Regression Models for Event Pricing

What Regression Models for Event Pricing Actually Measure

Regression models for event pricing exist to answer one question a trader asks dozens of times a day: given everything you know right now, what price should this contract actually trade at? On Kalshi and Polymarket, a "yes" price is a probability wrapped in a dollar sign, and that probability drifts based on inputs — polling averages, weather forecasts, macro releases, injury reports, order flow — that update on their own schedules. A regression model takes those inputs, weights them against historical outcomes, and outputs a fitted probability you can compare against the live market price. The gap between the two is your signal.

This isn't a novelty for quants. It's the same logic sportsbooks and options desks have used for decades, adapted to binary contracts. What's changed is that retail traders now have access to the same category of tooling, and platforms like PillarLab AI have built structured pipelines specifically to run this analysis against live Kalshi and Polymarket order books rather than static historical data.

Building a Pricing Model: Feature Selection for Prediction Markets

The quality of a regression model lives or dies on feature selection, not on the sophistication of the algorithm. A linear regression with five well-chosen features will outperform a gradient-boosted ensemble stuffed with noise. For event contracts, useful features generally fall into four buckets:

• Base rate features — historical frequency of the outcome class (how often does an incumbent win reelection, how often does a favorite by this spread cover).
• Time-decay features — days to resolution, since uncertainty compresses non-linearly as an event approaches.
• Market-structure features — bid-ask spread, order book depth, and volume, which proxy for how much informed money has already moved the price.
• External signal features — polling, weather models, injury data, macro prints — anything with a documented correlation to the outcome.

If you're new to reading the raw price itself before you get to modeling it, it's worth working through How to Read Prediction Market Odds first — a regression model is only useful once you understand what the number it's predicting actually represents.

Logistic Regression vs Linear Regression for Binary Contract Pricing

Because Kalshi and Polymarket contracts settle at $0 or $1, you're modeling a binary outcome, which means logistic regression is almost always the correct default over ordinary linear regression. Linear regression will happily output a fitted probability of 1.14 or -0.08, which is meaningless on a contract bounded between 0 and 1. Logistic regression squashes outputs through a sigmoid function, keeping every prediction interpretable as a probability.

That said, linear regression still has a role: modeling continuous sub-components that feed into the final probability. If you're pricing a contract on "will the Fed cut rates by at least 50bps," you might run a linear regression on the distribution of dot-plot projections first, then convert that into a binary probability as a second stage. Chaining models this way — continuous regression to estimate the underlying distribution, then logistic regression or a direct probability transform to price the binary event — is standard practice for anyone building a serious pricing stack rather than a single-shot model.

Regularization and Overfitting Risk in Small-Sample Prediction Markets

Most event markets have brutally small sample sizes. You don't get 10,000 historical instances of "will this specific senator be indicted before March." You get a handful of loosely analogous cases and a lot of judgment calls about which historical instances even count as comparable. This is where regression modeling for prediction markets diverges sharply from regression modeling for, say, credit risk or fraud detection, where you have millions of labeled rows.

The practical fix is aggressive regularization — L1 (Lasso) if you suspect most of your candidate features are irrelevant and want the model to zero them out, L2 (Ridge) if you believe most features carry some real signal but want to shrink their weights to avoid overreacting to noise. Cross-validation on a five-feature model with forty historical rows is still going to be noisy, so treat your regression output as a prior to be updated, not a final answer. A model that's 4 points off the market isn't automatically wrong; it might be correctly capturing a real edge, or it might be underfit garbage. You need a second signal — order flow, a competing model, or a fundamentals check — before you treat the divergence as tradeable.

