Binary Events: Does Liquidity Trade The Tails?

In our v1 analysis we looked at what it costs to split a single question into multiple binary contracts on Polymarket. The dataset was the full census of multi-market events — 18,863 events containing 172,869 binary contracts across 6 categories. Two pathologies came out cleanly. Volume concentrates in the top 5 markets per event regardless of how many markets the event contains. Ghost market rate (we defined as <$1k lifetime volume) scales with N (number of markets) — 36% of markets dead at N=11–20, 72% at N=51+.

That cut was multi-market vs single-market — what does splitting cost compared to running the question as one market? But v1 treated all multi-market events the same. "Who wins the NBA championship?" and "What price will BTC close at this month?" sat in the same dataset. One is a list of named teams — a genuinely unordered set. The other is a continuous quantity bucketed into arbitrary price ranges. The concentration findings held across both, but the argument that a continuous-distribution primitive could fix these problems only applies to the second type.

The question for v2 was simple — when we separate events that discretise a continuous quantity (price ranges, margin-of-victory percentages, temperature brackets) from events that list named entities (election candidates, sports teams, award nominees), do the pathology findings survive?

The answer turned out to be more interesting than "yes" or "no". Some findings held across both types. One finding — the ghost market scaling — turned out to be largely a categorical phenomenon, obvious in hindsight but enlightening nevertheless.

We built a heuristic classifier that labels each of the 18,863 multi-market events based on the structure of its sibling market questions. The method extracts the varying fragment across siblings (strip the common prefix and suffix from each question title), then tags each fragment as numeric or categorical using pattern-matching signals.

Categorical dominates by volume because of a handful of very large events — the 2024 Presidential Election ($3.7B), NBA Champion ($1.7B), Super Bowl ($1.2B). The continuous slice is $6.7B across 7,751 events, driven by crypto price thresholds, weather brackets, political margin-of-victory questions, and date timing events.

The 42 discrete numeric events are all central bank rate decisions ($2.8B). We excluded these from the continuous headline because the Fed only chooses between a small fixed set of basis-point moves. A continuous-distribution primitive does not add resolution where the outcome set is not continuous in the first place. We explored expanding this exclusion to other institutions (tariff rates, turnout, vote counts, medal counts) and found none of the other candidates are genuinely policy-bounded the way Fed events are. The full decision rules, keyword lists, and QA spot checks are documented in the sprint notes.

The classifier is an experimental model. The point is transparency — the reader can check our working and argue with any specific decision.

By event count, continuous has been growing fast. In 2026Q1 continuous events overtook categorical for the first time — 3,012 new continuous events vs 1,192 categorical. By volume, categorical still dominates historically because of election-cycle spikes ($5.3B in 2025Q3 alone). But continuous volume has been growing steadily — from $452M in 2025Q1 to $1.7B in 2025Q4 — driven by crypto and weather events that don't spike with political cycles.

Crypto is 95% continuous. Weather is 99%. These are almost entirely events that discretise a continuous quantity into binary buckets — BTC price brackets, temperature ranges, precipitation thresholds. Sports is the opposite — 99% categorical (team winners). Politics is the battleground: $3.8B continuous (margins, timing, seat counts) alongside $12.6B categorical (election winners).

The growth trend matters because it means the discretisation cost analysis applies to a growing share of the platform. As Polymarket expands beyond high-attention election markets into crypto, weather, and finance, a larger fraction of its events are the type where continuous-distribution primitives would be the natural fit.

For each event we ranked markets by volume and computed the cumulative share at each rank. The question is the same one from v1: how many of the N markets do you need to account for most of the trading?

Both curves are steep and flatten before rank 10. The median continuous event reaches 90% of total volume by rank 6. Categorical gets there by rank 5.

Concentration in the top handful of markets is a property of the multi-market binary architecture. It holds on both labels with similar magnitude. Categorical is slightly more concentrated because in an election or championship the favourite naturally dominates. In a price-bracket event the "at-the-money" bucket is hot but doesn't swallow 43% of volume because adjacent brackets also carry meaningful probability.

The small gap between the labels is worth noting. Continuous events spread volume slightly more evenly across their top buckets, which means there is real multi-bucket trading activity. Traders are engaging with 5–6 buckets, not just one. A continuous distribution would capture that existing demand on a single shared instrument instead of splitting it across 5–6 separate order books.

Continuous events distribute better at higher N. The cumulative curve shows median behaviour across all N values. This chart tests whether adding more markets helps spread volume more evenly. We plotted top-3 concentration against N for every event, with a red reference line showing where uniform allocation (3/N) would sit.

A ghost market is a market within a multi-market event with less than $1K in lifetime volume. v1 found ghost rates of 36% at N=11–20, 60% at N=21–50, and 72% at N=51+. The implication was that adding more buckets creates dead markets.

v2 shows that finding was largely driven by categorical events.

Categorical ghost rate is roughly 2–3× higher than continuous at N=6–50. Sports tournaments with longshot teams, election fields with no-hope candidates, primary races with placeholder names — these are the events where Polymarket creates many binary contracts and most go dead. On continuous events (BTC price brackets, weather temperature ranges, margin percentages) the bucketing is more functional. Most buckets at intermediate N do get traded.

Continuous events still show meaningful ghost rates at N=11–20 (40%) and N=51+ (45%), so the architecture is not perfect.

The ghost chart uses a fixed $1K threshold. To show where liquidity actually drops off as a continuous function, we computed a survival curve: at each volume threshold from $10 to $1M, what fraction of markets have at least that much lifetime volume?

Continuous markets survive longer at every threshold. 65% of continuous markets have at least $1K in volume vs 49% of categorical. At $10K the gap is 37% vs 27%.

The more interesting view is the continuous slice broken out by event size:

The liquidity cliff shifts left as N grows. At N=2–10 the cliff is at ~$10K. At N=21+ it is at ~$100. The architecture handles continuous bucketing reasonably well at low N and breaks at high N. The failure point is a smooth function of event size.

v1 told a story about binary discretisation creating dead markets and un-tradeable tails. v2 splits the dataset by event type and finds the story is more specific than that.

Concentration is a property of the architecture. Both continuous and categorical events reach 90% of total volume by rank 5–6. This holds on both sides of the split with similar magnitude.

But continuous events distribute better as N grows. At N=21–30 the top 3 markets capture only 33% of continuous event volume (vs 63% for categorical). Traders on continuous events are already distributing capital across more buckets. The demand for multi-bucket expression is visible in the data.

Ghost markets are largely a categorical problem. The v1 finding that 60–72% of markets are dead at high N was driven by sports tournaments and election long-shots. Continuous events have substantially fewer ghosts at every N tier. The architecture handles continuous bucketing reasonably well at intermediate N, but this changes as the threshold for "ghost" increases.

The liquidity cliff shifts left with N. The survival curve shows continuous markets at N=2–10 stay above 80% alive until ~$10K. At N=21+ the cliff starts at ~$100. The architecture works at low N and breaks at high N, and the failure point is a smooth function of event size.

Polymarket's continuous activity is growing. Continuous events overtook categorical by event count in 2026Q1. Crypto (95% continuous) and Weather (99% continuous) are growing categories. The discretisation cost analysis applies to a growing share of the platform.

Analysis based on 18,863 multi-market events and 172,869 individual markets from the Polymarket Gamma API (July 2022 – March 2026). Classification methodology and reproducible notebooks: github.com/igorfunctionspace/polymarket-discretisation/tree/main/v2