# Statistics

`analysis/report.py` computes every number in the report from `results/v1/runs.jsonl`.

## Pass rate

Counted per side over all runs. A run error (the pair could not be run or judged) would be counted separately; v1 has none left after reruns.

## Efficiency

Efficiency compares only pairs where both sides passed: the same task and the same run number, run at the same time. A pair where one side failed says nothing about how efficiently a correct result was reached, so it is left out of efficiency (and shows up in the pass rate instead).

For each metric (time, model requests, input tokens, output tokens, browser calls):

```
change = Σ Mirasim / Σ ChatGPT − 1        over all pairs in the table
```

A ratio of totals, rather than a mean of per-pair ratios, weights each pair by its size, so a 10-minute task counts more than a 1-minute one, in proportion to the cost a user would see.

## 95% interval

Runs of the same task are not independent: some tasks are long, some short, and the same task tends to favour one side across its runs. The interval therefore resamples tasks, not runs:

1. Group the pairs by task.
2. Draw as many tasks as there are, with replacement; take all pairs of each drawn task.
3. Compute the change for that sample.
4. Repeat 4000 times; the 2.5th and 97.5th percentiles are the interval.

The random seed is fixed (1) and the tables are computed in a fixed order, so the report is reproducible to the digit. The interval reflects variation between tasks and between runs of a task, including the model's own day-to-day variation within the run window; it does not cover other models, other machines or other versions of the tools.

## Other tables

- By action: a task tagged with several browser actions counts in each of their rows; changes are ratios of totals as above, without intervals.
- By group and per task: plain totals and per-run times.
- Sensitivity: the totals again without the 6 pairs where one side ran at low reasoning effort.