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Basketball Median Probabilities

Set a player's game median (points, rebounds, or assists) and see the Over/Under probability at each half-point line around it.
Stat
Points
Model
Normal
Median
20.5
Std Dev
6.15 (auto)
Offset Line P(Over) Over Odds P(Under) Under Odds
-5 15.5 79.19% -381 20.81% +381
-4 16.5 74.23% -288 25.77% +288
-3 17.5 68.72% -220 31.28% +220
-2 18.5 62.75% -168 37.25% +168
-1 19.5 56.46% -130 43.54% +130
median 20.5 50.00% -100 50.00% -100
+1 21.5 43.54% +130 56.46% -130
+2 22.5 37.25% +168 62.75% -168
+3 23.5 31.28% +220 68.72% -220
+4 24.5 25.77% +288 74.23% -288
+5 25.5 20.81% +381 79.19% -381
Normal N(median, σ²): symmetric, best for points (a sum over many possessions is ≈ normal) and fine for higher-count rebounds. Auto-SD scales with the median: points ≈ max(4.0, 0.30×median), rebounds ≈ max(1.8, 0.38×median), assists ≈ max(1.6, 0.42×median).

Negative binomial: a right-skewed count model for rebounds / assists. The mean is solved so the median line sits at 50/50, and the spread comes from the variance/mean ratio φ (φ = 1 would be Poisson; defaults ≈ 1.30 rebounds, 1.35 assists). The skew mainly shifts lines far from the median — a bit more Over on high lines, less Under on low lines — which a symmetric normal misses. Its effect is largest for low counts and shrinks as the count grows (assists > rebounds > points ≈ none), so it's offered only for rebounds and assists.

Lines are half-integers, so no pushes. Odds shown are fair (no-vig) American odds derived directly from the probabilities.
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