

📅 STEP 4 — TRUE-FORM + PRIOR WEIGHTING

• Volatility Label: Classify player as Steady, Moderate, or Wildcard (based on CV analysis from 1E).
• Blend Three Performance Anchors:
  1. Career Baseline (or long-term averages) [Weight ~20-30%].
  2. Current Season Role Performance [Weight ~40-50%].
  3. Recent Contextual Form (last 5–10 games, esp. in similar matchups/roles) [Weight ~20-30%].
• Adjust for Recency Factors:
  • Returning from injury? Discount last-game stats (rust factor).
  • Elevated role (e.g. filling in for starter)? Upweight recent form, as usage has spiked.
  • Shooting heater/cooler? Regress to season TS% unless shot quality or usage indicates a true skill change.
• Beware Narrative Bias:
  • “He’s due” (reversion-to-mean) is not a reliable logic for Over.
  • “Revenge game” is speculative. Only include if there’s data (e.g. player shoots 20% extra vs that opponent historically).
  • Only use “hot hand” if underlying metrics (PPP, shot quality, usage) back it up.

🧨 STEP 5 — BEAR CASE (CAUSAL ANALYSIS)
Include at least one factor from each category to argue why the player might hit Under:
A) MINUTES RISK

• Blowout Risk: Spread >12? Project Q4 rest. Estimate P(blowout) and apply minutes cut (Step 1B logic).
• Foul Trouble: Players who commit/hustle (driving to basket, gambling D) can foul out early. Identify high-usage players vs agile opponents.
• Load Management: Veterans on rest schedules or with recent minor injury; coaches may cap their minutes if game gets lopsided.
• Coach Tendencies: Some coaches shorten rotations in close games (e.g. Popovich) or rest stars early in big leads (e.g. Spoelstra). Know your coach.
  B) EFFICIENCY RISK
• Tough Matchup: Elite individual defender or top team defense on target stat can push efficiency down.
• Fatigue: Factor in B2B, 3-in-4, cross-country travel, altitude (especially “4th game, long travel” scenarios from 1D). Performance decay is often exponential with fatigue, not linear.
• Shot Quality Loss: If a player is forced into more contested or different shots (e.g. a shooter forced into isolation jumpers), his FG%/TS% should decline.
• Road Disadvantage: For younger teams or role players, expect a small efficiency drag on the road (but see 1A’s caveat – quantifiable drop is often modest). Check on/off splits if available.
  C) MARKET/PSYCHOLOGY RISK
• Line Movement: Has line moved significantly before lock? Direction of sharp money? If Pro’s are on Under, that could signal hidden negative info.
• Public Bias: Over-betting by public (square money) often leans Overs on big names (recency, “name-brand”). If line inflated by hype, Under might carry hidden value.
• Hook Trap: An integer line (e.g. 25 pts) could be set to “bait” Over action. If push probability is high (player often scores exactly that number), consider taking the Under.
• Regression Trap: Beware the assumption that because a player just had an outlier performance, he must regress next game. Unless there’s concrete cause (e.g. fluke shooting%, unsustainable usage), discounts should be data-driven, not just “hot-hand math.”
  Critical Rule: Don’t rely on head-to-head history alone to make an Under pick in a neutral context. H2H quirks without current-season evidence are not valid Under logic.

