From behind the three-point line, everything feels the same—the rim doesn’t move, the distance doesn’t change, and my form stays consistent. But the results? They fluctuate more than most people realize.
I’m a 40% three-point shooter. That’s my average—my “mean.”
But if you watch me game by game, you might not believe it.
Some nights I can’t miss.
Other nights, nothing falls.
That’s not inconsistency—that’s variance.
📊 The Math Behind Every Shot
If I translate my game into numbers, it looks like this:
Where:
-
μ (mean) = my expected shooting percentage (0.40)
-
xᵢ = what actually happens in a game
-
n = number of games
Every game I play becomes a data point.
🎯 A Real Shooting Simulation
Let’s say I take 10 three-point shots per game over 7 games:
|
Game |
Shots Made |
Shooting % |
|---|---|---|
|
1 |
4 |
0.40 |
|
2 |
6 |
0.60 |
|
3 |
2 |
0.20 |
|
4 |
5 |
0.50 |
|
5 |
3 |
0.30 |
|
6 |
7 |
0.70 |
|
7 |
1 |
0.10 |
On paper, I’m still a 40% shooter.
But look at the spread—10% to 70%.
🧮 Calculating the Variance
Now let’s break it down.
First, I compare each game to my average (0.40), then square the difference:
|
Game |
xᵢ |
xᵢ − 0.40 |
(xᵢ − 0.40)² |
|---|---|---|---|
|
1 |
0.40 |
0.00 |
0.0000 |
|
2 |
0.60 |
0.20 |
0.0400 |
|
3 |
0.20 |
-0.20 |
0.0400 |
|
4 |
0.50 |
0.10 |
0.0100 |
|
5 |
0.30 |
-0.10 |
0.0100 |
|
6 |
0.70 |
0.30 |
0.0900 |
|
7 |
0.10 |
-0.30 |
0.0900 |
Add them up:
Divide by number of games:
Standard deviation:
📉 What This Means on the Court
A 20% standard deviation is huge.
It means:
-
I can shoot 70% one night 🔥
-
And 10% the next ❄️
-
Without changing who I am as a shooter
That’s the reality of high-variance shooting.
🧠 First-Person Insight
When I miss three shots in a row, it’s easy to think something is wrong.
When I hit four in a row, it’s easy to feel unstoppable.
But both are illusions.
What matters isn’t the streak—it’s the underlying percentage.
⚖️ Volume Changes Everything
If I take:
-
10 shots → results swing wildly
-
100 shots → results stabilize closer to 40%
That’s why great shooters keep shooting.
They trust the long-term average, not short-term outcomes.
🏀 Final Reflection
From beyond the arc, I’ve learned something important:
I don’t control whether the next shot goes in.
I control the quality of the attempt.
Because in the end:
👉 The percentage is the truth
👉 The game-to-game swings are just variance
And every time I release the ball, I’m not chasing perfection—
I’m trusting the math behind the shot.
Written by juridex in Costa Rica — BASKETBALL coverage, published on April 14, 2026.
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