Prediction Market Position Sizing and Fractional Kelly

To size a prediction-market position, compare three inputs: your estimated probability p that the contract pays $1, the executable base purchase price c per contract, and a defined bankroll. For a fully funded YES contract with no fees, the Kelly fraction of bankroll to spend is (p − c) ÷ (1 − c), which is positive only if p exceeds c.¹ That is the standalone expected-log-growth optimum under the stated assumptions, before additional exposure caps or fractional-Kelly reductions, if p were the true probability—not a safe allocation or a recommended stake when p is only an estimate. In practice, a predetermined fraction of the Kelly amount is limited by a hard cap and rounded down to whole contracts; applicable costs must be included before the final order is placed. The theoretical stake and the executable stake are different numbers, and passing on the contract is a valid outcome. Most of the practical work is deciding the fraction and the cap, and writing both down before the contract is bought.

This article covers that translation from probability, price, and bankroll into a bounded size, and what estimation error does to it. It does not cover whether your probabilities are calibrated, which prediction market probability calibration addresses, or how to measure the slippage and execution costs of your fills, which trading slippage and execution costs covers. It also does not replace stop-based sizing for trades that have an invalidation level; that is the job of position sizing in trading. And it is educational, not a recommendation to hold any contract or use any particular fraction.

How do you size a prediction-market position?

Define the bankroll this activity draws from.
Set contract-level and aggregate (per-event and total) exposure caps before you look at any contract.
Record your probability estimate p before calculating any size.
Confirm the contract pays $1 or $0 under its actual settlement terms.
Obtain a preliminary executable quote and identify the applicable entry costs; if the restricted fee case below applies, use c_eff, where c is the executable base contract price, k is the fixed, non-contingent entry fee per contract, and c_eff = c + k.
Evaluate whether an estimated positive edge remains after applicable costs, by whatever margin your rule requires.
Calculate a preliminary Kelly size under the appropriate payoff model.
Apply the predetermined fractional multiplier and risk caps.
Convert the provisional stake into whole contracts, rounding down.
Check actual order-book liquidity, total execution cost, fees, and existing aggregate exposure against all applicable limits.
Recalculate or reduce the quantity if execution terms change; reject the order if the estimated edge disappears or constraints cannot be satisfied.
Record planned size versus executed size.

An executable order must satisfy all applicable limits using actual committed capital. The fractions and caps above are illustrative rules for you to set, not recommendations. A small multiplier does not validate an unsupported probability estimate, and a positive estimated edge is not proof that a genuine advantage exists. If the estimate lacks sufficient support, not taking the position is a legitimate outcome.

Why does a binary contract change the sizing calculation?

Stop-based sizing starts from a distance: the gap between entry and the price at which the trade idea is invalidated. A contract held to resolution has no such distance. A fully funded long contract settling at zero can lose its entire committed purchase cost, including applicable non-refundable entry fees.² The fee-free examples below isolate the theoretical purchase-cost component; actual worst-case loss is fee-inclusive. So the quantity you choose is not “units at a per-unit risk” but a stake: the share of your bankroll you are willing to see go to zero if the event does not happen.

Three quantities are easy to conflate here: the contract price, the actual probability of the event, and your own probability estimate. A 40-cent price is what you pay for a claim on $1. Dividing it by $1 gives a convenient benchmark, the price-implied probability of 40%, but that is not an established 40% event probability. Wolfers and Zitzewitz show that prediction-market prices are usually close to the mean beliefs of traders, while noting that the correspondence can be biased.³ Meister’s preprint argues, in a stylized log-utility model, that prices and beliefs can differ markedly, and that treating price as probability is incorrect in general.¹ Neither shows that a particular price equals the true event probability, and your estimate p is a third, separate number.

What the price does fix is your break-even. Before fees, a contract bought at c has an expected profit per contract of p − c under your estimate, where p is your estimated probability that it pays $1 and c is the executable purchase price in dollars. Its break-even frequency is c: on average it loses money if the event happens less often than that. An estimate of 50% against a 40-cent price implies +$0.10 per contract. The same 50% against a 48-cent price implies +$0.02, a margin that costs and estimation error can erase. A positive p − c is an estimated edge, not proof that an edge exists.

What is the Kelly fraction for a prediction-market contract?

John Kelly’s 1956 paper derived a betting fraction that maximizes the long-run exponential growth rate of capital,⁴ which is equivalent to maximizing the expected logarithm of wealth. Applied to a single all-or-nothing contract with price c and your estimated probability p of a $1 payout, with borrowing prohibited, the maximizing fraction works out to:¹

YES contract:  f* = (p − c) / (1 − c)   if p > c;  otherwise f* = 0
NO contract:   the same formula, with c = the NO price you can actually pay
               and p = your estimated probability that the NO contract
               pays $1 (for a two-outcome market, one minus your YES estimate)
f* is a fraction of bankroll spent on the position, not a count of contracts.

