Conditional Harmony

Hold every solo frequency still. Do the pairs survive?

A hot ball automatically makes all its pairs look hot. Curveball shuffles the incidence matrix while preserving every draw size and every ball total, then asks what remains.

Largest conditional pair residuals

SiVinceTutto6/90 era · since Sep 2024104 draws

37 + 38+7.55σ

41 + 44+6.82σ

6 + 21+6.21σ

65 + 76+5.40σ

37 + 80+5.29σ

44 + 47+5.29σ

66 + 86+5.29σ

51 + 72+5.29σ

4 + 34+4.53σ

74 + 88+4.43σ

7 + 59+4.39σ

19 + 32+4.28σ

37 + 67+4.28σ

50 + 90+4.28σ

60 + 71+4.28σ

61 + 66+4.28σ

41 + 57+4.23σ

65 + 74+4.23σ

Curveball conditional Monte Carlocurveball-pairs-v1seed 2026082759 samples; row and column margins fixed

Observed bars sit over the conditional mean. Ranking by |z| is exploratory across every pair.

The maths, in plain language

Condition on the margins

Represent draws as a binary draw-by-ball matrix. A Curveball trade exchanges non-shared entries between two rows, preserving both row sums $k$ and every column total. Pair counts in the randomised matrices form a conditional reference distribution, read as $z=(O-\mu)/\sigma$ .

The story behind it

The glow a hot ball lends its neighbours

Most “favourite pair” tables ask the wrong question. If 7 appears often, every pair containing 7 inherits the glow. Conditioning removes that easy explanation. The remaining extremes still face a large look-elsewhere effect: this page ranks clues, not discoveries.