skysniper
Joined 9 years ago
Joined 9 years ago
also added per battle stats in battle detail page
all network error, provider error, openclaw error are excluded from ranking calculation actually, so that is not the reason.
Real reason:
The absolute score is not consistent across tasks and cannot be directly added/averaged, for both human and LLM. But the relative rank is stable (model A is better than B). That is exactly why Chatbot Arena only uses the relative rank of models in each battle in the first place, and why we follow that approach.
a concrete example of why score across tasks cannot be added/averaged directly: people tend to try haiku with easier task and compare with T2 models, and try opus with harder task and compare with better models.
another example: judge (human or llm) tend to change score based on opponents, like Sonnet might get 10/10 if all other opponents are Haiku level, but might get 8/10 if opponent has Opus/gpt-5.4.
So if you want to make the plot, you should plot the elo score (in leaderboard) vs average cost per task. But note: the average cost has similar issue, people use smaller model to run simpler task naturally, so smaller model's lower cost comes from two factor: lower unit cost, and simpler task.
methodology page contains more details if you are interested.
Essentially I'm using the relative rank in each battle to fit a latent strength for each model, and then use a nonlinear function to map the latent strength to Elo just for human readability. The map function is actually arbitrary as long as it's a monotonically increasing function so it preserves the rank. The only reliable result (that is invariant to the choice of the function) is the relative rank of models.
That being said, if I use score/cost as metrics, the rank completely depends on the function I choose, like I can choose a more super-linear function to make high performance model rank higher in score/cost board, or use a more sub-linear function to make low performance model rank higher.
That's why I eventually tried another (the current) approach: let judge give relative rank of models just by looking at cost-effectiveness (consider both performance and cost), and compute the cost-effectiveness leaderboard directly, so the score mapping function does not affect the leaderboard at all.