The result holds only inside these assumptions:

The purchased contract pays $1 or $0, and 0 < c < 1.
The position is fully funded, with no leverage or borrowing.
There are no transaction fees.
No other positions are included; this is a standalone calculation.
The probability p is treated as correct inside the optimization.

If p ≤ c, the fee-free expected profit p − c is zero or negative, and the model does not justify a long position: the permitted long-side fraction is zero. A negative output is not an executable position, and whether the opposite contract qualifies is a separate calculation with its own price and probability. YES and NO prices need not sum to exactly $1 once spread and fees are included, so do not derive one price from the other. Full Kelly is the standalone expected-log-growth optimum under the stated assumptions, before additional exposure caps or fractional-Kelly reductions. It is not a universally safe allocation and not an unconditional ceiling, because it inherits every assumption, including that p is right.

The same probability edge produces very different fractions at different prices, which is worth seeing before using the formula:

Contract price	Estimate 5 points above price	Estimate 10 points above price
20¢	6.25% of bankroll	12.5%
50¢	10%	20%
80¢	25%	50%

These are arithmetic on the formula, not observations. They show that a modest-looking edge at a high price can imply staking a quarter or half of the bankroll on one outcome, which is the first sign that the raw output should not be used as an order size. Kelly sizing is the growth-maximizing answer to a specific mathematical problem. Thorp, whose chapter is a standard practitioner reference, suggests long-term compounders consider it and says investors with less tolerance for intermediate-term risk may prefer a smaller fraction.⁵

What happens when your probability estimate is wrong?

The formula’s input is the probability you believe, not the probability that is true. When the two differ, the fraction is computed from the wrong number, and the cost of overbetting is not symmetric with the cost of underbetting.

To evaluate that, separate the unknown true probability q from your estimate p. If you stake a fraction f of bankroll on a fee-free contract at price c, a win multiplies the bankroll by 1 + f × (1 − c) ÷ c, and a loss multiplies it by 1 − f. The expected change in the natural logarithm of the bankroll, evaluated at the true probability, is:

G(q, f) = q × ln(1 + f × (1 − c) / c) + (1 − q) × ln(1 − f)

Take a contract priced at 50 cents, where you estimate 60%. Full Kelly on that estimate is 20% of the bankroll. The table reports G in percent per contract for three stakes and three hypothetical true probabilities, assuming zero fees and repeated independent contracts on the same terms.

True probability	Stake 20% (full Kelly on estimate)	Stake 10% (half)	Stake 5% (quarter)
60% (estimate right)	+2.01%	+1.50%	+0.88%
55% (edge half as large)	−0.01%	+0.50%	+0.38%
50% (no edge)	−2.04%	−0.50%	−0.13%

These figures are the article’s own calculation from G. They are expected logarithmic wealth changes under hypothetical assumptions, not observed returns, guaranteed compound growth, or evidence about actual prediction-market performance. Expected log growth is also not identical to the geometric growth rate: over repeated identical bets the geometric mean growth per bet is exp(G) − 1, so a G of 2.01% corresponds to about 2.03% per bet, and any realized sequence will differ. Three things stand out. If the estimate is right, half Kelly gives up about a quarter of the growth (1.50 versus 2.01). If the true probability is 55%, a true five-point edge in this model, staking the full 20% produces essentially no growth, because 20% is twice the 10% that would have been optimal. And if there is no edge, full Kelly loses the most while quarter Kelly loses little.

Published work points the same way, but it is three different kinds of evidence, not one result. In Thorp’s continuous-time analysis, when an estimated edge is twice the true one, betting the full estimated Kelly amount gives zero growth, and overbetting is penalized more heavily than underbetting.⁵ In a separate double-or-nothing coin-flip analysis, Meister’s preprint finds that, to leading order, the growth rate falls with the square of the deviation from the optimal fraction, which is a local approximation near the optimum; it is a different model from the prediction-market pricing discussion cited above.¹ Baker and McHale argue that when a win probability is estimated rather than known, the bet should be shrunk below the raw Kelly amount; in a simulation study and an analysis of tennis betting data, their shrunken approaches improved on raw Kelly.⁶ None of this establishes a universally optimal fraction for prediction markets.

What does fractional Kelly actually buy?