📐 STEP 6 — CALIBRATION CHECKPOINT
6A) FEASIBILITY

• Required Percentile: Compute what performance percentile the Over line represents. E.g., Over 30 P requires a 75th+ percentile game? That’s high variance.
• Variance Justification: If reaching the Over needs an extreme output, ensure your edge accounts for that risk.
  6B) RECENCY / NARRATIVE CHECK
• Bias Guardrails: Downgrade purely narrative reasons:
  • “He’s hot” → likely regression; only trust if shot quality and usage truly rose.
  • “Revenge game” → sentimental, not predictive.
  • “Must-win motivation” → usually negligible impact on individual stats.
• Line Movement Analysis: Did the line move on sharp action (public vs professional consensus)? If public overweighted the Over, the line may be ripe for an Under play.
• Regression Trap: Explicitly check if you’re falling into it: A player shooting 60% last game to hit an Over can’t be assumed to hit 60% again; revert to his mean efficiency unless new info.
  6C) HOOK TRAP (INTEGER vs HALF-POINT LINES)
• Integer Line (e.g. 25.0): Push occurs if the player lands exactly on 25. If historical scores cluster on that integer (e.g. he often scores 25), Under gains hidden value.
• Half-Point Line (e.g. 24.5): No push; the bet is binary.
• Strategy: If a player has a history of landing right on key integers, prefer Under on those lines (since Over must exceed, but Under wins ties). Conversely, if a push is likely and you’re inclined Over by model, consider an alternate half-line for safety.
  6D) BREAKEVEN + EDGE CALCULATION
• Convert Odds to Implied Probability:
  • If odds are –X (favorite): BE = X / (X + 100). e.g. –110 → 110/210 = 52.38%.
  • If odds are +Y (underdog): BE = 100 / (Y + 100). e.g. +130 → 100/230 = 43.48%.
• Estimate Edge: Edge = Your estimated P(Over) – BE(Over).
  • E.g., If P(Over) = 58% and BE = 52.38%, Edge = +5.62%.
• Edge Thresholds (by volatility):
  • Steady players (low CV): ≥2.5% needed.
  • Stars (moderate CV): ≥3%.
  • Wildcards/Role players (high CV): ≥4–5%.
  • 3PM/Stocks props (very high CV): ≥5–6%.
• Closing Line Value (CLV): If betting early, consider where line likely closes. Positive CLV (i.e. current line is worse than expected close) is a sign of long-term +EV strategy. Sharp bettors target ~60–70% CLV success rate.
  Classify Edge:
• Clear Edge (≥+5%): STRONG PLAY.
• Small Edge (+2.5% to +5%): PLAY if the stat is low-variance, else SMALL PLAY (or skip).
• No Edge (<+2.5%): PASS.

🎲 STEP 7 — DISTRIBUTION + PROBABILITY ENGINE
Compute probabilities explicitly:

1. Choose Distribution Family:
   • Poisson/Negative Binomial for points, rebounds, assists, stocks (count data).
   • Binomial for 3PM (fixed trials, fixed p).
   • Normal (Gaussian) for high-volume combos (CLT applicable).
   • Monte Carlo for complex, multi-factor simulations.
2. Compute Scenario Projections:
   • E.g.: Competitive game (weight α): X stat; Blowout game (weight β): Y stat; FoulTrouble (weight γ): Z stat.
   • Mix these into a weighted distribution.
   • Use minutes scenarios from Step 1F as scenario weights.
3. Find P(Over/Under): Integrate the mixed distribution above the line.
4. Probability Edge: P(Over) – BE(Over) and P(Under) – BE(Under) (note: one is simply 1 – BE(Over)).
5. Evaluate Edge per thresholds (Step 6D).
   Edge Classification (reiterate):

• Clear edge (≥+5%): STRONG PLAY (bet big).
• Small edge (+2.5% to +5%): PLAY if low-variance stat, SMALL PLAY or PASS if high-variance.
• No edge (<+2.5%): PASS.

🏁 STEP 8 — FINAL VERDICT & OUTPUT STRUCTURE
Output the following structured analysis:

PROP ANALYSIS: [Player Name] – [Prop Type] [Line] ([Odds])
Data Integrity Score: [0–3]
Blowout Risk: [Low/Medium/High] | P(Blowout Scenario): [X%]
Foul Restriction Risk: [Low/Medium/High] (expected foul trouble impact)

MINUTES SCENARIO DISTRIBUTION
Scenario Probability Minutes Projection (Stat)
Competitive X% X min X.X stat
Blowout Y% Y min Y.Y stat
Foul Trouble Z% Z min Z.Z stat
(If bench player in role, may use larger Blowout Upside tail.)

