Perfect Matching in World Marathon Major Selecting
In the world of elite marathoning, most professional marathon runners run 2 marathons each year. Marathoners dedicate three to four months of preparation for this singular, 26.2 mile race, so it is crucial for them to select the correct marathon. There are 6 marathons that make up the Abbott World Marathon Majors: Tokyo, Boston, London, Berlin, Chicago, and New York City. Likewise, each of these marathons try their best to attract a high quality field of elite athletes, hoping that more fans and viewers will tune online or in person if they see runners that they like. In order to do this, the marathon majors offer elite athletes an appearance fee, paying them to show up to the start line and complete the marathon. As the LetsRun article describes, this is the singular biggest driving force for elite marathon runners when choosing where to run their Spring and Fall marathons, and the World Major Marathons make values to how much they are willing to pay for each elite athlete. In this blogpost, I will analyze this process through the lens of perfect matching.
As we learned in class and as the Github article describes, a bipartite graph is two groups of nodes with all edges running from nodes in one group to nodes in the other group. Perfect matching is an assignment of left nodes to right nodes such that: all nodes are assigned and every node is linked to what it gets.
In the case of marathon selection, we can assume that it is the fall marathon season, and only the Chicago, Berlin, and New York City Marathons are occurring. We can set the marathon type as the right group of nodes, as seen below. On the left group of nodes, we can set it as the top three female marathoners at the moment: Brigid Kosgei, Ruth Chepngetich, and Peres Jepchirchir. See below:
Next, we can add the values that each marathon has for the three elite marathon runners above. This value is based on several factors, including the appearance fee they are offering them, media obligations, and more. The values for each athlete are shown underneath their respective initials.
After the values are assigned, we start the matching procedure, which yields two possible cases.
In case 1, the matching value = 10 + 7 + 5 = 22
In case 2, the matching value = 10 + 9 + 6 = 25
Thus, the perfect matching scenario for the fall marathon season with the top three female marathoners is seen in case 2. This can also be done for mens marathon selection, as well as the entire elite field.
References:
https://11011110.github.io/blog/2020/02/22/applications-maximum-matching.html
https://www.letsrun.com/news/2021/10/rrw-pro-marathon-contracts-explained/#:~:text=Appearance%20fees%20can%20range%20from,fees%20always%20come%20with%20conditions.