Archery tournament design

Over the last couple of days, I switched on the TV in order to “jinx” two of India’s more promising archers in their respective games at the Olympics. On Monday evening, I switched on the TV to see R Banerjee (forget his first name) lose a close game in the round of 32. Yesterday, I watched Tarundeep Rai shoot well but still get well beaten by an absolutely in-form guy named Kim (from Korea, where else?). As I watched these matches, I was thinking about the nature of competition in archery.

Archery is a fundamentally single-player event. You are competing against yourself, and how well you do is not supposed to be affected by how well someone else does. There is no direct opponent you are playing against who tries to prevent you from scoring. In some ways, you can consider it to be similar to running. The only element of competition is the pressure that is exerted upon you be opponents competing simultaneously. In this context, it is indeed surprising that the archery event has been designed as a one-on-one knockout, like you would expect for a direct-opposition sport like tennis.

An event directly comparable to archery in terms of fundamentals is shooting – there again, there is no impact of one player on another’s performance but for the pressure exerted by means of simultaneous competition. Shooting, however, goes the “races” (running/swimming) way by means of having heats where only one’s absolute performance matters in terms of score matters (there is no limit on the number of the number of finalists from one heat; the best 8 or 10 participants across heats make it).

Then why is it that archery, which is fundamentally similar to these sports in terms of fundamental concepts, relies on head-to-head competition, and that too with no repechage? Yesterday, I watched Tarundeep Rai come up against an absolutely inspired Kim – Kim was in such imperious form that irrespective of how well Rai would have done he wouldn’t have qualified. Rai didn’t play badly, “against” any other opponent or on another day, he would have definitely done better. In a “direct combat” sport (such as tennis), one can point to the luck of the draw and similar matters. But in a distinctly non-combative sport such as archery why should artificial tournament standards be designed and that extra bit of luck be introduced?

I hope the archery administrators realize the stupidity of the curent format and move to one that is similar to what we see in shooting today.

What Should Mexico Do?

If Mexico and Uruguay draw their last league game, then both of them go through to the second round irrespective of what France and South Africa do. However, on account of a better goal difference, Uruguay will qualify as group winners and face the second-placed team from Group B, while Mexico will qualify second and meet the Group B winners, likely to be Argentina.

Uruguay’s option is clear. Play for a draw. If Mexico go for a win, Uruguay should just sit back and try hit back on the counterattack (and in terms of players and style, they are very well equipped for that). Simple case of getting men behind the ball and putting gaaji.

Mexico’s strategy is not so straightforward. The “greedy” thing to do would be to play for a draw, in which case they will most likely end up facing Argentina in the second round (if you remember, Mexico went out last World Cup by losing to Argentina at the same stage). On the other hand, if Mexico beat Uruguay, they will top Group A and meet a potentially inferior team (Korea or Greece) in the second round.

As mentioned earlier, if Mexico go for a win, Uruguay will simply defend and play a counterattacking game which they are good at, so I don’t know if they are going to go for it.

Thinking about it, it comes down to Mexico’s payoff function. I’m sure their payoff is an increasing function of how far they progress in the tournament. However, we should be able to identify one particular “jump” in payoff – some kind of a discontinuity, where the payoff increases considerably for one additional round of progress in the tournament.

If this “jump” is for the second round, Mexico can afford to put Ranatunga Principle, get a peaceful draw against Uruguay and claim their “jump reward”.

If the “jump” is for the quarter-finals, however, then Mexico will want to take the risk at this round in order to get themselves easier opponents in the round of 16 (I’m assuming here that Mexico consider Korea or Greece as much easier opponents than Argentina).

If the “jump” occurs further down in the tournament, I think there is way too much randomness about their potential quarterfinal opponents (especially given the fuzzy results in Groups C and D) and opponents as hard as  (or harder than ) Argentina cannot be ruled out. Nevertheless, they would rather face one tough opponent than two (and I’m assuming here that no team is significantly “harder” for Mexico than Argentina) and so they should put fight to avoid Argentina and thus go for a win.

Considering that they have reached the Round of 16 with reasonable regularity in the last few World Cups, I presume that their “payoff jump” will occur later in the tournament. And based on the above reasoning that means they should go for a win against Uruguay, so that they can try avoid Argentina.

And it is on this thin thread that the French are hanging their hopes (though first they need to thulp South Africa, no easy task).