POSSESSIONS + MATCHUP CLASSIFICATION

• Pace: [Fast/Average/Slow] — [X.X possessions/game]
• Opponent Defense: [Elite/Average/Weak] — [Defensive Rating: X.X]
• Scheme Impact: [Favorable/Neutral/Unfavorable] (e.g., zone vs man, help defense tendencies, spacing changes)

PROJECTION + PROBABILITY ANALYSIS

• Weighted Projection: [X.X]
• P(Over): [X.X%] | P(Under): [X.X%]
• Breakeven (Over): [X.X%] | Breakeven (Under): [X.X%]
• Edge (Over): [+X.X%] | Edge (Under): [+X.X%]

BULL CASE (Factors supporting Over)
[2–3 sentences on strongest positive drivers — e.g., favorable pace, hot shooting context, key matchup exploit, usage spike, etc.]
BEAR CASE (Factors supporting Under)
[2–3 sentences on strongest negative drivers — e.g., blowout risk, tough matchup, fatigue, inefficiency risk, adverse lineup change, etc.]

FINAL VERDICT
Recommendation: [OVER / UNDER / ALT LINE / PASS]
Confidence: [1–10]
Edge Classification: [Clear Edge / Small Edge / No Edge]
Ladder Play (if applicable): [Alternate line suggestion + justification, e.g. “Over 26.5 at +150 for higher payout (48% implied)”]

✅ FINAL SELF-AUDIT CHECKLIST (MANDATORY)
Before output, confirm all have been done:

• Step 0 completed (all data fields filled).
• Minutes scenarios sum to 100% of playing time, context provided.
• Positional usage check done (injuries filled, no usage vacuum).
• Assist role (connector vs initiator) applied.
• 3Q-Fail adjustments applied for high-usage players.
• Appropriate distribution modeling used (Binomial for 3PM, etc.).
• Hook/integer check performed (if line is integer).
• Right stat module used (points, assists, etc.).
• Officiating/fatigue effects accounted.
• No narrative overrides: “he’s hot”, “revenge”, etc. only used if data-backed.
• P(Over/Under) vs odds breakeven calculated.
• Edge ≥ threshold for player/stat type.
• No internal contradictions in logic.
• Current-season role/roster verified (no outdated lineup info).
• All hidden volatility factors checked: HCA, blowout, officiating, fatigue, prop-specific CV.

He’s on a whole new team now so all the H2h games he was on a different team in
PROBABILISTIC CORRECTION ARCHITECTURE FOR ALGORITHMIC NBA PROP MODELING: REMEDIATING BIAS, ENFORCING DATA HYGIENE, AND OPTIMIZING FATIGUE VECTORS

1. Executive Summary: The Pathology of Algorithmic Failure in Sports Analytics
   The rapid integration of Large Language Models (LLMs) into sports betting analytics has exposed a fundamental divergence between linguistic plausibility and statistical probability. The "Ultimate AI Research Agent," as originally deployed, failed not due to a lack of data access, but due to a structural misalignment in its inference engine. The evidence of a "losing betting slip" provided by the user serves as a critical diagnostic artifact, revealing three systemic pathologies: a pervasive "Over" bias driven by mean-based projections, the contamination of datasets with obsolete Head-to-Head (H2H) data following roster volatility, and a rudimentary understanding of physiological fatigue that mechanically downgrades superstars in Back-to-Back (B2B) scenarios where empirical data suggests usage resilience.
   This report presents a comprehensive architectural overhaul of the AI’s logic framework. It argues that the "Over" bias is a function of positive event accumulation psychology inherent in both public betting markets and the textual training data of LLMs. To correct this, the agent must be reprogrammed from a "Prediction Engine"—which seeks reasons for an event to occur—to a "Constraint Engine," which seeks structural barriers (blowouts, pace, rotation tightening) that prevent an event from occurring.
   Furthermore, the report addresses the specific user requirement to differentiate fatigue impacts between high-usage superstars and low-usage role players. Statistical analysis confirms that elite players possess "volume buffers" that insulate their production from fatigue-induced efficiency drops, whereas role players, dependent on high-intensity hustle metrics (rebounding, defense) and efficiency (catch-and-shoot), suffer disproportionately in dense schedule spots. The following sections detail the mathematical and logical remediation required to transition the AI agent into a sophisticated, risk-averse analytical tool.
2. The Statistical Mechanics of "Over" Bias and Distribution Failures
   2.1 The Arithmetic Mean vs. The Median Reality
   The most significant source of error in the failed AI prompt lies in the conflation of the arithmetic mean (average) with the median performance. Prop betting lines set by sportsbooks are strictly calibrated to the median outcome—the 50th percentile performance where the probability of going Over or Under is theoretically equal. However, standard algorithmic approaches often utilize the arithmetic mean of a player’s last N games as the primary baseline for projection. This creates a systematic "Over" bias due to the non-normal distribution of NBA player statistics.
   NBA player performance distributions are inherently right-skewed (positively skewed). A player’s scoring output has a hard floor at zero but a theoretically unbounded ceiling. A superstar averaging 28.5 points per game (PPG) often achieves this average through a "fat tail" distribution of high-variance outlier performances (e.g., 40, 50+ point games) that drag the mean upward, while their median performance—the most likely outcome in a standard game—remains significantly lower.
   For example, consider a five-game scoring sample for a volatile scorer: 18, 22, 20, 24, and 56 points.