Fractional Kelly stakes a fixed share of the Kelly amount. In Thorp’s continuous-time model, half Kelly gives three-quarters of the maximum growth rate, and the chance of ever losing half the starting capital falls from 1 in 2 at full Kelly to 1 in 8 at half Kelly.⁵ Those figures follow from his model’s assumptions, including a known edge; they are not guarantees or real-world probabilities for a set of binary contracts. The trade is visible in the hypothetical table above too: the growth given up is small compared with the protection against a wrong estimate.

There is a second, less mathematical cost of full Kelly. A 20% stake means a single loss costs a fifth of the bankroll. If three positions lose in sequence, each risking 20% of the bankroll as it stands after the previous loss is realized, the bankroll falls to 0.8 × 0.8 × 0.8 = 0.512, about 51% of the start. That is a sequential scenario. Three simultaneous stakes of 20% of the same initial bankroll are a different exposure: 60% of the bankroll committed at once, with 40% left if all three lose. Under independent 60% contracts, any given run of three ends in three losses 6.4% of the time. A stake that turns ordinary variance into a visible drawdown is more likely to be abandoned or abruptly resized in the middle of the sequence. Thorp reports that, in his experience, most people strongly prefer the added safety and psychological comfort of half Kelly.⁵ Robinhood’s own educational guidance for event contracts says many disciplined participants keep each position at 2% to 5% of their total buying power.² Its denominator is buying power, not this article’s separately defined bankroll, so those percentages are platform educational guidance rather than a directly comparable sizing rule or an industry standard.

Which inputs does the formula depend on that you cannot see in it?

The probability. The formula does not know whether your estimate was formed before the contract moved, whether it was adjusted after you decided how much you wanted to buy, or whether estimates in this category have been calibrated. Whether an estimate is admissible as a sizing input is a separate gate, covered in confidence calibration for position sizing. A probability estimate is not automatically validated, and a positive estimated edge is not proof that a genuine advantage exists. Shrinking an unsupported Kelly estimate does not validate it. Historical calibration is useful evidence, but the quality and independence of the underlying information also matter. If the estimate lacks sufficient support, not taking the position is a legitimate outcome.

The price and costs. Use a preliminary executable quote to estimate edge and provisional size, not the displayed midpoint. After that provisional quantity is calculated, check the actual order-book liquidity and average fill price for the whole order; available liquidity can raise the average fill price as an order takes deeper levels of the book. If execution terms change, recalculate or reduce the quantity, and reject the order if the estimated edge disappears or a limit cannot be satisfied. This is a feasibility check, not necessarily an exact globally optimal quantity when average prices or fees depend on quantity. For variable prices or non-linear fees, use the actual payoff and cost structure; if an exact solution is unavailable, use a conservative feasible quantity without claiming mathematical optimality. Every cent of entry cost lowers the estimated edge, and Meister’s derivation ignores fees and other costs.¹ The hard cap applies to total committed capital, including any entry fees, and fees that depend on order size or are rounded at the order level can change the actual cash cost after the contract count is set, so recheck the final order.

In one restricted case the fee can be folded into the price. If a known, non-contingent fee k is charged per contract at entry and a winning contract still pays exactly $1, the cash committed per contract is c_eff = c + k, and when 0 < c_eff < 1 the same formula applies with c_eff in place of c. This substitution is not general. If fees depend on order quantity, are rounded at order level, apply at settlement, or otherwise change the outcome-contingent payout, model the actual net win and loss amounts instead. This article assumes no particular fee level for any platform.

Settlement terms. The $1/$0 binary sizing model applies only when the contract’s actual payoff and settlement terms match those assumptions. Cancellation, voiding, alternative settlement, or materially different payout rules mean the payoff model has to be reconsidered before any fraction is applied.

Sensitivity to probability error. For f* = (p − c) / (1 − c), where the fraction is positive, the change in the theoretical Kelly fraction per unit change in your estimate is df*/dp = 1 / (1 − c). That sensitivity rises with price. At 20 cents, a five-point error in p moves the theoretical fraction by 6.25 points; at 80 cents, the same error moves it by 25 points, which the price table above already shows. This is a property of the formula. Empirical favorite-longshot bias is a separate question about pricing and realized outcomes, namely whether low-priced contracts have earned lower average returns than their prices implied, and the answer depends on how results are averaged. The formula does not say longshots carry the largest sensitivity, and the bias literature does not make any price region safe to size aggressively.

