Monday, 16 September 2013

Inspiring Mathematical Applications: Cage-Fighting (which should really be called MMA).

The amount to which Mathematics can be applied to almost any real-world phenomena is simply astonishing (which is not exactly the same as saying is SHOULD be applied to everything). Most students don't ever see this. Most adults never see this. One of my favourite reactions when I do a #3Act lesson is "Why are we watching this, sir? This isn't Maths", because I know that they'll be happily modelling the situation in the next 5 minutes.

Anyway, I also like to bring in unexpected, interesting uses of Maths as a sort of show and tell in some of my classes and I thought that I'd share some of them on my blog.

To kick off, we're starting with my favourite sport: MMA, and one trainer in particular's use of basic game theory to plan out fights. Original Article.

Nodes
Every fight starts off with both fighters standing just out of striking range. We can call this the initial node. From there, a fighter can move in with a punch, a kick or by trying to grab hold of the other for a clinch or take-down. After each move you end up in a different position or node. Each of those moves lead to a different set of optional follow-up moves and fighters can chain together as many of these moves as possible, traveling from node to node. You can visualize this in a diagram. The nodes are circles with the edges being the moves to get there:


Greg Jackson uses these diagrams and adds success probabilities to each edge using data he collects by watching previous fights and sparring sessions. From there you can calculate the optimal nodes to aim at in order to allow for the highest probability of success later on. You can also block off the routes that lead to your opponent's strongest nodes to 'take them out of their A game'.

More data is used from an MMA data collection website: FightMetric