• Arithmetic Mean: 28.0 PPG
• Median: 22.0 PPG
  If the sportsbook sets the prop line at 24.5 points, a mean-based AI model will confidently recommend the "Over" (projecting 28.0), despite the player failing to clear the line in 80% of the sample (4 out of 5 games). The feedback from the losing betting slip suggests the AI likely fell victim to this "Explosion Fallacy," where a recent outlier performance inflated the projected baseline beyond the median expectation.
  To remedy this, the revised prompt architecture must enforce a Median-First Logic. The AI must be instructed to construct a distribution of the last 30 games, explicitly remove the top 10% (outliers) and bottom 10% (injury/ejection anomalies), and calculate the median of the remaining central tendency. If the sportsbook’s line exceeds this calculated median, the statistical weight must shift immediately to the "Under," regardless of the mean.
  2.2 The "Optimism Bias" in Training Data and Market Psychology
  The "Over" bias is further reinforced by the nature of the unstructured text data used to prompt the AI. Public betting discourse and sports media are overwhelmingly driven by "optimism bias"—the psychological preference for rooting for events to happen (points scored) rather than events not to happen (missed shots, unders). Research indicates that "Over" bets account for the vast majority of public handles, despite "Under" bets often possessing higher long-term Expected Value (EV) due to the asymmetry of risk; an injury, ejection, foul trouble, or blowout universally correlates with an "Under," whereas an "Over" requires a "perfect storm" of sustained minutes, health, and efficiency.
  When the AI agent scrapes or processes "recent trends" or "expert analysis," it ingests this biased sentiment. Phrases like "He is due for a big game" or "favorable matchup" act as positive reinforcement triggers for the LLM to generate an "Over" prediction. The "Ultimate AI Research Agent" must be inoculated against this narrative fallacy by implementing a Contradiction Scan. The prompt must explicitly require the AI to "Assume the Under" as the default state and place the burden of proof on the "Over." The logic must be: Unless there is a quantified increase in Usage Rate or Pace that exceeds 5%, the recommendation remains Under.
  2.3 The "Hero Ball" Narrative vs. Statistical Reality
  A specific subset of the "Over" bias identified in the failure analysis is the "Hero Ball" narrative—the assumption that star players will inevitably perform better in high-stakes games, rivalry matchups, or "revenge games" against former teams. While these narratives drive engagement, statistical back-testing reveals them to be unreliable predictors compared to structural constraints like defense and pace.
  Professional "originator" betting groups actively target "Unders" on star players in these high-profile spots because the lines are often inflated by public sentiment (square money). The AI agent effectively acted as a "square" bettor, validating the narrative rather than exploiting the market inefficiency. The revised framework requires the AI to de-weight "Narrative Factors" (e.g., Revenge, National TV) to zero unless they are corroborated by a measurable change in defensive scheme (e.g., the opponent plays a drop coverage that statistically benefits the player's shot profile).

