The proper average to use in standings

[silver83p]

Hi!

When I occasionally look at https://www.argio-logic.net/classificaco ... ummary.php -- I have to disregard the total points column, because it's so obviously flawed. For example, someone with a single 1st place would have 1000 points, but someone with a 1st and 7th would have 500 (average rank 4th, so 2000/4). This also penalizes people for participating in more popular contests and failing to complete all of the contest's puzzles.

Just now, however, it occurs to me that this would be quite easy to fix. Namely, if the "average" were the harmonic mean, rather than the arithmetic mean, then this would be aligned with the score calculation and would be equivalent to summing up (1000/rank) for each contest. (The arithmetic mean for {r_1, ..., r_n} is (r_1 + ... + r_n)/n, while the harmonic mean is n/(1/r_1 + ... 1/r_n).)

I calculated my own harmonic mean as 8.07, compared to the arithmetic mean of 9.2, which isn't too different, because my rankings tend to be fairly consistent.

But for, e.g., InWLuFFy, the harmonic mean is 1.89, while the arithmetic mean is 6.29, which is more than a threefold difference.

[gabriele]

thanks Silver,
let me think about it