Archive / Prediction markets / E807
Long-shot baseball player props are not overpriced
Buying NO on the top two rungs of baseball player-prop ladders priced 30 cents or less for YES lost 2.45 cents per contract after spread and fee, on 15,477 contracts over 50 game days.
A common belief says that bettors overpay for long shots. On a US event-contract exchange, each baseball player gets a ladder of contracts such as "2 or more hits", "3 or more", "4 or more". We took the top two rungs of each ladder when the YES price was 30 cents or less and bought the opposite side (NO) before the game. After spread and fee this lost 2.45 cents per contract on 15,477 contracts. The long shots came true 11.9% of the time, close to the average YES bid of 10.1 cents; a YES buyer pays the ask, which is above the bid. The mid-ladder control lost 3.3 cents.
Retail bettors overpay for long-shot outcomes, so the highest thresholds on a player's ladder are too expensive and the opposite side is cheap.
Why people believe it
People argue that a bettor who likes a big night, such as four hits or ten strikeouts, pays more for that ticket than its true chance justifies. If so, the YES price of the top rungs is too high and the NO price is too low.
Why it would persist The argument, as stated before testing
People argue that the buyers of such contracts are casual and price-insensitive, and that the market has no large informed participants who would push the top rungs back down.
We looked at settled baseball player-prop contracts in six families: strikeouts, hits, home runs, total bases, runs batted in, and hits plus runs plus runs batted in. All rungs of one player in one game form a ladder. For ladders with at least three priced rungs we took the top two rungs priced at 30 cents or less for YES. We took the last valid price in the 30 minutes before the scheduled start and bought NO at the price a taker pays, 1 minus the best YES bid. We held to settlement, charged the exchange fee and compared the result with zero. A control used rungs priced near the middle.
At least 300 lottery contracts on at least 25 days; equal-weight mean at least +1.0 cent; game-day 95% interval lower bound above 0; at least two thirds of prop families with 30 or more contracts positive; volume-weighted mean above 0.
Equal-weight mean at or below +1 cent, or the game-day interval includes 0.
Fee 0.07 x NO price x (1 - NO price) per contract, unrounded, on top of crossing the spread. P&L per contract = 1 if the result is NO, minus the NO price, minus the fee.
Mid rungs with a YES mid price of 50-70 cents (all ladders). YES-price buckets (up to 5 cents, 5-15 cents, 15-30 cents). Split by prop family. Equal-weight mean as primary and a mean weighted by market volume. The control had to be within 1.5 cents of zero for any gain to be read as a long-shot effect.
The equal-weight mean of -2.45 cents is at or below the +1 cent kill line; the interval-includes-zero clause did not fire, because the whole 95% interval is below zero.
- On 15,477 lottery contracts across 50 game days, buying NO lost 2.45 cents per contract after spread and fee (game-day 95% interval -3.25 to -1.73 cents). Weighted by market volume the loss was 5.98 cents.
- The long shots came true 11.9% of the time, close to the average YES bid of 10.1 cents. A YES buyer pays the ask, which is above the bid.
- Every price bucket lost: -2.2 cents at YES prices up to 5 cents, -2.3 cents between 5 and 15 cents, -3.2 cents between 15 and 30 cents.
- None of the five prop families with at least 30 lottery contracts was positive. The home-run family had 2 lottery contracts.
- The control of mid-ladder rungs priced 50-70 cents lost 3.3 cents per contract, about the cost of crossing the spread and paying the fee. It was outside the 1.5-cent band around zero, so no positive reading of the long-shot result was possible in the first place.
- Of 43,818 settled markets in 898 sampled games, 40,342 had a valid pre-game quote.
The long-shot side loses, and the whole interval is below zero
Net result of buying NO on lottery rungs, equal-weight, with the game-day 95% interval. The pass rule needed the mean at or above +1 cent and the interval above zero; the interval lies entirely below zero.
Chart data (cents per contract)
| Mean | 95% low | 95% high | |
|---|---|---|---|
| Lottery rungs, equal-weight (n 15,477) | -2.45 | -3.25 | -1.73 |
Every price bucket loses, as does the mid-ladder control
Net result of buying NO by YES-price bucket of the lottery rungs, next to the volume-weighted figure and the mid-ladder control. No bucket is positive. Interpretation: the control's loss is about the cost of crossing the spread and paying the fee at any price.
Chart data (cents per contract)
| Net per contract | |
|---|---|
| YES up to 5 c | -2.2 |
| YES 5-15 c | -2.3 |
| YES 15-30 c | -3.2 |
| All lottery rungs, volume-weighted | -5.98 |
| Control: mid rungs 50-70 c | -3.3 |
Why it failed Interpretation · not established
The numbers fit prices for single-game player outcomes that track how often the outcomes happen, so that a taker who must cross the spread and pay the fee loses, as the mid-ladder control also shows. A long-shot bias large enough to cover roughly 2.5 cents of cost does not appear in this sample.
Lesson
A popular bias such as overpriced long shots has to be larger than the spread plus the fee of the side being traded. Compare the outcome frequency with the quoted price first; the taker's loss then separates "no bias" from "bias smaller than the cost of crossing".
Scope of this result
Covers pre-game baseball player-prop contracts in six families, a sample of up to 150 games per family, event starts 2026-08..2026-10, bought by a taker at the last quote in the 30 minutes before the start and held to settlement. It does not cover other sports or quotes taken at other times.
A rejected experiment applies to the tested conditions and does not prove an idea can never work. bp = basis point, 0.01%.
1. Test design
Pre-registeredDataUniverseSignalExecutionCostsControlsSample splitPass criterionKill criterionPower2. Result
ObservationsInstrumentsNet mean95% intervalMedianWorstFinding 1Finding 2Finding 3Finding 4Finding 5Finding 63. Interpretation
Why it failedLessonScope4. Reproducibility
StepsGrade