Sport competition is based on risk. In any sport there is some element of risk. Ice fishing – the ice might crack and deposit you in freezing water where you can die of hypothermia. Trap shooting – a fault in your gun might cause it to explode in your face. The 400 meter run – you could trip, fall, and break your leg. The 400 meter relay – bad judgement or faulty technique at the baton pass could cause the baton to drop. Sumo – in your charge off the shikiri-sen, your opponent might do a hanka, sidestepping to pull you down with hatakikomi. Baseball – you might swing at and miss a pitch that you should have let go for a ball. Football – you could call the play the other team was waiting for, and get sacked 20 yards behind the line of scrimmage. And the list goes on.

The range and probability of bad outcomes varies in each sport based on the rules and customs of the sport, the surface on or the medium in which it is played, the equipment used, whether the sport is outdoors or indoors, the level of the contest, the condition of the athletes, and the athletes’ willingness to press the limits of their potential performance. Bad outcomes themselves fall into two broad categories, (1) physical injury or sickness and (2) failure to meet the athlete’s goals for the event. And bad outcomes fall on a continuum from horrifically bad to mildly disappointing to – believe it or not – quite satisfying. It depends on the realism of expectations and whose goals you are considering. Only winning two bouts, but scoring on every opponent, in your first ever local unclassified fencing tournament might be disappointing to a fencer who thinks the world of himself, but at the same time be very satisfying to a trainer who knows that winning one bout or getting touches on all opponents is a very respectable first time out.

The classic formula to determine risk is:

risk = probability of an event happening X the impact if it does

Thus, when I step forward in an advance (the event) I know that my opponent attacks on advances 10 percent of the time (the probability) and that the attack will be successful adding a touch to her score (the impact). In this case, these is a 10% chance of the opponent scoring on my advance step.

risk = .10 x 1 = .10 (or 10 percent)

I am going to put a caveat in for the mathematician who is reading this. This is not a completely accurate statement because the risk is actually that the opponent will score .10 touches on my advance, but operationally it is a lot easier to understand if we express this as a probability of being hit.

But if the opponent only scores on half of those attacks because of a jerky lunge with poor point control, we have to further refine the formula:

risk = probability of an event happening X (the impact if it does X the probability the opponent can deliver that impact)

In this case the computation is:

risk = .10 x (1 x .5) = .05 (5 percent)

Now I know that if I am going to step forward there is a 10% chance the opponent will attack, but only a 5% chance the opponent will attack and successfully hit me.

The question is whether I am willing to accept a 5% risk of being hit on my step forward as I advance? If I am alert and ready to parry and riposte, I am under almost all circumstances ready to accept that risk.

And here is where the numbers become important. I have to know what my tolerance for risk is in a wide variety of situations. For example, a touch has been scored, making it 4-3 for me, with 4 seconds left in the bout. Am I going to attack in that situation, especially because getting to 4 has been difficult (my attacks have only scored 15% of the time) against the opponent’s strong parry-riposte that scores 30% of the time? You don’t even have to do the math – I am ahead, I have a 30% chance of getting hit and only a 15% chance of hitting. Absent any other factor, a full attack seems like a very risky proposition. If the opponent scores, we are going to go into overtime, I may lose the coin toss for priority, and I will have to continue to fight a difficult opponent who is close to even with me in tactics. I am going to be risk averse in this case, protect my lead by avoiding the opponent’s efforts, and run out the clock.

The opponent, however, has a different situation. If she does nothing, she will lose. She has to score to force it to overtime, where she may win priority and has a reasonable chance of getting the first touch if she does not (she has scored 42.8% of the touches so far in the bout). Under these conditions, with little time remaining, she becomes tolerant of any level of risk in the attempt to score.

I have seen several examples of risk acceptance in this situation in one or two touch difference bouts with 5 seconds remaining in Olympic and World Championships bouts (4 by Chinese women epee fencers and 2 by a stateless male fencer). On the command fence, the fencers simply ran full speed at the opponent with the arm extended – reminiscent of the old days when sabre fleches ran the length of the piste. You would think that this is a very risky tactic. Risky yes, desperation yes, but of the 6 instances, 2 scored hits – a demonstrated 67% chance of failure or a 33% chance of success.

Given the average math skills in the United States, the limited amount of time available for decision making, and the stress of the bout, it is unlikely that you will do the math to use the formula to assess the risk of all of your actions on the strip. However, and this is really important, you have to learn to identify the approximate risk of situations, decide how much risk you are willing to accept, and work constantly to make good tactical choices in these situations. Not doing so carries with it significant penalties. I will close with an example that happened in the Y14 event in a North American Cup several years ago.

The score is 3-3 at the end of regular time. The Salle Green fencer wins priority. And on the very first phrase of the 1 minute he attacks, the opponent parries, ripostes, and hits. The bout is over in under 10 seconds, with a loss to our side. Given that overtime is almost always a moderate to highly risky situation, I asked the fencer what his tactical decision making was in this case. I will never forget the answer “I just wanted to get it over.” For this fencer, the risk was in continuing to fence. And he selected an approach that resulted in a successful outcome in avoiding that risk. It is hard to argue with success, although this was hardly the success I was hoping that he would have.