Sample Size and the Small-Sample Traps in Prop Hit Rates
Hit rates are the most-quoted number in prop research, and the most over-trusted. "He's gone over in 9 of his last 10" sounds like a pattern. Often it is a small sample doing what small samples do. This article lists the common traps and shows how to read the "of N" that ArchivePicks prints beside each percentage. The exact definitions are on the methodology page.
The basic problem
A hit rate is a count of games, so it can only move in big steps. With 5 games each result is worth 20 percentage points. With 10 games each is worth 10. One unusual night changes the whole story.
Chance alone also produces streaks. A fair coin comes up heads 8 or more times in 10 flips 56 times in 1,024, or about 5.5% of the time. Run that across a few hundred players on a board and some of them will show 8-of-10 or better against their lines with nothing special going on. Seeing a high rate is not proof of anything until you know how many chances there were to see one.
Trap 1: reading the percentage without the "of N"
3 of 3 and 18 of 18 are both 100%. They are very different evidence. Look at the "of N" first, then the percentage. The glossary defines sample size in a line, and our guide to reading a hit rate goes deeper.
Trap 2: windows that overlap
L5, L10 and Season are not three independent confirmations. The last five games are inside the last ten, which are inside the season. When all three say 70%, that is one story told three ways, not three votes. See which window to trust.
Trap 3: a line that moved after the games were played
A hit rate is measured against the number on the board today. If the player was a 58.5 guy and the line is now 63.5, his old games are being re-scored against a harder bar. ArchivePicks recomputes the rate at whatever number you choose, which is useful, but it means the rate describes the past at a new line. It does not mean the player was ever priced there.
Trap 4: games that were different
Games are not interchangeable. A player might have had a different role in the first half of the sample, or played with a teammate who is now out. A rate that mixes those games blends two situations. The bar chart on a player's page shows each game so you can see whether the games line up.
Trap 5: cherry-picking the number
If you drag a line around until the rate looks good, you have searched, and what you found is partly noise. The more numbers, stats and windows you try, the more likely one looks impressive by luck.
Trap 6: tiny head-to-head samples
A player usually meets a given opponent about once a season, so head-to-head history is a handful of games at most. The methodology page says to treat it as context, not a pattern. See head-to-head history.
Trap 7: zeros that aren't zeros
If a stat was not recorded for a game (the player was inactive, say), ArchivePicks leaves the game out instead of counting a zero. That keeps the rate honest, but it also shrinks N. A rate is shown only when the player has enough games to fill the window; otherwise the cell is left blank rather than computed from a shorter sample.
A worked example (hypothetical numbers)
Imagine two players with the same line type.
- Player X: over in 3 of 3.
- Player Y: over in 14 of 20.
X shows 100% and Y shows 70%. If each had a true clear rate of 50%, X's result happens 12.5% of the time (half, three times in a row) and is easy to produce. Y's 14 or more of 20 would turn up only about 6% of the time at a true 50%. That is why Y's 70% says more than X's 100%, though neither number is a forecast.
Now add context: X had three games as a starter after an injury to the team's usual starter. N is tiny and the role may not last. Y has played 20 games in a stable role. The percentages point in a different direction from the evidence.
Habits that help
- Always read N first.
- Prefer longer windows when the role is stable, shorter ones only when you know something changed, and know they are noisier.
- Look at the game-by-game chart, not just the rate.
- Do not stack three versions of the same sample as separate reasons.
- Remember that a hit rate is history. It does not know about injuries, matchups or weather, and ArchivePicks does not turn it into a prediction.
FAQ
How many games is enough? There is no magic number. More is better, and 20 or more games in a stable role says more than 5, but even then a rate is a clue, not a verdict.
Why is a rate blank on the board? The player has not played enough games to fill that window, so ArchivePicks leaves it empty rather than use a shorter sample.
Is a higher hit rate always better evidence? No. A rate near 100% over a few games is weaker than a moderate rate over many.
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