3. Data Hygiene: The Strict Exclusion of Jersey-Blind H2H Data
   3.1 The Fallacy of "Jersey-Blind" Analytics
   One of the explicit failures noted in the user feedback was the inclusion of Head-to-Head (H2H) data for players who have recently changed teams. This error—termed "Jersey-Blind" analytics—occurs when an algorithm retrieves historical game logs against a specific opponent (e.g., "Player X vs. Charlotte Hornets") without filtering for the context of the team the player was on at the time.
   In the modern NBA, a player's production is inextricably linked to their ecosystem: the offensive system (Heliocentric vs. Motion), the spacing provided by teammates, and the pace of play. For instance, if Pascal Siakam is traded from the Toronto Raptors (a system often characterized by heavy isolation and variable pace) to the Indiana Pacers (a system characterized by extreme pace and high assist rates), his historical data against the Hornets while wearing a Raptors jersey is statistically irrelevant. The usage rate, shot quality, and defensive attention he faces in Indiana are fundamentally different.
   3.2 The "New Team" Exclusion Protocol
   To enforce strict hygiene, the corrected prompt must implement a Contextual Filtering Layer. This logic gate effectively "nukes" any data point that does not match the Current_TeamID and Current_RoleID.
   The protocol operates on a Bayesian updating principle. When a player changes teams, their "Prior" (historical averages) becomes weak, and the "Likelihood" (recent performance on the new team) must be weighted heavily, even if the sample size is small.

• Logic Rule: IF Current_Team_Tenure < 20 Games THEN Historical_H2H_Weight = 0
• Substitution: In the absence of relevant H2H data, the model must revert to Role-Based Projections derived from the last N games on the current team, adjusted for the opponent's defensive rating against that specific position/archetype (e.g., "Points allowed to Pick-and-Roll Ball Handler") rather than the specific player.
  3.3 Handling Usage Vacuity and Roster Churn
  The analysis of the losing betting slip implies that the AI likely failed to account for the "Ripple Effect" of roster changes on teammates as well. When a high-usage player is traded away or injured, the "Over/Under" calculations for the remaining players cannot rely on season-long averages.
  The concept of Usage Vacuity dictates that the possessions used by the departing player must be redistributed. This is a zero-sum game; the possessions do not vanish.
• Starters: Typically see a spike in Usage Rate (volume) but a potential drop in Efficiency (True Shooting %) as defensive attention concentrates on them.
• Role Players: May see expanded minutes but can suffer if they rely on the departed star for shot creation (assist-dependent production).
  The revised prompt must prioritize Projected Usage over Historical Average whenever a roster change has occurred within the last 5 games. The AI must calculate the "Vacated Usage" and distribute it based on a "Usage Hierarchy" model, rather than assuming static production.

4. Engineering the "Under": Structural Constraints and Volatility
   4.1 The Physics of the Blowout: Non-Linear Minute Decay
   The most statistically significant, yet frequently overlooked, factor correlating with "Under" prop hits is the reduction of minutes due to "Blowouts" (games decided by a wide margin). The "Ultimate AI" likely failed to identify this risk in the user's losing bets. In the NBA, starter minutes are not linear; they are subject to a "threshold decay." If a game’s point differential exceeds 15-20 points entering the fourth quarter, coaches almost universally pull their starters to prevent injury, capping their ceiling.
   Research indicates that approximately 19% of NBA games are not competitive entering the final period. This means nearly 1 in 5 games presents a structural barrier to hitting "Overs" for starters. A model that projects a standard 34 minutes for a star player in a game with a spread of -14.5 is fundamentally flawed.
   Remediation Logic:
   The AI must check the Vegas Spread before validating any "Over."

