Wherever we look in the world, we see competition between different groups or beings. Whether it’s two animals trying to earn the right to a watering hole, people trying to assert their social influence, or simply two sports teams playing against each other, this sort of interaction appears in many different situations. As humans, we have a natural desire to rank things that are in direct competition: which is better? Who would win if they faced each other? How does their rivalry compare to others?

We want to know the answers to these questions because it makes us enjoy the competition more, and we feel that we learn more about it. Imagine being able to correctly predict who would win every football match for the rest of the season, you’d probably feel pretty pleased with yourself… But, apart from the inevitable bragging rights, being able to rank competing entities and predict outcomes is an extremely useful skill in many different areas of research, including sociology, economics and ecology.

Of course, you need a bit of maths if you’re going to rank things reliably; you can’t just trust a hunch! There are many different methods that have been used before for rankings, but a group of scientists at the Santa Fe Institute in the USA have come up with a new way of doing it using springs!

So, the ranking system is… a trampoline?! Not exactly. This ingenious method, called SpringRank, treats each interaction as a physical spring, so the model is a whole system of connected springs. Think of a football league: between each pair of teams there is a spring in each direction, and the force of each spring is determined by how many times they have beaten each other in the past. For example, Manchester United have played Liverpool 200 times, winning 80 matches and losing 65. In our spring system, this means that the spring connecting the two teams is biased towards Manchester United – it requires more force to move closer to Liverpool than it does to move towards Manchester United. With this setup, it turns out that the best ranking of the teams is found when you make the total energy in all of the springs as low as possible.

But why use springs? The bonus is that we’ve been studying springs for hundreds of years and so we know the physics behind how they work, which makes it easy to do the calculations. We can use the positions of the springs to work out the rankings of millions of different teams in just seconds! Not only is the maths simple, but it’s also very effective, especially compared to other methods currently used for ranking. In tests run by the researchers, SpringRank performed much better at ranking competitors, as well as predicting the outcomes of future clashes, than existing methods. The data set covered topics as varied as animal behaviour, faculty hiring and social support networks, demonstrating just how versatile the method can be.

This research is a wonderful example of how different areas of science can be combined to create a tool that can actually be put to use in the real world. When learning the subjects separately at school, it’s hard to imagine that you could take centuries-old ideas from physics, turn them into mathematical models, and stick them into a computer program! But here we are, able to work out who is likely to become friends (and enemies), which animals will make it through the heatwave, and whether it’s worth bragging about your favourite team before the game has even happened. So next time you’re challenged to guess the league winner, reach for SpringRank and jump ahead of the competition!

Kai Laddiman