Statistical Analysis of the International Mathematical Olympiad
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very year, participating countries send six of their best high-school math students to compete in the prestigious International Mathematical Olympiad (IMO). The selection process varies for each country, but students will typically participate in several rounds of competition with increasing difficulty, with many countries sending their highest-scoring students to intensive training camps. Presently, over 100 countries participate, and over the past sixty years, there have been over 18,000 contestants attending this prestigious competition. A massive number of scoring results are publicly available, and we analyze this data, elucidating a unique perspective on the world’s toughest math competition. Some of the key analyses in this paper include:
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• identifying some of the most difficult and least difficult problems on the IMO; • identifying countries that have the best performance on the IMO and exploring their performances over time; • showing how certain countries do much better or worse on certain problem types (algebra, combinatorics, number theory, and geometry); • demonstrating the home-field advantage of hosting the IMO; and • exploring gender differences in participation rates by country and performances by problem type.
The Data The official IMO website1provides data on each contestant’s gender, country, and score on each of the six contest problems. In addition, the name of the host country for each year as well as the country of origination of each contest problem was collected from published IMO shortlists and the IMO Compendium book.2 Additionally, each contest problem has been classified into one of four groups: algebra, combinatorics, geometry, or number theory. There are many contest problems that span multiple classifications, and for those problems, the classification into a single category can be somewhat subjective. Nevertheless, many of the officially released shortlisted problems provide official classifications of the problems into these four categories. The data from some of the early years of the competition are rather incomplete, and those years were excluded from the analysis, leaving 45 years of nearly complete scoring data. In Figure 1(A), we see that the number of IMO participants has dramatically increased over time. Consistent with the increase in number of participating countries is a decrease in the average scores, as shown in Figure 1(B). Additionally, there is substantial variation in the scores each year, as depicted in Figure 1(C). In order to remove the variability in the year-by-year scoring, the scores are
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https://www.imo-official.org. Dusˇan Djukic´, Vladimir Jankovic´, Ivan Matic´, and Nikola Petrovic´. The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2009, 2nd ed., Springer, 2011.
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2020 Springer Science+Business Media, LLC, part of Springer Nature https://doi.org/10.1007/s00283-020-10015-z
Figure 1. (A) Number of IMO participants by year. (B) Mean of the total scores (out of 42 points) by year. (C) St
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