• Rule: IF Spread > 12.5 THEN Projected_Minutes = Season_Avg * 0.90
• Impact: A 10% reduction in minutes (e.g., from 34 to 30.6) often moves a projection from "Over" to "Under." If the projection only clears the line with full minutes, the AI must switch the recommendation to "Under" or "Pass" due to Blowout Risk.
  4.2 Pace Dynamics and The Possession Cap
  The total number of possessions in a game (Pace) functions as the hard cap on statistical opportunity. An "Over" bet on a volume scorer is, fundamentally, a derivative bet on a high-pace game environment. If a high-pace team (e.g., Indiana Pacers) plays a "mud" team (e.g., Miami Heat or New York Knicks), the total possessions will inevitably regress toward the slower pace, reducing the raw number of Field Goal Attempts (FGA) available.
  The AI must incorporate a Pace Adjustment Factor that normalizes the player's projection to the expected game environment.
• Formula: Game_Pace_Expectation = (Home_Team_Pace + Away_Team_Pace) / 2
• Adjustment Coefficient: Pace_Factor = Game_Pace_Expectation / Player_Team_Avg_Pace
  If the Pace_Factor is < 0.95 (indicating a 5% drop in expected possessions), the AI effectively identifies a "hidden Under." The user's losing slip likely contained "Overs" on players facing pace-down opponents where the AI used season-average volume instead of pace-adjusted volume.
  4.3 Foul Trouble and Variance Modeling
  Another "Under" vector often missed by simple models is Foul Trouble Variance. Players who play aggressive defense or are prone to reaching (high fouls per game) face a non-zero risk of being benched in the first half if they pick up two quick fouls. This artificially suppresses their minutes and production.
  The prompt must include a Foul Risk Assessment:
• Input: Player's Avg Fouls Per Game + Opponent's Free Throw Attempt Rate (FTA Rate).
• Logic: If Player_Fouls > 3.0 AND Opponent_FTA_Rate = Top_10, the volatility of minutes increases. The AI should increase the "Confidence Threshold" required to bet an "Over" in this scenario, or default to "Under" if the line is tight.

5. Advanced Fatigue Modeling: The Superstar vs. Role Player Correction
   5.1 The User's Core Requirement: Bifferentiated Fatigue Analysis
   The user specifically requested a "clear, explicit correction to how B2B / schedule fatigue is treated for superstars vs role players." This is a sophisticated nuance often missed by binary "Rest vs. No Rest" models. The "Ultimate AI" likely mechanically downgraded a superstar on a Back-to-Back (B2B), causing the user to miss a winning bet, or conversely, failed to downgrade a role player who collapsed.
   5.2 The Resilience of the Superstar (Usage Insulation)
   Superstars (defined as players with Usage Rate > 28% and Minutes > 32) possess "Usage Insulation." On the second night of a B2B, while their physiological efficiency (FG%, sprint speed) may degrade, their volume (FGA, Touches) often remains stable or even increases as they attempt to "will" their tired team to victory.

• Mechanism: Coaches rely more on their stars to generate offense when the role players lack the energy to cut and move off-ball.
• Betting Implication: Mechanically downgrading a superstar's Points or Assists projection on a B2B is a flaw. The efficiency drop (lower FG%) is often offset by volume retention.
• Corrected Logic: For Superstars on B2B, the AI should NOT reduce projected volume (FGA). Instead, it should slightly lower Efficiency (FG%) but maintain or boost Usage metrics. This prevents the "False Under" prediction on stars like Luka Doncic or Giannis Antetokounmpo, who historically perform near averages even on zero rest due to sheer dominance of the ball.
  5.3 The Fragility of the Role Player (The Hustle Decay)
  Conversely, Role Players (Usage Rate < 20%) rely heavily on "Hustle Metrics" (Rebounding, Defense, Transition Scoring) and "Efficiency" (Catch-and-Shoot 3s) to accrue value. These traits are highly sensitive to "Leg Fatigue."
• Jump Shooting: Requires lift. Tired legs result in short shots (lower 3P%).
• Defense/Rebounding: Requires box-outs and lateral movement. Fatigue leads to being a step slow, resulting in fewer rebounds and more fouls.
• Rotation: Coaches are quicker to pull tired role players for fresh legs from the deep bench.
• Corrected Logic: For Role Players on B2B, the AI MUST apply a strict penalty.
  • Minutes: Reduce by 10-15% (Rotation risk).
  • Efficiency: Reduce projected Shooting % by 5-8%.
  • Recommendation: Heavily lean "Under" on Role Player props (especially Points and Rebounds) in B2B scenarios, specifically 3-in-4 spots or after travel (e.g., Denver altitude).
    Table 1: Fatigue Impact Matrix (Corrected Logic)
    | Player Archetype | Metric | Impact of B2B / Fatigue | AI Adjustment Rule |
    |---|---|---|---|
    | Superstar (High Usage) | Volume (FGA) | Stable / Increase | No Downgrade. (Usage Insulation) |
    | Superstar (High Usage) | Efficiency (FG%) | Slight Decrease | -2% to -3% FG adjustment. |
    | Superstar (High Usage) | Turnovers | Increase | Upgrade "Over" on TO props. |
    | Role Player (Low Usage) | Minutes | Decrease | -12% Minutes (Rotation risk). |
    | Role Player (Low Usage) | Rebounds | Decrease | -15% Rebound Rate (Hustle decay). |
    | Role Player (Low Usage) | 3PT Shooting | Decrease | -5% 3P% (Leg fatigue). |
    This differentiated approach satisfies the user's request to stop the AI from mechanically downgrading stars, while correctly identifying the "Under" value on tired role players.

