Methodology

1 · The model

index = Σ (component_score × weight)

Normalization: the one function that matters. Each component produces a z-score, mapped linearly to 0–100 and clamped:

def z_to_score(z: float, z_cap: float = 2.0) -> float:
    """Map z ∈ [-z_cap, +z_cap] linearly onto [0, 100], clamped."""
    z = max(-z_cap, min(z_cap, z))
    return 50 + (z / z_cap) * 50

2 · Component formulas

All examples below use plausible numbers for the 2026 team (45–44, .506 as of July 4).

2.1 Momentum weight 0.25

p_L10    = wins in last 10 games / 10
p_season = season win pct
z        = (p_L10 - p_season) / SE,   where SE = sqrt(p_season × (1 - p_season) / 10)
score    = z_to_score(z)

SE is the binomial standard error of a 10-game sample, i.e., "how much should a 10-game stretch naturally wobble for a team of this quality?"

2.2 Offense Trend weight 0.10

rs_15     = mean runs scored per game, last 15 games
rs_season = mean runs scored per game, full season
sigma     = std dev of the 15-game rolling RS series this season (floor 0.40)
z         = (rs_15 - rs_season) / sigma
score     = z_to_score(z)

2.3 Run Prevention Trend weight 0.10

ra_15     = mean runs ALLOWED per game, last 15 games
ra_season = mean runs allowed per game, full season
sigma     = std dev of the 15-game rolling RA series (floor 0.40)
z         = -(ra_15 - ra_season) / sigma        # INVERTED: fewer runs allowed = greed
score     = z_to_score(z)

Sigma floor rationale for both: per-game run totals have sd ≈ 3, so a 15-game rolling mean wobbles ≈ 3/√15 ≈ 0.77 under independence; 0.40 is a conservative floor for early-season stability. (The old combined run-diff component used 0.50 because the difference of two noisy series has higher variance than either side alone.)

2.4 Playoff Pulse weight 0.25

delta = playoff_odds_today - playoff_odds_7_days_ago     # percentage points
z     = delta / 5.0                                       # 5 pts/week ≈ 1 sigma
score = z_to_score(z)

FanGraphs playoff odds already integrate schedule, roster, and opponents: the level is the best single summary of the season. The 7-day delta is the fear/greed.

2.5 Regression Watch weight 0.10 · the contrarian component

pythag_wpct = RS^1.83 / (RS^1.83 + RA^1.83)
gap         = actual_wpct - pythag_wpct
z           = -(gap / 0.030)          # NOTE THE MINUS SIGN
score       = z_to_score(z)

Overperforming your Pythagorean expectation means you're winning more than your runs justify: luck, sequencing, one-run records. That's regression risk, i.e. latent fear, so the sign is inverted. 0.030 (~5 wins over a season) ≈ 1 sigma of typical Pythag gaps.

This is the "put/call ratio" of the index: it disagrees with the mood on purpose. Keep its weight low (0.10): it's a seasoning, not a base.

2.6 Hope Premium weight 0.20

market_p = Polymarket World Series yes-price        (fraction)
model_p  = FanGraphs wsWin                          (fraction)
both clamped to [0.001, 0.99]     # FG rounds dead teams to 0.0000; market tick-floors

premium = ln( odds(market_p) / odds(model_p) )      # odds(p) = p/(1-p)
if market_p <= 0.005 and model_p <= 0.005: premium = 0   # both at the floor: tick noise
z = premium / 0.7                 # ln 2: the crowd paying 2× the model is a strong day
score = z_to_score(z)             # +-2 cap, so a 4x ratio saturates the dial

The premium is already a spread (market vs model), so the deviation principle is built in and the level is scored. The record stores ws_market and ws_model (percents) plus a deterministic summary string:

Fallback: if either source fails, reuse yesterday's value and mark "hope_premium" stale. Replaced Fan Sentiment (Reddit + LLM) 2026-07: Reddit now requires commercial licensing, and the market spread is the more honest instrument anyway: real money wagered on feelings, net of fundamentals.

3 · Full worked example: one team, one day, end to end

An example team: the 2026 Mariners, 45–44 on July 4, hold WC3, just beat the Angels 1–0 behind Bryce Miller.

Notice what the split buys: the headline 59 hides that offense reads 33 while prevention reads 70: "pitching is carrying cold bats," legible at a glance.

{ "date": "2026-07-04", "index": 59, "zone": "WATCHFUL", "delta_1d": +3, components: {...} }