When the analysis says "62% confidence Braves win," that's not certainty — it's the CENTER of a probability distribution. The real win probability could be 55%, 62%, or 70%. We have uncertainty about the uncertainty.
The right tool for this in math is the Beta distribution. It's a curve that shows how likely each possible "true win probability" is.
Adjust α (alpha) and β (beta) to see how the distribution shape changes:
If you've only seen 8 wins and 5 losses, the "true win rate" could be anywhere from 35% to 80%. Your point estimate (61.5%) is meaningless.
After 120 wins and 75 losses, the distribution tightens around 61.5%. NOW you can trust the number.
Win/loss is binary (0 to 1). Beta naturally lives in this range. Gaussian (the bell curve) goes from -∞ to +∞ — wrong shape for probabilities.
For things like point spreads (margin of victory), use the Normal/Gaussian distribution. NBA point spreads have a Gaussian-ish shape — most games land near the spread, with diminishing tails.
If Pistons are favored by 4.5, the average expected margin is 4.5 — with a standard deviation of maybe 10-12 points. The probability they cover (margin > 4.5) is roughly 50%.