Binary and continuous sporting events

Long jump and high jump are fundamentally different - one has "continuous" outcomes, while the other is "binary".

When it comes to Olympic disciplines, there is a very fundamental difference between long jump and high jump - the former is a “continuous” event, while the latter is “binary”. I’m talking about the outcomes of a single jump here.

Also, for the purposes of this post, I’m only talking about non-adversarial sports, such as jumps, throws, weightlifting and so on. In these sports, different competitors takes turns to compete, and then their respective “scores” at the meet are tallied up to declare a winner.

Now that the disclaimer is out of the way..

The outcome of a long jump is a real number, truncated to a particular number of decimals. It is determined by measuring the distance from the line (from behind which the contestant should jump) to the first point beyond the line where the jumper lands.

So Bob Beamon jumped 8.90m (in the rarefied high air of Mexico City). Mike Powell jumped 8.95m. You see, real numbers rounded to the nearest 5 cm. When they made their jumps, this number that they jumped was recorded.

High jump doesn’t work this way. Yesterday I was watching this YouTube video on Javier Sotomayor (the only high jumper whose name I can remember between Dick Fosbury and Mondo Duplantis since Dick Fosbury). In high jump, the jumper has to pre-decide a height of bar that he/she wants to scale. And the outcome of that jump is binary - either you make the jump or you don’t.

If you think about it, the fundamental strategy between “long jump” (also includes all discus, hammer and javelin throws, and shot putt) events and “high jump” (also includes pole vault and weightlifting) events differs. In both, you are optimising for different things.

In long jump, in each jump you just go give it your all (while making sure you don’t overstep the line, or foul in any other way). There is no pre preparation required. Before you jump, you don’t need to set yourself a target. You just go there and jump.

In high jump, you need to set yourself a target. And so game theory gets involved - you want to set targets that you can achieve, but you think not enough of your opponents will. So apart from being a physical game, it also becomes a mind game.

And once you have set yourself a target, which is where the bar is placed, your performance is now entirely binary - you only need to clear the bar. Whether you clear by a millimetre or a metre makes no difference. There is no bonus to outperformance here, but a huge downside to underperformance.

In a way, if you think of it, it is like playing bridge. While bridge does reward overtricks (making more tricks than your bid), the reward is low enough that you are encouraged to bid as high as possible (there are discrete steps, though, such as game, slam and grand slam). Not making your bid is severely punished, though.

I was thinking about this difference between high jump and long jump events when I learnt about the javelin throw finals earlier this week. Arshad Nadeem threw a nearly impossible 92.97m - over 3 meters more than what Neeraj Chopra in second place threw.

Given their relative reputations before the event, this kind of a relative performance would be absolutely impossible in a high jump style event. If javelin throw were like high jump. then both competitors would have typically set a “safe” second throw (which they would be confident of beating), and then a “stretch” third throw - with the outcome determined by who managed to actually do their stretch. A 3m margin would never occur in such a circumstance.

I realise the only “sporting activity” I do on a regular basis (what is called “powerlifting”, though is more about strength than power - ironically, Olympic weightlifting is fundamentally a display of power!) is more of a long jump kind of activity than a high jump kind.

Before every session, I need to determine for myself what weight I will go for that day - do I deadlift 160kg or 165 or 170 or 180. And once I have loaded my weight on the bar, it is about making the lift (I don’t do this competitively - it is for my own satisfaction). So there is no overperformance. But high chance of underperformance (not making the lift, or not making enough repetitions of it). Consequently, I think I’m conservative in what I lift, and not pushing myself enough.