4 ms·

But luck in [0,1] would even make less sense as luck^n (as it goes to 0), while as luck in [0,1000] could scale a successful startup by the factor of up to 1000

• nawitus 10y ago
  It doesn't matter if you're comparing "0.001" success to "1" success or "1" success to "1000" success.
• throwawayReply 10y ago
  What I meant by 'n' was a weighting. I wasn't clear. Let's say you have 4 factors a, b, c, d. If we are summing them then we can just sum them straight: score = a + b + c + d If we want to place more importance on some of them we weight them, with (constant) weights w, x, y, z by doing this: score = w * a + x * b + y * c + z * d. If it's a multiplicative relationship however then we multiply straight: score = a * b * c * d If we tried add weighting in the same way: score = w * a * x * b * y * c * z * d Then all we've done is scale the previous score by (w * x * y * z) which is constant, so hasn't actually affected any ranking. To weight a multiplicative relationship requires the weights to be exponents: score = a^w * b^x * c^y * d^z The scores can be in [0..1] or [1..N], the increased weights still increase relative power of the input parameter. If you take logs it's clear why. log(score) = w * log(a) + ... + z * log(d) which is our weighting when summing again, and log is monotonic (proof of which is left to the reader), log(S1) < log(S2) implies S1 < S2. Edit: Fixed formatting, it thinks * is italic.