Comparing Model Outputs to Kalshi and Polymarket Live Prices

Once you have a fitted probability, the actual trade decision comes down to comparing it against the live contract price across venues, since Kalshi and Polymarket frequently diverge on the same underlying event due to differences in liquidity, user base, and settlement rules. A regression output of 62% against a Kalshi price of 58 cents and a Polymarket price of 54 cents on the same event isn't a coincidence you can ignore — it's either an arbitrage-adjacent gap or a sign your model is missing something one venue's order flow already knows. If you haven't mapped out how the two platforms differ structurally, Kalshi vs Polymarket 2026 covers the settlement and liquidity mechanics that explain a lot of these persistent spreads.

This cross-venue check should be a standing part of your workflow, not an occasional gut-check. Venue-specific quirks — a thinner order book on one side, a slower-to-react user base on the other — mean the "market price" isn't one number, it's two or three numbers that regression models can help you reconcile.

Applying Event-Pricing Regression to Sports and Politics Markets

Sports contracts and political contracts require different regression architectures because their information environments behave differently. Sports markets get dense, high-frequency inputs — injury reports, line movement, weather, pace-of-play stats — that update multiple times before resolution, which favors models that can ingest features close to game time and reweight quickly. Political and macro event contracts get sparse, slow-moving inputs — a poll every few days, a single Fed statement — which favors models built around fewer, higher-conviction features and wider confidence bands.

If sports is your focus, the feature engineering question is less "which algorithm" and more "which inputs update fast enough to matter," a topic covered in more depth in Best AI for Sports Betting. For political and macro contracts, you're generally better served by simpler models with explicit uncertainty ranges than by anything that looks like it was built for a 10,000-row sports dataset, because the sample size simply isn't there to support complexity.

How PillarLab AI Fits Into This

PillarLab AI runs this entire pricing workflow as a structured process rather than leaving you to assemble features and fit models by hand. Every contract you analyze gets scored across a 9-pillar framework — covering base rates, market microstructure, time decay, sentiment, cross-venue pricing, and more — so the regression-style comparison between fitted probability and live price happens automatically instead of requiring you to build and maintain your own model.

Because PillarLab pulls real-time data directly from Kalshi and Polymarket order books, the edge-detection layer isn't working off stale historical snapshots — it's comparing its pillar-weighted probability estimate against the price that's actually live on both venues right now, which is exactly the cross-venue check described above, done continuously rather than manually. When a contract's live price diverges meaningfully from the model's fitted probability across a majority of pillars, that gap surfaces as a flagged opportunity rather than something you'd have to notice by scanning spreadsheets.

This matters most for traders who understand the regression logic conceptually but don't want to rebuild a feature pipeline and refit a model every time a new contract lists. The 9-pillar structure is effectively a standing regression framework, tuned across base rates, market structure, and external signals, applied consistently to every market you're evaluating instead of ad hoc. You still bring the judgment call on which flagged gaps are worth acting on — PillarLab's job is making sure you're never missing the comparison in the first place.

Frequently Asked Questions

Is logistic regression better than linear regression for prediction market pricing?

Yes, for the final probability output, since contracts settle at $0 or $1 and logistic regression naturally bounds predictions between those values, unlike linear regression.

How much historical data do you need to build a reliable pricing model?

There's no fixed threshold, but small-sample event markets require heavy regularization since most contracts have far fewer comparable historical instances than traditional statistical models assume.

Can a regression model predict Kalshi or Polymarket prices exactly?

No. It produces a fitted probability estimate to compare against live prices — divergence signals a potential edge, not a guaranteed outcome, since markets price in information your model may lack.

Why do Kalshi and Polymarket sometimes show different prices for the same event?

Differences in liquidity, user base, and settlement rules cause venue-specific pricing gaps, which is why cross-venue comparison is a standard step in event-pricing analysis.

Does PillarLab AI build a custom regression model for each market?

PillarLab applies a consistent 9-pillar analytical framework across markets, comparing real-time Kalshi and Polymarket data to surface pricing gaps without requiring you to build models manually.

Start free with 10 credits and see how the 9-pillar framework compares fitted probabilities against live Kalshi and Polymarket prices on the contracts you're already tracking. Start free with 10 credits