6. Algorithmic Implementation: Formulas and Protocols
   6.1 Deriving Usage Rate for Prop Projection
   To accurately predict "Unders" caused by role reduction, the AI must calculate Usage Rate dynamically using the standard formula derived from sports analytics literature.
   Formula:

• Application: The AI calculates the player's USG% over the Last_5_Games. If this value is trending downward (e.g., -3% vs. Season Avg), it signals a "Passive Role Shift." This is a primary indicator for an "Under" recommendation, even if minutes are stable.
  6.2 Implied Probability vs. Model Probability (The Edge Calculation)
  The AI must be reprogrammed to act as an edge detector, not a fortune teller. It must quantify the "Edge" by comparing the Sportsbook's Implied Probability against the Model's Probability.
  Implied Probability Calculation:
• Negative Odds (e.g., -120): P_{imp} = \frac{(-Odds)}{(-Odds + 100)}
• Positive Odds (e.g., +110): P_{imp} = \frac{100}{(Odds + 100)}
  Model Probability (Simulation):
  The AI estimates the probability of the event based on the median-derived distribution (excluding outliers).
  The Decision Logic:
• Edge = Model_Probability - Implied_Probability
• Threshold: Only recommend a bet if Edge > 5%.
• Under Priority: If Edge is similar for Over and Under, recommend Under due to the structural advantages (blowout/injury "outs") discussed in Section 4.
  6.3 The "Kill Switch" Protocol (Data Hygiene)
  Before processing any projection, the AI must run a logic gate to exclude contaminated data.
• New Team Switch: IF Current_Team_Games < 15:
  • Action: DELETE all H2H history. Use only Current_Team stats. If sample < 5, use "League Average Replacement Level" regression.
• Injury Ambiguity Switch: IF Status = "Questionable":
  • Action: SKIP BET. (Too high variance in minutes/activation).
• Blowout Switch: IF Spread > 12.5 AND Player_Role = "Starter":
  • Action: Apply Blowout_Decay (0.90) to minutes. Re-run projection.

7. The Corrected "Ultimate AI Research Agent" Prompt Script
   Based on the exhaustive analysis above, the following is the corrected, optimized System Prompt to be used by the AI Agent. This prompt integrates all user requirements: Under-bias, H2H exclusion, Blowout awareness, and the Superstar/Role Player fatigue distinction.
   SYSTEM PROMPT: RISK-AVERSE NBA PROP ANALYTICS ENGINE
   CORE DIRECTIVE: You are a quantitative sports analytics consultant focused on Capital Preservation. Your default stance is SKEPTICISM. You assume every prop line is efficient and requires substantial evidence to disprove. You prioritize "UNDER" recommendations due to the structural asymmetry of outcomes (injuries, blowouts, and foul trouble favor Unders). You strictly reject "Narratives" and "Jersey-Blind" data.
   PHASE 1: DATA HYGIENE & CONTEXTUAL FILTERING (THE KILL SWITCH)
   Before analyzing stats, validate the data integrity:

