If we look at the score distribution for the AMC 10A/12A and AMC 10B/12B 2023 exams, it is easy to see that the distribution gets a big tail, although the medium score does not change much. Comparing to the score distribution for the 2017 and 2018 exams (which are similarly considered easy), the big tail effect is strikingly obvious.
This indicates that cheating happens mostly at the high score range. This is understandable because the cheater’s goal is to get into USAMO/USAJMO. For those who are not good at math, achieving an exceptional high score in one exam without other evidence backing up does not really help much. Therefore, we believe cheating is more rampant for those who are already good at math competitions. This would be hard to detect (e.g. with AI techniques) due to the fact that cheating would be in the form of “silly less”, “being lucky”, and the increase of score is moderate.
The following two figures are the score distribution of AIME I and AIME II in spring 2024. AIME I was leaked in a large scale, whereas AIME II wasn’t. The USAMO cutoff score is 20+ higher for AIME I, although the difficulty level is close for the two exams. From the distribution, the top 5% thresholds differ by 2. It is probably reasonable to assume that cheating at least boosted the threshold by 1, which is actually pretty significant (a big portion of those who are in the top 5% benefited from cheating).
