Looking at the English keyboard and the English digraphs, it doesn't seem like the coverage is that well optimized. We are currently capturing 8.65% of the digraph weight, but just getting the top-5 would account for 5% by itself.

I also feel like distance travelled is the wrong (or an incomplete) metric. Change in direction seems like a good proxy for mental or physical effort. To take it to an extreme, I'd be very satisfied with a keyboard that had me move my thumb in a circle as on the original iPod, provided it just read my mind and inputted the right text. That's extreme distance but little effort.

https://pi.math.cornell.edu/%7Emec/2003-2004/cryptography/su...

See also: https://en.wikipedia.org/wiki/Typewise

    +---------+---------------+-----------+-------------------------------------+
    | Digraph | Frequency (%) | Adjacent? | Pair on Keyboard                    |
    +---------+---------------+-----------+-------------------------------------+
    | TH      | 1.52          | Yes       | T is right of H                     |
    | HE      | 1.28          | No        | Separated by O and [Space]          |
    | IN      | 0.94          | Yes       | I is top-left of N                  |
    | ER      | 0.94          | Yes       | E is below R                        |
    | AN      | 0.82          | No        | A is bottom-center; N is top-right  |
    | RE      | 0.68          | Yes       | R is above E                        |
    | ND      | 0.63          | No        | N is top-right; D is bottom-right   |
    | AT      | 0.59          | No        | Separated by [Space] and S          |
    | ON      | 0.57          | No        | Separated by H and T                |
    | NT      | 0.56          | Yes       | N is top-right of T                 |
    | HA      | 0.56          | No        | Separated by [Space]                |
    | ES      | 0.56          | No        | Separated by [Space]                |
    | ST      | 0.55          | Yes       | S is below T                        |
    | EN      | 0.55          | No        | N/E are on opposite sides           |
    | ED      | 0.53          | No        | E is center-left; D is bottom-right |
    | TO      | 0.52          | No        | Separated by H                      |
    | IT      | 0.50          | Yes       | I is above T                        |
    | OU      | 0.50          | Yes       | O is below U                        |
    | EA      | 0.47          | Yes       | E is top-left of A                  |
    | HI      | 0.46          | Yes       | H is below-left of I                |
    | IS      | 0.46          | No        | Separated by T                      |
    | OR      | 0.43          | Yes       | O is below R                        |
    | TI      | 0.34          | Yes       | T is below I                        |
    | AS      | 0.33          | Yes       | A is below-left of S                |
    | TE      | 0.27          | No        | Separated by H and [Space]          |
    | ET      | 0.19          | No        | Separated by H and [Space]          |
    | NG      | 0.18          | Yes       | N is above G                        |
    | OF      | 0.16          | Yes       | O is below F                        |
    | AL      | 0.09          | Yes       | A is right of L                     |
    | DE      | 0.09          | No        | E/D are distant                     |
    +---------+---------------+-----------+-------------------------------------+