Independence and correlation. The standalone expected-log optimization for one binary contract does not require independence from unrelated future wagers. Repeated independent, identically distributed betting is a simplifying assumption used in particular long-run analyses, including the table above. The problem appears when you hold several contracts at once. Contracts exposed to the same event, factor, or thesis may create correlated losses even when individually compliant with position limits; they do not necessarily have identical payoffs or perfect correlation. Check cumulative exposure against aggregate limits. Gross committed capital remains distinct from scenario-specific portfolio loss: it is a conservative exposure proxy, not always the exact worst-case loss, because opposing positions can offset. Do not treat two superficially opposite contracts as a perfect hedge without checking their exact settlement terms. The practical takeaway is to define aggregate exposure limits before independently sized positions accumulate.

The bankroll. The fraction applies to a defined pool of capital. Decide what counts as the bankroll and when its value is refreshed, in advance, rather than letting it drift toward whatever balance feels available.

How a written rule looks in practice

Suppose a trader sets a $5,000 prediction-market bankroll, a cap of 5% on this contract position ($250), and a rule of one quarter of the Kelly fraction, all written before the session. A contract is priced at 40 cents, executable, and the trader’s estimate is 50%, which clears the preset margin over price. This example assumes zero transaction fees and sufficient liquidity at $0.40 for the whole order.

Full Kelly         = (0.50 − 0.40) / (1 − 0.40)  = 16.6667% of bankroll
Quarter Kelly      = 16.6667% × 0.25             =  4.1667% of bankroll
Theoretical stake  = $5,000 × 4.1667%            = $208.33
Cap check          = 5% cap = $250               → cap does not bind
Whole contracts    = floor($208.33 / $0.40)      = 520  (520.83 rounded down)
Executable stake   = 520 × $0.40                 = $208.00 (4.16% of bankroll)
If YES: pays 520 × $1 = $520.00    Gross winning profit = +$312.00
If NO:                             Gross losing outcome = −$208.00

The theoretical stake ($208.33) and the executable stake ($208.00) differ because contracts come in whole units. The count is rounded down so the order never exceeds the sized amount or a binding cap; 521 contracts would cost $208.40.

Now suppose the same contract carried a hypothetical non-contingent entry fee of $0.02 per contract, with a winning contract still paying $1. This is an illustration of the restricted case above, not any platform’s fee schedule. Then c_eff = $0.42, and full Kelly is (0.50 − 0.42) ÷ (1 − 0.42) = 13.793103% of bankroll, displayed as 13.79%. All intermediate calculations use unrounded Kelly fractions; displayed percentages are rounded. Quarter Kelly is 3.45%, a theoretical stake of $172.41 including fees, which buys floor($172.41 ÷ $0.42) = 410 contracts for $172.20 (3.44% of bankroll). A win pays $410.00 for a profit of $237.80, a loss costs $172.20, and the $250 cap still does not bind. The fee lowered the estimated edge from ten points to eight and cut the executable stake from $208.00 to $172.20, and every figure in this variation uses the fee-inclusive price.

The numbers are illustrative, not a suggested fraction. The point is that every quantity in the decision was fixed by the rule and the inputs, so afterward it is possible to check whether the stake followed the rule. If the trader wanted 800 contracts ($320) because the setup felt strong, that wish has no place in the arithmetic, and it would exceed the cap. It would show up as a deviation from the rule, which is exactly what a review should catch.

Common ways prediction-market sizing goes wrong

Sizing off conviction. Feeling sure is not the same as a probability that has a track record, and the formula will faithfully turn an inflated estimate into an inflated stake.

Working backward from the size you want. Nudging the probability estimate up until the formula returns the stake you already had in mind turns the calculation into a justification.

Using full Kelly on an unsupported estimate. The table above shows how a true edge in the model can still produce no growth when the stake is twice what the true probability supports.

Treating a small multiplier as validation. Quarter Kelly on an unsupported estimate is a smaller bet on an unsupported number, not evidence of an edge. If the estimate lacks sufficient support, not taking the position is a legitimate outcome.

Sizing the same thesis several times. Contracts exposed to the same event, factor, or thesis may create correlated losses even when individually compliant with position limits. They do not necessarily have identical payoffs or perfect correlation, so check cumulative exposure against aggregate limits while keeping gross committed capital distinct from scenario-specific portfolio loss. The correlated event exposure article covers how to group contracts by shared driver and measure that scenario loss.

Growing the stake after a run of wins. Resizing because recent results were good, rather than because the rule and the bankroll changed, is a form of size drift that a scheduled review should look for.

Treating the formula as advice. It computes a fraction from assumptions you supply. It does not tell you whether the contract is worth holding.

