For hypergammon I'd focus only on hitting-type of contact and define amount of contact as the sum of both players' pipcounts measured as if the opponent's farthest checker was the bear off tray (or a 0 pt.). Other way of saying this is to count the sum of pips that measure distance from one's checkers to the farthest checker of the opponent (do this for both sides). Not sure if it's clear (sorry for my poor English), so let me give an example:
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| XGID=---------a----aAA---A---a-:0:0:1:00:0:0:0:0:10 | |||||
| Blue on roll, cube action? | |||||
eXtreme Gammon Version: 2.10
White's farthest checker is at Blue's 9pt, so Blue's "pipcount" is 6 + 7 + 11 = 24. Blue's farthest checker is at White's 5pt, so White's "pipcount" is 6 + 11 = 17. The metric produces a result of 24 + 17 = 41.
The idea is to highly rate positions where the forces are farthest apart. These positions produce most ways to interact between forces. They might get into a multiple-shot direct range positions like 3 split checkers vs 3 split checkers, all in 6-away range, but even before this, they might interact by finding hits with some large indirect numbers. Also, the highest-rated positions are positions in which breaking the contact is the hardest (if you'd like to measure contact by a negative of amount of rolls or sequences that let you break contact).
For this metric, the position with the highest amount of contact seems to be the starting position. (or actually all checkers on the bar if we consider unreachable positions)