kelly-js

The sports bettor's math toolkit. Kelly Criterion, CLV, EV, bankroll stats, odds conversion — TypeScript, zero dependencies, tree-shakeable.

import { kelly, clv, bankrollStats } from '@ianalloway/kelly-js';

const k = kelly(0.58, -110);
console.log(k.fraction);         // 0.0714
console.log(k.halfDollars(1000)) // $35.71

const c = clv(-108, -115);
console.log(c.verdict);          // 'positive'

const stats = bankrollStats(myBets, 1000);
console.log(stats.roi);
console.log(stats.maxDrawdown);

Install

npm registry publish pending (needs granular token with Bypass 2FA). Until then:

npm install github:ianalloway/kelly-js
# or
pnpm add github:ianalloway/kelly-js

API highlights

Kelly Criterion

kelly(winProbability, americanOdds)

Returns Kelly sizing, half/quarter Kelly, dollar sizing, expected value, and edge.

kellyParlay(legs)

Sizes a multi-leg parlay as one combined bet — multiplies leg probabilities and odds together, then runs the same Kelly formula against the result.

kellyParlay([
  { probability: 0.55, americanOdds: -110 },
  { probability: 0.60, americanOdds: -120 },
]);
// { fraction: ..., combinedOdds: ..., combinedDecimal: ..., trueWinProb: 0.33, ... }

Odds conversion

impliedProb(american)
toDecimal(american)
toAmerican(decimal)
convertOdds(american)
removeVig(side1, side2)

Expected value

expectedValue(winProbability, americanOdds, stake?)

Closing Line Value

clv(openLine, closeLine)
clvSummary(bets)

Bankroll tracking

betPnL(stake, americanOdds, result)
bankrollStats(bets, startingBankroll?)

Monte Carlo growth simulation

simulateGrowth(winProbability, americanOdds, betsPerPath?, paths?, startingBankroll?, kellyMultiplier?, seed?)

Simulates many independent bankroll paths, each placing sequential fractional-Kelly bets, and reports the distribution of outcomes — because a positive edge tells you nothing about variance.

const sim = simulateGrowth(0.55, -110, 500, 2000, 1000, 0.5, 42);

sim.medianFinal       // 1675.81 — median final bankroll across 2000 paths
sim.p10               // 802.69  — 10% of paths ended at or below this
sim.p90               // 3498.68 — 10% of paths ended at or above this
sim.ruinRate          // 0       — fraction of paths that dropped below 10% of start
sim.medianMaxDrawdown // 0.3891  — median worst peak-to-trough drawdown (39%)

Reading the percentiles: p10/p90 bracket the realistic range of outcomes. In the example above, a genuine 55% edge at -110 with half-Kelly sizing still loses money in over 10% of 500-bet runs and a typical run suffers a ~39% drawdown — useful context before sizing up. Pass an integer seed for reproducible results (seeded mulberry32 PRNG); omit it for a random run.

Line shopping

lineShop(books)

Ranks American odds across sportsbooks for one side of a bet and quantifies how much implied probability you save by taking the best line instead of the worst.

lineShop([
  { book: 'DraftKings', odds: -112 },
  { book: 'FanDuel',    odds: -108 },
  { book: 'BetMGM',     odds: -115 },
]);
// {
//   bestBook: 'FanDuel',
//   bestOdds: -108,
//   impliedProbAtBest: 0.5192,
//   shoppingEdgePct: 1.57,   // percentage points of implied prob saved vs. worst book
//   ranked: [...]            // all books sorted best-to-worst for the bettor
// }

A 1.57-point shopping edge is often the difference between a losing and a break-even bettor — line shopping is the cheapest edge available.

Advanced / extras

These cover more specialized use cases (portfolio sizing, arbitrage/dutching, DFS, and a Poisson totals model). All are exported from the same package — nothing here needs a separate install.

kellyPortfolio(bets, maxExposure?)      // size several simultaneous Kelly bets under one exposure cap
optimalFractionalKelly(edge, variance, maxDrawdown, riskOfDrawdown?)
kellyGrowthRate(winProbability, americanOdds, fraction) // compare growth rate at any staking fraction
parlayAnalysis(legs)                    // true EV/win prob for a multi-leg parlay
arbitrage(oddsA, oddsB, totalStake?)    // guaranteed-profit stake split across two books
dutching(outcomes, totalStake?)         // guaranteed-profit stake split across 3+ outcomes
marketConsensus(books)                  // de-vig and average odds across books
poissonModel(lambda1, lambda2, maxGoals?) // win/draw/loss + totals model for scoring sports
ownershipLeverage(projectedPoints, ownershipPct) // DFS contrarian-play score
stackBonus(qbProj, receiverProj, correlation?)   // DFS game-stack correlation bonus

Why this repo matters

This is a compact, reusable package that turns betting math into something easy to import and test. It’s a better signal than a giant monorepo because the scope is clean and the API is obvious.

Math notes

• Kelly formula: f* = (bp - q) / b
• CLV is the gap between your line and the close
• Full Kelly is optimal in theory; half Kelly is usually the practical default

Testing

npm run lint       # Type-check source and tests
npm test           # Run Jest tests
npm run test:dist  # Rebuild dist/ and verify published exports

Author

Ian Alloway

License

MIT