Position Sizing Diagnostics on Polymarket

Convexly's wallet analyzer computes three sizing diagnostics per Polymarket wallet: average actual fraction, average Kelly fraction (using in-sample category win rate as p_true proxy), and over-sizing risk vs fractional Kelly, the ratio of actual stake to Kelly-optimal. It also returns a concentration risk score, the share of realized PnL attributable to the wallet's single largest event. Under Hill alpha = 1.28 on Polymarket PnL, full Kelly is unsafe and Kelly itself is a Mediocristan reference that fails on fat tails; the defensible frame is Taleb's barbell (Antifragile Ch. 11) with fractional Kelly as a secondary constraint inside the speculative leg.

The three diagnostics

• Actual fraction: mean stake as a share of bankroll per bet. Computed from the wallet's realized dollar exposure per position.
• Kelly fraction: the Kelly-optimal stake given the wallet's own in-sample category win rate as proxy for p_true. This is a descriptive diagnostic, not a recommendation. In- sample win rate is upwardly biased by selection.
• Over-sizing risk vs fractional Kelly: actual divided by Kelly-optimal. A ratio of 1.0 means the trader matched full Kelly. Below 1.0 means under-sized relative to Kelly, which is often correct under fat tails. Above 1.0 means over-sized relative to even full Kelly, which is aggressive. Kelly itself is the Mediocristan upper bound; the Taleb-defensible anchor is quarter-Kelly inside a barbell.

Concentration risk score

Concentration is the share of realized PnL attributable to a wallet's single largest event, on a 0 to 100 scale. On Convexly's 8,656-wallet reference cohort:

• Median concentration: 51
• 25th percentile (less concentrated): 27
• 75th percentile (more concentrated): 86
• Wallets with concentration above 80 have most of their PnL riding on one event outcome

A high Edge Score driven by the conviction pillar is often structurally not copy-tradeable. A wallet with concentration 86 and a big single win had the right stake on the right event at the right time; copy-trading that wallet going forward replicates the concentration but not the timing judgement.

Why full Kelly is unsafe on Polymarket

The Kelly criterion maximizes long-run logarithmic growth under known p_true, known b (net odds), and no path-dependence. On Polymarket:

• p_true is never known. The trader's subjective estimate has error; Kelly assumes zero error.
• The PnL distribution is fat-tailed: Hill alpha = 1.28 with CI 1.20 to 1.36 on the 8,656-wallet cohort. The variance of single-event returns is formally infinite.
• Full Kelly is provably ruin-optimal if p_true is wrong. Half-Kelly halves the expected growth rate in return for ~2x drawdown reduction; quarter-Kelly is even safer.
• Correlated simultaneous positions (e.g., multiple Ethereum price-range bets in the same event) compound drawdown risk beyond what single-position Kelly captures.

The defensible heuristic: half-Kelly or quarter-Kelly as the size ceiling, with a hard cap at 5-10% of bankroll per single event regardless of what Kelly recommends.

How the composite uses sizing

Edge Score V3b does not use total dollars risked or any capital proxy. Sizing enters the composite only through the conviction pillar (concentration) and the discipline pillar (position count). The composite is explicitly sizing-independent at the bankroll level; wallets are compared on pattern, not on how much capital they deployed. This was a deliberate design choice: an earlier variant V3 that included log(total_risked) was rejected because its composite correlated +0.30 with total dollars risked, meaning the model was partly measuring wallet size rather than wallet behaviour.

Tool

Paste any Polymarket wallet at convexly.app/tools/polymarket-wallet-analyzer to get the full diagnostic: actual fraction, Kelly fraction, over-sizing risk vs fractional Kelly, concentration risk score, plus Edge Score percentile + pillar breakdown. Free, no signup, no private key.