The mathematically optimal formula for position sizing given your edge and the odds. Why most traders need to bet smaller than they think — and how fractional Kelly keeps you in the game.
Finding a positive expected value trade is hard. But it's not the hardest part of prediction market trading. The hardest part — the part that actually determines whether you survive — is answering this question: how much should I risk on this trade?
Get this wrong and nothing else matters. A trader with a genuine 7% edge who sizes at 50% of their bankroll per trade will go bust faster than a trader with a 3% edge who sizes at 2%. Edge is necessary. Sizing is survival.
In 1956, John Larry Kelly Jr., a physicist at Bell Labs, published a paper that solved this problem mathematically. The formula he derived — now called the Kelly Criterion — calculates the exact fraction of your bankroll you should risk to maximise long-term growth, given your edge and the payoff odds.
For prediction markets with binary contracts (pay $1 or $0), the Kelly formula simplifies to:
f* = (p - price) / (1 - price)
Where p = your estimated probability and price = the market price of the contract (in decimal, e.g. $0.55).
If you believe a contract has a 62% chance of resolving Yes, and the market price is 55¢:
f* = (0.62 - 0.55) / (1 - 0.55) = 0.07 / 0.45 = 15.6%
Full Kelly says: put 15.6% of your bankroll on this trade. With a $10,000 bankroll, that's $1,556.
That feels aggressive because it is. Full Kelly maximises long-term geometric growth — but the ride is brutally volatile. Drawdowns of 40–60% are mathematically expected even with a genuine edge. This is why no professional uses full Kelly.
The Kelly Criterion assumes three things that are never true in practice:
First, that your probability estimate is exactly right. It never is. If your "62%" is actually 57%, you're dramatically oversized. Second, that you can execute at exactly the market price. Slippage and bid-ask spreads eat into your edge. Third, that you're emotionally comfortable with the drawdowns that full Kelly produces.
The solution is fractional Kelly: multiply the full Kelly fraction by a constant less than 1. The most common choices:
| Fraction | Bankroll % | Position ($10K) | Character |
|---|---|---|---|
| ⅒ Kelly | 1.6% | $156 | Ultra-conservative. For uncertain edges or new strategies. |
| ¼ Kelly | 3.9% | $389 | The default for most professional traders. Good balance of growth and survivability. |
| ½ Kelly | 7.8% | $778 | Moderate. Acceptable when you have high confidence in your probability estimate. |
| ¾ Kelly | 11.7% | $1,167 | Aggressive. Only for well-calibrated models with long track records. |
| Full Kelly | 15.6% | $1,556 | Theoretical maximum. Almost never used in practice. |
At ¼ Kelly, you capture about 75% of the theoretical long-term growth rate while reducing variance by roughly 75%. The trade-off is massively in your favour: you give up a quarter of the upside to eliminate three-quarters of the pain.
Start with ¼ Kelly. Move to ½ Kelly only after 100+ trades that confirm your edge is real. Never use full Kelly unless you're running a simulation. If you're unsure about your probability estimate, use ⅒ Kelly — you can always size up later.
The two ways traders destroy themselves:
Oversizing. Betting 20% or 30% of your bankroll on a single binary event because "you're really confident." Even with a genuine 60/40 edge, three losses in a row (which happens 6.4% of the time) reduces your bankroll by 50%+ at 20% sizing. This is the Risk of Ruin problem — it's not a matter of if, but when.
Flat sizing. Betting the same dollar amount on every trade regardless of edge size. A 7pp edge and a 2pp edge get the same position size. This is better than oversizing but wastes capital — you're dramatically undersized on your best opportunities and oversized on your thinnest edges.
Kelly optimises for the long run. Each trade gets a position proportional to its edge. Big edge, bigger position. Small edge, tiny position. No edge, no trade. The math compounds in your favour over hundreds of trades.
Prediction markets add a specific nuance to Kelly because the payoff structure is binary: your contract resolves to $1 or $0. There's no partial win, no stop-loss, no trailing exit. You either collect $1 or lose your stake.
This makes Kelly particularly important for PMs because the variance of binary outcomes is inherently high. A diversified stock portfolio can have a bad month where it drops 5%. A single prediction market position is either worth $1 or $0 — there's no middle ground. Fractional Kelly is the tool that domesticates this variance into something manageable.
It also means pre-resolution trading changes the Kelly equation. If you plan to sell at 70¢ rather than hold to resolution, your effective payout structure is different — and your Kelly fraction should reflect the expected exit price, not the binary $1/$0 outcome.
Kelly requires an input that you never truly have: your exact probability estimate. Everything flows from this number, and if it's wrong, your sizing is wrong.
This is why serious traders focus as much on calibration as on prediction. Being "roughly right" matters more than being precisely wrong. If your model says 62% and reality is somewhere between 58% and 66%, ¼ Kelly protects you across that entire range. If your model says 62% and reality is 50%, even ¼ Kelly will slowly bleed your bankroll — because there is no edge to size for.
The Reference Pricing approach (coming in 302) helps here: by using Pinnacle's vig-removed lines as a probability benchmark, you're outsourcing the hardest part of the calibration problem to the sharpest market in sports. Your job becomes comparing two prices — Pinnacle's implied probability vs. Polymarket's contract price — rather than building a probability estimate from scratch.
We've built a live Kelly Criterion calculator that implements everything in this article. Input your probability estimate, the market price, your bankroll, and your preferred Kelly fraction — and get the mathematically optimal position size instantly.
The calculator also shows the Value Signal classification (Watch / Trade / Strong) used across the Akte Bundesliga prediction network.
Fortune's Formula by William Poundstone tells the full story of Kelly, Shannon, and Thorp — how information theory became a betting system and eventually a hedge fund strategy. It's the best book on the subject and highly readable.
For the original paper: J.L. Kelly Jr., "A New Interpretation of Information Rate," Bell System Technical Journal, 1956. Dense but short — and the core insight is in the first three pages.