I applied the EGD Adjusted Time (TA) formulas to calculate predicted maximum total game time for the time settings for which you listed statistics, ordering them by your observed p99 (i.e. soft max) total game time (listing rounded minutes).
| Time setting | p50 | p90 | p99 | TA |
|---|---|---|---|---|
| Blitz | ||||
| 30s+3s | 10 | 14 | 17 | 16 |
| 30s+5x10 | 11 | 17 | 22 | 16 |
| Rapid | ||||
| 5m+5s | 21 | 31 | 35 | 35 |
| 5m+5x20s | 16 | 27 | 38 | 40 |
| 10m+5x20s | 20 | 32 | 44 | 50 |
| 5m+5x30s | 22 | 34 | 50 | 55 |
| Full | ||||
| 10m+5x30s | 23 | 39 | 54 | 65 |
| 20m+5x30 | 28 | 49 | 67 | 85 |
| 10m+10s | 26 | 52 | 69 | 70 |
| 20m+10s | 37 | 64 | 85 | 90 |
(hoping I didn’t make a mistake there)
(Edit: added 10m+5x20s later on)
From that I note that
- The TA formula gives a pretty good estimate for Fischer p99 total game time. With byoyomi the TA formula is not as good a fit with blitz and full time settings. I suppose that is because byoyomi time gets progressively more wasted as the basic time and the byoyomi period get longer, so the total game time is not increasing linearly with the byoyomi period (while it does with Fischer time). In hindsight that does make sense, but it means that my previous assumption that overtime usage is a linear function of byoyomi time does not hold (and perhaps the TA formula should be modified to account for that. Although I wonder if TA might still be good to predict a more extreme maximum game time like p99.5 or p99.9).
- In practice, full 10m+10s and full 20m+5x30 are pretty much equivalent. My proposals of using either full 20m+10s or 10+5x30s were not good ideas. Your tentative choice seems pretty much optimal.
- With rapid it seems a bit harder to pick a byoyomi setting that fits well to 5m+5s Fischer. If you prioritise maximum total game time (p99 and TA), my proposal of using 5m+5x20s seems to be a better fit, but if you prioritise typical total game time (p50 and p90) and move pacing 5m+5x30s seems to be a better fit. I suppose players should pick Fischer rapid when they have a hard limit of ~40 minutes to finish the game, while they should pick byoyomi rapid if they want a somewhat more relaxed rapid game with a reduced chance of a time-out, accepting that the game might take an hour to finish (usually it takes less than half an hour to finish a rapid game).
Do you perhaps also have statistics for byoyomi rapid 10m+5x20s? I don’t think those settings have been mentioned yet in this thread, so perhaps it’s not very popular, but it might be a nice fit between full 20m+5x30s and blitz 30s+5x10s (at least I now assume it would be a better fit than rapid 5m+5x20s that I proposed earlier).
What are you considering to use as max values for Fischer time bank for blitz/rapid/full?