Math Through Sports
Sample size and swing
7 min · Small samples bounce around. That bouncing has a name: variance.
- Sample size
- Variance
The stat
Small samples bounce around. That bouncing has a name: variance.
Learn the number
Sample size is how many observations a number is built from. 7 of 10 and 70 of 100 are both 70%, and they are not equally believable.
Variance is how much results spread out around their average. Small samples have room to land far from the true rate purely by chance.
This is why a hot week is weak evidence: there were not enough games for the luck to average out.
Read the stat
A 50% shooter takes 4 shots, then takes 400.
- In 4 shots, going 3 for 4 (75%) is entirely ordinary — it happens often by chance alone.
- In 400 shots, hitting 75% would mean 300 makes.
- For a true 50% shooter, 300 of 400 is so far from expectation it would be astonishing.
- Same gap in percentage terms; completely different amounts of evidence.
The bigger the sample, the harder it is for luck alone to produce a big gap.
Your turn
Team A is 3–0. Team B is 21–9. Both are winning at a high rate. Which record is stronger evidence, and why?
Explain what it means
Ask "out of how many?" before you trust any rate. A percentage without its denominator is a headline, not a measurement.
Make a prediction
Find a player having a hot 5-game stretch. Predict whether their next 10 games look more like the hot streak or more like their season average.
Review what happened
Check. Most hot streaks drift back toward the season number — that drift is regression toward the mean, not a slump.
Check your understanding
0 of 3 correct
Every question has to be right for this lesson to count as complete. Miss one and you can try it again.