After a year without international events, I watched the fencing European zonal qualifier for the Tokyo Olympics with excitement. As is custom in fencing, I watched a match run away from a fencer who was clearly better, more experienced than their opponent — someone 300 spots ahead in the world ranking. So what happened?
A recap for the novice: fencing consists of 3 weapons: foil, epee, and sabre. Epee seems to get a lot more "upsets" than the other two. When looking at stats, it’s harder for top epeeists to maintain consistently high world ranking points compared to foilists. This lack of consistency makes it harder for narratives and rivalries to form, which are the lifeblood of spectator enthusiasm.
"The Idea is to install a best 2-out-of 3, or 3-out-of-5 (15 touch) bouting system... The idea would be to enhance three aspects of the sport; the athleticism of the competitors, emphasize consistency of results, and increase spectator enjoyment.
As any fencer knows, 15 touch bouts are very short in the grand scheme of things – many times these bouts can complete before the first period has expired. In this time period – even simple mistakes can lead to a devastating end... How many times have we seen upsets of physically, technically, and more consistent athletes by unorthodox lesser athletes?"
The Format of a Fencing Match
A fencing competition consists of a sequence of bouts to 15 (3x3 minutes). There are 64 fencers in the final draw, which happens on a single day, with 6 direct elimination bouts to win the tournament. In this part, I'll use model simulations to evaluate how different formats could reduce the number of upsets.
1. Simple Modelling Framework
We can model a hit as a biased coin flip. If a fencer is more skilled, they might have a 55% probability of scoring any given hit (heads). In a "first to 1 hit" match, they win 55% of the time. But in a 15-hit bout, the laws of large numbers help: the superior fencer wins 71% of the time. If it's best-of-3 legs (to 15), the probability jumps to 79%.
2. Why Epee is So Hard
One of the main differences between the weapons in fencing is their rules. Sabre and foil both have what's called the "right of way," which means that only a single fencer can be awarded a hit at a time. It's up to the referee to decide who that is, if both fencers hit their opponent at the same time. This is done based on who had the initiative, e.g. starting the attack, taking the last parry etc. This is kind of like having the ball in football. To score, you need to have the ball. If your opponent doesn't have the ball, they can't score, and to score they need to steal the ball first. That's also why we talk about fencing "phrases," as the exchanges between fencers become almost conversation-like.
In Epee, the ref doesn't have as much of a say. Fencers can hit each other simultaneously and one point is awarded to each. That's basically as if each football team had their own ball. This, combined with a whole-body target area, makes Epee's risk management incredibly complex. You don't only have to protect your torso; there's also the feet, the hands, the head etc.
There's also a significant "lead advantage" in Epee. Once ahead, you can minimize risk and force your opponent to take vulnerable attacks. It’s like "parking the bus" in football.
3. Lead Dynamics in Epee
If we model this "lead advantage" (e.g., fencer 2+ hits ahead gets +2.5% win probability), the underdog's win probability in a 15-hit match jumps from 29% to 33%.
My simulations show that increasing the number of hits doesn't stabilize results much in Epee. The only way to make outcomes more reliable is to increase the number of legs (sets).
Separating the scoring into legs would also add excitement. Tennis wouldn't be as exciting if it wasn't split into sets and games that create mini-dramas throughout a long match.