Turn the rule into a reviewable decision

Field	Record before the contract is bought
Bankroll and its valuation date	The pool and its size when the rule was applied
Contract, side, executable price, and fees	The fill price and entry costs actually used, not the display
Probability estimate and how it was formed	Written before checking the fraction
Margin over price required by the rule	The threshold the estimate had to clear
Kelly fraction and chosen multiple	The calculation and the fraction of it allowed
Hard cap and event-level total	The limit the calculated stake had to stay under
Planned size and executed size	Contracts and cost for each, and the reason for any gap

At a scheduled review, look at whether stakes matched the rule, whether the estimate was recorded before the size was chosen, whether the same event was sized more than once, and whether the amounts drifted upward after a winning stretch. Those are process questions. They say nothing about whether any single contract was a good idea.

Where Costante fits

Costante’s relevance here is limited. Its core workflow is built for discretionary intraday traders: planning rules before a session, making self-defined guardrails visible, running pre-trade and in-session checks against the plan, logging decisions with low friction, and reviewing repeated drift afterward. The connection to this article is conceptual. A trader who has written a sizing rule like the one above before acting has something concrete to compare planned size with executed size, so repeated deviations from the written size can be reviewed instead of relying on memory.

Costante does not calculate Kelly fractions, choose or recommend a fraction, validate event probabilities, detect pricing edges, connect to prediction-market platforms, exchanges, or brokers, execute or block contracts or orders, enforce a stake cap, or provide a dedicated prediction-market portfolio system. The bankroll, the fraction, the cap, and every order remain the trader’s own.

Frequently asked questions

What is the Kelly criterion formula for a prediction market?

For a fully funded YES contract at executable price c (0 < c < 1) that pays $1 if the event occurs, and a probability estimate of p, the fee-free Kelly fraction of bankroll is (p − c) ÷ (1 − c). If p ≤ c, the fraction is zero. For a NO contract, use the NO price and your estimated probability that the NO contract pays $1. The result is a log-growth-maximizing fraction under the assumption that your probability is correct, and it ignores fees.

Is full Kelly safe for prediction markets?

It is designed to maximize long-run growth, not to minimize loss, and it depends on the probability being right. In Thorp’s continuous-time model, overbetting is penalized more heavily than underbetting, and a stake based on an edge estimate twice the true edge produces no growth. Full Kelly can also mean single-outcome stakes of 20% or more of the bankroll.

What fraction of Kelly should I use?

There is no fraction that is correct for everyone. In Thorp’s continuous model, half Kelly retains about three-quarters of the growth rate while cutting the modeled chance of a deep loss, and Baker and McHale support shrinking bets when the win probability is estimated. Neither research result identifies a single best fraction for prediction markets. Choose the fraction and a hard cap in advance, based on how uncertain your estimates are and how large a drawdown you can follow your rule through.

How is this different from sizing a trade with a stop-loss?

A stop-based trade has an invalidation price, so size follows the distance to it. A contract held to resolution has no such distance: you can lose the full stake, so size is chosen as a share of the bankroll. The two use different inputs, which is why the position sizing in trading method does not carry over directly.

Sources

Costante provides educational workflow tools, not financial advice. Trading involves risk.

Meister, B. K. (2024). Application of the Kelly Criterion to Prediction Markets. arXiv:2412.14144, v1 submitted 18 December 2024. Preprint; the arXiv record does not mark it as peer reviewed. It writes the market price as p and the trader’s belief as q (this article uses c and p), assumes log utility, and explicitly ignores fees, other costs, and mirror markets. Its double-or-nothing sensitivity analysis is a separate model from its prediction-market pricing discussion. ↩ ↩² ↩³ ↩⁴ ↩⁵
Robinhood Learn (updated March 20, 2026). Managing Risk in Event Contracts: Position Sizing, Edge & Psychology. Platform educational material from a platform that offers event contracts; it describes common practice as a share of total buying power and is not an independently validated standard. ↩ ↩²
Wolfers, J., & Zitzewitz, E. (2006). Interpreting Prediction Market Prices as Probabilities. NBER Working Paper 12200. Working paper, not a journal article. It concerns how prices relate to traders’ mean beliefs, not whether a price equals the true event probability. ↩
Kelly, J. L., Jr. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926. Peer-reviewed journal article. ↩
Thorp, E. O. (2006). The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market. In Handbook of Asset and Liability Management, Volume 1, Chapter 9, Elsevier. See section 7.3, “The case for fractional Kelly.” The half-Kelly growth and drawdown figures come from the continuous-time model in that chapter and depend on its assumptions. ↩ ↩² ↩³ ↩⁴
Baker, R. D., & McHale, I. G. (2013). Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion. Decision Analysis, 10(3), 189–199. Peer-reviewed journal article; results come from a simulation study and tennis betting data. ↩