# Weird rumble scores

Fragment of a discussion from Talk:BeepBoop

I’m experiencing similar thing. Score is constantly dropping as more battles come.

But is’s not hard to explain.

1. For bots you get 100%, when getting more battles, it’s either changing to 100% or less than 100%, and the more battles the higher probability it gets less than 100%, so score can only decrease as more battles come.

2. For bots saving data, it’s only getting better the more data they have.

Since this affected a lot of bots, affecting 0.1~0.2 APS is quite common.

Worth mention that 1 APS decrease in 10 bots is enough to give you -0.1 APS.

Btw, 1 season is generally not enough to get stable results. For reliable result, 50000 or even 100000 battles are needed. Anyway comparing after ~30000 battles is generally acceptable.

Xor (talk)19:00, 24 June 2021

2 would explain a bit of a score decrease, although not that many bots save data. I don't think 1 is true; sure some 100%s will become 99.5%s but also some 99%s will move up to 99.5%. Without 2, the APS estimated from a small number of battles should be an unbiased estimate of the true APS. And it takes 1 APS decrease in 100 bots to get -0.1 APS since there are ~1000 bots in the rumble!

23:35, 24 June 2021

Have a look at 0.14 and 0.14a, the APS is 0.3 diff. And if only looking at the simplest bots to beat, 0.14a is having more 100% than 0.14, simply because it haven’t got enough battles.

99% going to 99.5% does happen, but they do move to 98.5% as well. It’s mostly balanced.

But the 100% part is onesided, causing it to constantly move down before reaching some “stable point”.

0-1 is balanced, but since you don’t get 0, it’s unbalanced then. Averaging on unbalanced distribution is biased sometimes, there exists better calc of APS to avoid score shifting, e.g. Using walson score lower bound for each bot instead of some 40 window moving average.

Xor (talk)03:24, 25 June 2021