inspired by gwern

Yes. And this is where things get actually good instead of just sorting placements like little pebbles.

Strictly speaking, order statistics are the sample values after sorting them, like min, median, max, quantiles. An index number in standard statistics usually means a value measured relative to a base period, which is a different idea. So “index statistics” is not really the standard formal opposite of order statistics. But in the esports sense, the useful contrast is: order stats sort placements; index stats preserve the tournament index or time order. (Wikipedia)

That distinction matters a lot:

• Order statistics tell you about tails, spread, and best/worst finishes.
• Time-indexed statistics tell you about streaks, regime shifts, collapse/recovery, patch sensitivity, and whether a player is a different organism on big stages.

So the most interesting index statistics are usually these:

1. Regime-switch index

Does the player have distinct eras, like “mediocre for months, then suddenly lethal”? This is more interesting than raw variance because it detects phase changes rather than random wobble.

2. Streak-length distribution

Not just “how often top 4,” but “how long are the hot streaks and cold streaks?” Some players cluster their good results into bursts.

3. Event-importance elasticity

How much better or worse do they perform when the stakes go up? This is the “normal event vs giant stage” multiplier.

4. Upset residual time series

For each event, compare actual finish to what seed or Elo would have predicted. Then look at the sequence over time. That shows whether they are a stable overperformer, a stable fraud, or a chaos goblin.

5. Patch/meta sensitivity

How much does their performance swing when maps, meta, or prep incentives change?

6. Clutch delta