Methodology

Bradley–Terry calculation

P(A beats B) = 1 / (1 + 10^((Elo_B − Elo_A) / 400))
  • Mean 1000; Gaussian prior SD 400 Elo.
  • Ties count as ½ win.
  • Table intervals are 95% posterior credible intervals.

Excluded data

  • Internal testers.
  • Battles where either contestant failed.
  • Battles where either contestant has $0 recorded account spending, including sponsored provider endpoints.
  • Incomplete records.
  • Battles affected by the historical subagent bug.
  • With Exclude early voting: early picks and battles stopped before both contestants finished.

Bootstrap sample calculation

  • Developer-cluster bootstrap; B = 1,000 replicates.
  • Each replicate draws D developers uniformly with replacement from D observed developers, retaining all their battles and multiplicity.
  • Refit the maximum a posteriori Bradley–Terry estimate for each replicate.
  • Tied rank positions split their weight equally.
  • Ridgeline smoothing: Gaussian kernel density estimates, with bandwidth h = max(2, 1.06sB−1/5) Elo; s is the replicate standard deviation.
  • Ridgeline axis: from the lowest 0.5th to the highest 99.5th percentile of the ranked models' curves, rounded out to 25 Elo.

Provider selection

  • OpenRouter routes each model through a model-specific provider and endpoint allowlist.
  • Routing prioritizes throughput, requires support for the requested parameters, and applies per-model price caps.

Definitions

  • Rank likelihood: share of bootstrap samples at each rank.
  • Ridgelines: smoothed Elo distributions from bootstrap samples.
  • Raw win rate: excludes ties from wins.
  • Tokens per second: median per-run token rate.
  • Cost / time: median or arithmetic mean per task, using recorded values from eligible battles.
  • Pareto frontier: ranked models with no other ranked model having equal or higher Elo and equal or lower selected cost or time, with at least one strict improvement.
  • Pareto bars: 95% Elo confidence intervals.
  • Thin / thick bars: thin bar is the 95% confidence interval; thick bar is the 50% confidence interval.