Participation is the value players derive from playing in the tournament.
Unlike fairness, participation has a simple and obvious metric: the number of games played. Thus, a 16-team single elimination involves playing 15 games or matches, and so has a participation score of 15. The double elimination tournament gets a score of 30 involves 30 games (or possibly 31 – more about this in a future post).
This simple and obvious measure can be refined in any number of ways, most of which are more complicated and debatable. Here are some additional factors that might plausibly improve the simple count of games:
- It’s more fun to win than to lose. The participation score for each individual player is adjusted accordingly – rather than simply giving both players +1 for each game, give the winner +1.2, and the loser +0.8;
- It’s more fun to play an opponent that’s of about the same skill. +1.2 for even pairings, +0.8 for lopsided pairings;
- It’s more fun to play close games. +1.2 for squeakers, + 0.8 for blowouts;
- It’s particularly fun to score an upset. +2 for the upset winner, +0.2 for the favorite who lost unexpectedly;
- It’s more fun to win money (or trophies, or master points, etc.) +2 for the winner in games that secure some reward, but only +0.2 to the chagrined loser);
- After a while, players get tired, and additional games are less enjoyable. +1 in rounds 1-4, but +0.8 for rounds after that;
- It’s more fun to meet new opponents (and irritating to have to play rematches). +1 for new pairings, but only +0.5 for rematches;
- It’s fun to win elimination games but no fun to lose them. An additional +0.5 for the winner, but -2 for the loser.
This list could go on, particularly if you start to consider particular kinds of tournaments, and particular contexts. Imagine, for example, that you’re a cruise director organizing a shuffleboard tournament. In that context, the overriding consideration might be making pairings of players who will enjoy each other’s company. It might be a stroke of genius, for example, to set up a game between a happy retired couple celebrating their 40th anniversary and a pair of love-struck newlyweds – the former will be reminded of a happy past, and the latter given a vision of a happy future.
For the most part, I think tournament designers can be forgiven for taking the position that most of these factors, however plausible, are things that they simple shouldn’t be responsible for. But some of these factors can, and really should, be addressed in a tournament’s design. Next, I’ll look at one of these: the avoidance of repeated pairings.