I’m likely not to actually quantify ‘relative to’ - there might be an ordered list of players if it seems reasonable to me (for example, if one submission uses 10 soldiers to get a 50% winrate and one uses 2 soldiers to get a 49% winrate, I would feel comfortable ranking the second ahead of the first—or if all players decide to submit the same number of soldiers, the rankings will be directly comparable), but more likely I’ll just have a chart as in your Boojumologist scenario:

with one line added for ‘optimal play’ (above or equal to all players) and one for ‘random play’ (hopefully below all players).

Overall, I don’t think there’s much optimization of the leaderboard/plot available to you—if you find yourself faced with a tough choice between an X% winrate with 9 soldiers or a Y% winrate with 8 soldiers, I don’t anticipate the leaderboard taking a position on which of those is ‘better’.

Could you elaborate on this? I think I’d do better relative to best play with

high numbers of soldiers,

and do better relative to random play with

low numbers of soldiers,

so it’s not clear which way I should lean; also, I don’t know how you plan to quantify “relative to”.

I’m likely not to actually quantify ‘relative to’ - there might be an ordered list of players if it seems reasonable to me (for example, if one submission uses 10 soldiers to get a 50% winrate and one uses 2 soldiers to get a 49% winrate, I would feel comfortable ranking the second ahead of the first—or if all players decide to submit the same number of soldiers, the rankings will be directly comparable), but more likely I’ll just have a chart as in your Boojumologist scenario:

with one line added for ‘optimal play’ (above or equal to all players) and one for ‘random play’ (hopefully below all players).

Overall, I don’t think there’s much optimization of the leaderboard/plot available to you—if you find yourself faced with a tough choice between an X% winrate with 9 soldiers or a Y% winrate with 8 soldiers, I don’t anticipate the leaderboard taking a position on which of those is ‘better’.

That makes sense, ty.