Kelly Criterion Calculator — Optimal Bet Size for Sports Betting

The Kelly Criterion calculates the mathematically optimal bet size: f* = (bp − q) / b, where b is decimal odds minus 1, p is your true probability, and q is 1 − p. Full Kelly maximizes long-run growth but produces wild bankroll swings, so for sports betting fractional Kelly — Quarter Kelly is the standard recommendation — reduces variance dramatically while preserving most of the geometric growth. Use the calculator below to see Full, Half, and Quarter Kelly stakes for any bet, instantly.

Quick Answer

A Kelly criterion calculator estimates bet size from bankroll, odds, and perceived edge. It is most useful as a sizing guide, not a command. PropsBot users can pair Kelly math with EV checks, odds shopping, and bet tracking to keep stake decisions disciplined.

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What is the Kelly Criterion?

The Kelly Criterion is a bet-sizing formula that maximizes the expected logarithm of bankroll — equivalent to maximizing long-run geometric growth. Investopedia describes Kelly as “a mathematical formula relating to the long-term growth of capital developed by John L. Kelly Jr.” It was introduced in John L. Kelly Jr.’s 1956 Bell Labs paper “A New Interpretation of Information Rate” (Bell System Technical Journal, vol. 35, no. 4) — originally about transmitting information over noisy telephone lines, but quickly adopted by Edward Thorp at the blackjack tables and later by hedge funds, sharp bettors, and Warren Buffett’s right hand Charlie Munger as a position-sizing rule.

The intuition: bet too little and you leave growth on the table; bet too much and a single bad streak wipes you out. Kelly finds the unique bet size that maximizes geometric bankroll growth — not arithmetic — because compounding losses hurt more than compounding gains help. A 50% drawdown requires a 100% return to break even, which is why bet sizing matters more than win rate for long-run survival. Pinnacle’s Kelly Criterion explainer lays out the same growth-maximization argument with worked examples.

How to calculate Kelly stake

The Kelly fraction is the share of your bankroll to stake on a single bet:

• f* = (b × p − q) / b
• b = decimal odds − 1 (the net profit per $1 staked when you win)
• p = your true probability that the bet wins (decimal, 0–1)
• q = 1 − p (probability the bet loses)
• stake = bankroll × f* (zero if f* ≤ 0 — Kelly says don’t bet)

Worked example: $1,000 bankroll, +150 odds, 50% true probability

decimal odds = 1 + (150 / 100) = 2.5; b = 2.5 − 1 = 1.5
p = 0.50, q = 0.50
f* = (1.5 × 0.50 − 0.50) / 1.5 = 0.25 / 1.5 = 0.1667 (16.67%)
Full Kelly stake = $1,000 × 0.1667 = $166.67
Half Kelly = $83.33; Quarter Kelly = $41.67
Edge = 50% − 40% (book implied at +150) = +10 percentage points

Why fractional Kelly is recommended for sports betting

Full Kelly is mathematically optimal only if your true probability estimate is exactly correct. In sports betting, your p is always uncertain — it comes from a model, an AI projection, or your read of the matchup. A small estimation error compounds quickly at Full Kelly: overestimate your edge by 20% and Full Kelly bets you significantly more than optimal, with a much higher risk of ruin. Pinnacle’s research and the academic literature on Kelly agree that fractional Kelly is the right answer when probability inputs are noisy — which is always the case in sports.

The growth-vs-variance tradeoff is well documented: Half Kelly captures roughly 75% of the geometric growth of Full Kelly with about half the variance. Quarter Kelly captures roughly 44% of Full Kelly growth with one-quarter of the variance — meaning a sharply smoother bankroll curve. Sharp sports bettors and the team at Action Network’s bankroll-management primer typically size at Quarter Kelly or even smaller because real-world models are wrong often enough that the variance reduction is worth more than the lost growth.

Three practical reasons Quarter Kelly is the sports-betting default:

Model uncertainty — your true probability is an estimate, not a known value. Quarter Kelly hedges against overestimating edge.
Variance is brutal — even a +5% EV bettor regularly sees 20–40% drawdowns at Full Kelly. Quarter Kelly keeps drawdowns survivable.
Psychological staying power — most bettors quit during a drawdown, not because the math failed. Smaller bets keep you in the game.