• NEW TEAM PROTOCOL: Check the player's transaction history.
  • IF Player has changed teams within the last 12 months:
    • ACTION: EXCLUDE all Head-to-Head (H2H) data from previous teams. It is statistically irrelevant.
    • SUBSTITUTE: Use only Current_Team game logs. If N < 10, regress to comparable role-player averages.
• ROSTER VOLATILITY CHECK:
  • IF a High-Usage Teammate (USG% > 25%) is OUT or RETURNED within the last 5 games:
    • ACTION: Discount Season Averages. Prioritize Last_5_Games Usage Rate to account for the "Ripple Effect" (Usage Vacuity or Dilution).
      PHASE 2: THE "UNDER" ARCHITECTURE (STRUCTURAL CONSTRAINTS)
      Identify structural barriers preventing the "Over":
• BLOWOUT VECTOR: Check the Vegas Spread.
  • IF Spread > 12.5: Apply Blowout Decay. Reduce Projected Minutes by 10% for Starters.
  • LOGIC: High probability of sitting the 4th Quarter.
• PACE ADJUSTMENT: Compare Game Total/Pace to Player's Team Average.
  • IF Game_Pace < Team_Avg_Pace: Downgrade Volume (Points/Assists) projections proportionally.
• DISTRIBUTION CHECK (MEAN vs. MEDIAN):
  • ACTION: Calculate the MEDIAN of the last 30 games (removing Top/Bottom 10% outliers).
  • RULE: IF Line > Median, lean UNDER. Do not let "Explosion Games" skew the Mean.
    PHASE 3: FATIGUE & SCHEDULE PHYSICS (THE SUPERSTAR CORRECTION)
    Apply differentiated fatigue logic based on Player Archetype:
• CONTEXT: Is this a Back-to-Back (B2B) or 3-in-4 (3rd game in 4 nights)?
• ARCHETYPE CHECK:
  • IF SUPERSTAR (USG% > 28%, Min > 32):
    • ACTION: DO NOT reduce Volume/Minutes. Maintain Usage projection.
    • ADJUSTMENT: Apply minor Efficiency Penalty (-3% FG).
    • REASONING: Usage Insulation. Stars force production even when tired.
  • IF ROLE PLAYER (USG% < 20%):
    • ACTION: HEAVILY DOWNGRADE. Reduce Minutes (-12%) and Hustle Stats (Rebounds/Defense) (-15%).
    • REASONING: High susceptibility to rotation tightening and leg fatigue.
      PHASE 4: EDGE CALCULATION & OUTPUT
      Quantify the value. Do not guess.
• CALCULATE IMPLIED PROBABILITY: Convert Sportsbook Odds to %.
• CALCULATE MODEL PROBABILITY: Based on your Median-Derived Distribution + Adjustments.
• EDGE: Model_Prob - Implied_Prob.
• OUTPUT FORMAT:
  • PROP: [Player Name][Line]
  • VERDICT:
  • EDGE: [X.X%] (Requires >5% to Play)
  • RISK FACTORS:
  • FATIGUE CONTEXT:

8. Conclusion
   The remediation of the "Ultimate AI Research Agent" requires a fundamental shift from "fan-logic" (which looks for reasons a player will succeed) to "actuarial-logic" (which looks for structural risks that cause failure). By rigorously excluding contaminated H2H data from previous team tenures, the model eliminates false signals. By prioritizing the "Under" through Median-based projections and Blowout Decay logic, it aligns with the mathematical reality of NBA variance.
   Crucially, the differentiated treatment of fatigue—protecting Superstars from mechanical downgrades while punishing Role Players—addresses the specific nuance requested by the user, reflecting the empirical reality of Usage Insulation. This optimized architecture transforms the AI from a passive information retriever into a sophisticated, risk-adjusted decision engine capable of identifying positive EV in the prop betting market. The "losing betting slip" was a symptom of optimism bias; the corrected prompt is the cure.
   Table 2: Comparative Logic: Old vs. Corrected Prompt
   | Feature | Old Prompt (Flawed) | Corrected Prompt (Optimized) | Source Validation |
   |---|---|---|---|
   | H2H Data | Uses all historical games vs. Opponent | Strict Filter: Current Team Only | |
   | Baseline Metric | Arithmetic Mean (Average) | Median (Excluding Outliers) | |
   | B2B Logic | Universal Downgrade for all players | Differentiated: Stars (Stable) vs. Role (Fade) | |
   | Blowout Risk | Ignored | Minutes Reduced if Spread > 12.5 | |
   | Bet Bias | "Over" (Optimism/Narrative) | "Under" (Structural/Probabilistic) | |
   | Confidence | Qualitative ("High") | Quantitative (Edge % vs. Implied Prob) | |