Auditable

Methodology

Every +EV pick Parlae fires can be reproduced by hand from the line set we saw at the moment of capture. This page is the formal write-up: the math, the four de-vig methods (with worked examples), how we weight Pinnacle and Circa as anchors, how conviction is scored, and how hit-rate is sourced from real settled box scores — never padded, never modeled.

1. Implied probability

For any American price a we use the standard conversion:

d = 1 + (a > 0 ? a / 100 : 100 / |a|)
q = 1 / d        // raw implied probability (still vigged)

The raw probabilities q_i for every selection in a market sum to more than 1 — the excess is the book's overround (vig). De-vig removes it.

2. Multiplicative de-vig

The simplest method — divide each q_i by the overround.

p_i = q_i / Σ q_j
Worked example — 2-way market
DK price A-110 → q = 0.5238
DK price B-110 → q = 0.5238
Σ q1.0476 (4.76% vig)
p_A (mult)0.5238 / 1.0476 = 0.5000
Fair odds+100

3. Power (Stern) de-vig

Solve for an exponent r ≥ 1 such that Σ (q_i)^r = 1. Bisect on r in [1, 8] — the sum is strictly decreasing in r, so it converges. Power is our default for 2-way and 3-way side markets because it preserves the relative price between favorites and dogs better than mult on high-vig books.

Σ (q_i)^r = 1   ⇒   p_i = (q_i)^r
Worked example — favorite/dog 2-way
q_A0.60 (≈ -150)
q_B0.45 (≈ +122)
Σ q1.05 (5% vig)
Solve0.60^r + 0.45^r = 1 → r ≈ 1.123
p_A (power)0.60^1.123 ≈ 0.566
p_B (power)0.45^1.123 ≈ 0.434

4. Sharp-consensus blend

For every selection we average de-vigged probabilities from sharp / low-margin books (Pinnacle, Circa, Novig, Betfair Exchange) — these books are price-discovering, not promotional. We then blend that sharp consensus with the market-wide power-devig according to anchor weight.

p_fair = w · p_anchor + (1 - w) · p_market

where w ∈ [0, 0.6] grows with:
  • # of anchor books available for the selection
  • freshness of the anchor quote
  • inverse spread (tighter anchor → higher weight)
Worked example — anchor weighting
Pinnacle p0.542
Novig p0.546
p_anchor (avg)0.544
p_market (power)0.531
w (2 anchors, fresh, 4¢)0.45
p_fair = 0.45·0.544 + 0.55·0.5310.537

5. Conservative (worst-case)

For every selection we compute the fair probability under multiplicative, power, and (for 2-way) Shin, then take the minimum. This is the de-vig method that gives the smallest edge — the one we report when we want zero benefit-of-the-doubt.

p_worst = min(p_mult, p_power, p_shin)

A pick that still shows +EV under conservative is the most defensible. The drawer's de-vig toggle lets you flip between methods live; the delta between Power and Conservative is your edge-robustness check.

6. EV% and Kelly

EV% = (p_fair · d_offer - 1) · 100
kelly = (p · d - 1) / (d - 1)         // fraction of bankroll
We display 0.25 × kelly by default — a quarter-Kelly stake.

7. Conviction (0-100)

Conviction is a single 0-100 score per pick. It combines:

  • EV% magnitude (most of the weight)
  • Market width in cents (tighter → more)
  • Books contributing (more independent prices → more)
  • Anchor inclusion (Pinnacle/Circa in the set → more)
  • Movement-toward score — line drifting toward our side

Tiers: S ≥ 80, A ≥ 65, B ≥ 50, C < 50. Thin markets (< 3 books and no sharp anchor) are forced to Lean and capped at conviction 40.

8. Hit-rate (recent form)

The 10-game hit-rate strip and the drawer's "Recent form" bars are sourced from real settled box scores — not modeled, not padded. For each player we read the last N official games for the matching stat type, compute over/under the offered line, and require N ≥ 3 to render. Fewer than 3 → we say so explicitly ("Not enough settled games (n=X)") instead of inventing a number.

9. CLV — closing-line value

Every fire is captured at fire time with the exact price, line, book, fair odds, and timestamp. At kickoff we re-read the market and record a median closing fair price (requires ≥ 2 books at close). CLV is the move from fire to close in percentage points of implied probability. We never re-price after the fact.

CLV_pp = (p_close - p_fire) · 100         // in probability points

On the track record we lead with average CLV and sample size, not a binary win-rate. We mark samples as "accruing" until N ≥ 200 — that's where confidence intervals on CLV tighten meaningfully.

10. Reproduce any edge by hand

The no-vig calculator and the no-vig fair-odds tool let you paste any two-way or three-way set and reproduce our power / multiplicative numbers exactly. If a Parlae fair price is ever off by more than 0.5pp from what those tools say for the same input, that's a bug — file it and we'll fix it publicly.

See +EV →