Kelly examples

Notice the −110 / 50% row: even though 50% sounds like a coin-flip, the book’s vig at -110 implies 52.38%, so your true probability is actually below the implied price. Kelly correctly says skip — there’s no edge.

How we tested this calculator

The PropsBot team validated every formula in this calculator against four canonical test cases on May 1, 2026 and cross-checked the math against Kelly’s original 1956 paper, Pinnacle’s published examples, and the standard Kelly-fraction derivation. Test results:

• $1,000 bankroll, +150, 50% → f* = 16.67%, Full = $166.67, Half = $83.33, Quarter = $41.67, Edge = +10.00 pp (matches expected)
• $500 bankroll, -200, 70% → f* = 10.00%, Full = $50.00, Quarter = $12.50, Edge = +3.33 pp (matches expected)
• $1,000 bankroll, -110, 50% → f* = −5.00% (no edge, skip), Edge = −2.38 pp (matches expected)
• $2,000 bankroll, +200, 40% → f* = 10.00%, Full = $200.00, Quarter = $50.00, Edge = +6.67 pp (matches expected)

The math underlying the calculator follows the formal Kelly derivation in John L. Kelly Jr., “A New Interpretation of Information Rate,” Bell System Technical Journal, vol. 35, no. 4 (1956), pp. 917–926, as summarized by Investopedia’s Kelly Criterion entry and Pinnacle’s Kelly explainer. Validation rules (rejecting odds in the −99 to +99 range, true probability outside 0–100, and bankroll ≤ 0) match the input-sanitization conventions in the related PropsBot EV and No-Vig calculators. Bankroll-management guidance follows Action Network’s bankroll primer, and responsible-gambling guidance follows the American Gaming Association responsible-gaming framework.

Kelly Criterion FAQs

What is a “unit” in sports betting?

A unit is a bettor’s standard bet size, expressed as a percentage of bankroll rather than a fixed dollar amount. Most sports bettors define one unit as 1–2% of bankroll — close to a typical Quarter Kelly stake on a moderately +EV bet. Sizing in units (instead of dollars) keeps your bet sizing consistent as your bankroll grows or shrinks. A bettor with a $5,000 bankroll using 1% units bets $50/unit; if the bankroll grows to $7,500, units automatically scale to $75. Action Network’s bankroll guide describes the same unit-based approach.

Should I use Full Kelly?

Almost never for sports betting. Full Kelly is mathematically optimal only when your true probability estimate is exactly right — which is essentially never the case in sports, where projections are noisy. Full Kelly produces violent bankroll swings (40%+ drawdowns are normal even for positive bettors) and turns small estimation errors into existential risks. The vast majority of sharp bettors size at Half Kelly or smaller, with Quarter Kelly being the most common default. Pinnacle’s Kelly article and academic Kelly literature both reach the same conclusion.

What if my true probability estimate is wrong?

This is the core reason fractional Kelly exists. If you overestimate your edge by even 20–30% — common for amateur bettors — Full Kelly bets you well above the actual optimum and dramatically increases risk of ruin. Quarter Kelly is robust to this error: even if your probability estimate is meaningfully off, you stay below the optimal bet size and the worst case is slightly suboptimal growth instead of catastrophic loss. Tracking your closing line value (CLV) and EV across hundreds of bets is the only reliable way to know if your probability estimates are actually accurate.

Can Kelly be negative?

Yes — and when it is, Kelly says don’t bet. A negative Kelly fraction means your true probability is below the book’s implied probability, so the bet has negative expected value. The calculator clamps negative f* to zero and shows a “Skip — no edge” verdict. Kelly is only a sizing formula for positive-EV bets; for −EV bets, the optimal stake is always zero. This is one of Kelly’s most useful properties: it auto-filters out bets you shouldn’t take.

How does Kelly compare to flat betting?

Flat betting stakes the same dollar amount on every wager regardless of edge or odds. Kelly scales the stake up when your edge is bigger and down when it’s smaller, capturing more growth from your best bets. Over thousands of wagers, fractional Kelly meaningfully outperforms flat betting on geometric growth — but it requires accurate probability estimates. Many sharp bettors blend the two: they cap any single bet at a maximum unit size (e.g. 2–3% of bankroll) to avoid over-concentration, then use Quarter Kelly within that cap. This hybrid approach gives most of Kelly’s growth advantage with a hard ceiling on single-bet variance.

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