Same battles, different numbers

Elo replays the same 18 battles in two orders

Four chatbots (A, B, C, D) fought a round-robin: every pair battled 3 times, 18 battles total. Each battle updates ratings on the spot, starting at 1000, K=32.

Pick a battle order below. Same 18 wins and losses every time, only the order the ratings get updated in changes.
current order the other order

One matrix, one ranking

Bradley-Terry fits the aggregate win matrix by iteration

Same win matrix as Panel A: A beat B 2, C 3, D 3; B beat A 1, C 2, D 3; C beat B 1, D 2; D beat C 1. Drag the slider through the Zermelo (MM) updates.

P(A beats D)
0.500
pA / (pA + pD)
P(B beats C)
0.500
pB / (pB + pC)

Reshuffle the battles in Panel A as many times as you like: this fit never changes, because it only ever sees WINS[i][j], the totals, never the sequence.