You're right about "settlement". That was just me being too lazy to keep writing the phrase "gap between the head block and the last irreversible block".

I don't have formulas for the tables at all. I just made the tables and filled them in based on intuition, and it's hard to describe (probably because I still don't really even have a good grasp on it).

Table 1: 21^st witness

The first table shows the imaginary case where the top-20 witnesses all go in the same order, and the random 21^st witness is inserted into each of 21 possible positions.

Without witness21, every block would be "settled" in 15 blocks. However, witness21 is guaranteed to have a stale block, so that pushes the rest back and bumps the gap up to 16 each round until witness21 produces a block. When that happens, the gap drops to 15.

Table 2: top-20 witness shuffling

The second table shows the number of blocks confirmed in two consecutive rounds by a particular pair of witness placements. For example, if a witness goes last in the first round and first in the last round, it only confirms 1 block (lower left). If it goes first in the first round and last in the last round, then it confirms 41 blocks when it produces its own block (top-right). In order for the head block from that round to be marked as final, the witness would need to confirm at least 15 blocks. Thus, I marked the lower-left corner (14 confirmations or less) as yellow.

I reached the conclusion that this can't go beyond 22 by stepping diagonally up and right six times from the lower-left corner until I hit a 15. That was six steps. And 16 (from table-1) + 6 steps gives us 22 total.

Of course, all of this ignores the possibility for missed blocks, and I can't justify any of it empirically. It's just my intuitive attempt to visualize the way that things flow.

Update: I just noticed that I didn't count the starting position in those 6 diagonal steps, so make that 7 and 23.