A quiz first. How many possible combinations of matchups do you think there are, if you have eight people, who want to play two doubles games of, say, tennis, concurrently? So you have two courts. And if you have Players A, B, C, D, E, F, G and H, AB vs CD and EF vs GH are one such combination. AD vs CG and BE vs FH are another. Just have a rough guess. I don’t know if this would help, but if you only have four players and one court, the answer is three. For Players A, B, C and D, AB vs CD is one, AC vs BD is another and the remaining one is AD vs BC.
You may know already how to work it out generally. That’s a mathematical challenge you might like to tackle. To me, it was certainly a challenge. Thought about it for about a week, or maybe two.
Maybe I’ll give you a multiple choice. Is it
- under 20
- between 20 and 100
- between 100 and 1000
- more
The correct choice is 3, or 315 to be precise, which may or may not surprise you. So from one court with four people to two with eight, the number jumps from three to about a hundred times as many. So next, you guessed it, what’s the number if it is three courts with twelve people? The answer is a bit more than 150,000. This may well surprise you. For four courts with sixteen, it goes over a two hundred million. The point is the number goes up very, very sharply.
This ‘complexity’ –as a technical term, how the number grows with an input– is so large that no conceivable amount of computer power could handle within reasonable time. Probably ok with three courts. But certainly not with 20 courts with 80 people (the number of courts in Wimbledon, by the way). People sometimes say, given some complex calculation, well, that’s complex, but probably a super powerful computer can, or will in the future be able to, solve it in a minute. Not always true. There are issues which simply cannot be solved no matter powerful a computer becomes, and this seemingly simple matter of doubles matchups is one of them.
You basically need to skip most of the calculations to do this in reasonable time. In fact many so-called ‘algorithms’ are about how to skip steps in a complex problem, cleverly enough not to jettison ‘the baby out of the bath water’.
Well ‘reasonable’ of course is subjective. Big tech companies spend weeks or months on ‘training’ of models which they think is reasonable. In my app, ‘goodMatches’, I set a minute as its limit, realising how long a very small amount of time can seem when you’re using a mobile app, particularly on the move, or in this case, on court. This has been, and is, certainly a big challenge, given the quality of matchups pursued here. Random matchups are easy, that’s what you usually get from a ‘similar’ app. The current limit of 16 people is a result of this consideration. You should get good enough matchups well within a minute for 16 (and this wait only happens once at the beginning, or when you change the players).
So the lesson so far is, random matches can be made quickly, but good ones cannot be: pun intended, think how long it might have taken to find your partner! I’m very much aware however that on a club level, you would want to handle more players, more courts. It’ll improve: in terms of ‘how to cleverly skip unimportant stuff’ to save time without sacrificing quality. So watch this, or AppStore, space!