You shoot 7 out of 10 from the left wing today. Last week you shot 4 out of 10 from the same spot. Did you get better? Maybe. But it is just as likely that nothing changed and you saw luck at work. The fewer shots you have, the more luck decides the number.
Why a few shots tell you so little
Take a player whose true level from a spot is exactly 50%: over the long run, half of those shots go in. Even so, 10 shots will rarely come out as 5 and 5.
- That player makes 7 or more out of 10 about 1 time in 6.
- The same player makes 3 or fewer out of 10 about 1 time in 6, too.
So a "70%" session and a "30%" session can come from the very same shooter on two ordinary days.
Key point
- A percentage is only as steady as the number of shots behind it.
- Luck moves the result a lot at 10 shots and much less at 50 or 100.
- The result is real. What is uncertain is whether it shows your usual level.
How wide the luck range is
The table shows where a true 50% shooter's result will land about 95 times out of 100, which is a rough guide taken from the binomial distribution.
| Attempts | Likely range for a true 50% shooter |
|---|---|
| 10 | 20% to 80% |
| 20 | 30% to 70% |
| 50 | 36% to 64% |
| 100 | 40% to 60% |
Notice how slowly the range narrows. Going from 10 to 20 shots helps a lot, but to cut the range in half again you need roughly four times as many shots. That is why a single session is never enough to settle a question about one zone.
What ShootingStat does about it
ShootingStat does not hide small samples, but it does flag them:
- A zone appears among your best, weakest, hot or cold zones only after at least 10 attempts from it.
- A "small sample" hint shows when a zone has fewer than 10 attempts, or when a session has fewer than 20.
When you see the hint, read the percentage as a lead to follow, not a result to act on. The same goes for points per attempt, because PPA is just your percentage multiplied by the shot's value.
How to work with small samples
- Add sessions together. Combine the makes and attempts from sessions with similar conditions. Three sessions of 10 shots give 30 attempts, and a 50% shooter's results over 30 attempts land between about 33% and 67%, which is much tighter than the range for 10.
- Compare like with like. Use the same drill, the same distance and the same number of attempts each time. Then a change in the number is more likely to be a change in you.
- Look for repeats. One high number is a lead. The same high number in three sessions is worth believing.
- Log every shot you take. Zones fill up faster when you record all of your attempts. We explain what to record in What to Log on Every Shot.
Common mistake
- Don't change your form after one bad session. Chance alone can produce it.
- Don't celebrate one hot zone. A 9 out of 10 from one spot may be your real level, or it may be a good day. Check it again next week.
- Don't compare sessions with very different numbers of shots. A 60% from 10 attempts and a 55% from 80 attempts do not carry the same weight.
Takeaway
- A small sample shows what happened, not what will happen next.
- At 10 shots luck can move your percentage by 30 points in either direction. At 100 shots it moves it by about 10.
- Add sessions together, keep conditions the same, and wait for a pattern to repeat.
This week, pick one zone, shoot 10 from it in three sessions, and add the three results together before you decide anything.
