Round Robins

I want this blog to be about tournaments in general, not about one particular approach. There are many loose threads to be gathered in the discussion of elimination tournaments, which can, and probably will, keep tourneygeek busy more or less indefinitely. But it’s high time to open the conversation about that other basic form of tournament organization, the round robin.

Fortunately, the fundamentals are explained well in an unusually good Wikipedia article: Round-robin tournament. I’ll add round robin resources to tourneygeek at some point, but for now I’ll skip the basics. This first post will introduce round robins and relate them to the “FEPS” framework – fairness, efficiency, participation, and spectacle – introduced in four goals of tournament design. In subsequent posts, I’ll treat a few advanced topics that are not covered by Wikipedia or, as far as I know, anywhere else.

Looking at the four FEPS goals, there’s a lovely symmetry between elimination tournaments and round robins. The round robin excels in participation and fairness, while the elimination tournament shines in efficiency and spectator appeal.

Fairness

Fairness is a hallmark of the round robin. When everyone plays everyone else, a whole raft of possible biases disappear. There’s a lot of truth to the frequent observation that the round robin is the fairest kind of tournament.

But there are difficult fairness challenges that are characteristic of round robins, and these need to be acknowledged. They often stem from the fact that the positions and interests of the competitors change over time, and that can make the later fixtures in a round robin mean something very different from an earlier fixture between the same competitors.

For example, in the National Football League, it’s frequently the case that at the end of the season, one team has locked in its place in the playoffs, and can choose to rest its best players. This is hardly fair when the team they’re playing is competing for one of the last playoff slots against a team that earlier had to play the resting team when they were at full strength.

In extreme cases, one team may have a (real or perceived) incentive to lose rather than to win. It’s even possible to conceive circumstances where both teams think they’d be better off losing, though these are much less common in practice. Good tournament design tries to avoid these cases, but it’s not always possible.

There are also fairness implications for how round robin tournaments deal with ambiguous results, but that’s a complicated topic I’ll defer until I can give it its own post.

Efficiency

Round robin tournaments are inefficient – they consume lots of resources, and for that reason alone, the format is unsuited to many applications.

For a complete round robin, there need to be n(n-1)/2 individual matches, where n is the number of teams. That’s only six matches if there are four teams, but the number grows increasingly rapidly at the number of teams grows. Here’s the sequence for 2 teams, 3 team, 4, etc, up to 20: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190. This is the sequence of triangular numbers.

This inefficiency is not always undesired. For example, it does not grieve the English Premier League that they need 380 individual matches to complete a double round robin of the 20 teams each season. Each of those 380 matches is an opportunity to sell tickets and broadcast rights, and that’s basically the business they’re it. They don’t care that there are much more efficient ways to decide which is the best team in English football, or even to decide which are the best five, and the worst three, which is what they need to know to organize the next season.

Participation

Participation is, in many ways, the inverse of efficiency. A tournament with lots of games is one where there’s lots of opportunity to play. The 380 matches needed to complete an EPL season can be seen as highly inefficient, but it’s also highly participatory.

In many other formats, participation is skewed in favor of the more successful teams. Half the entrants in a single-elimination get to play only a single game. In sports like professional tennis, where single-elimination tournaments are the norm, the top players can be badly overworked, while the bottom players don’t get enough opportunity to play. In a round robin, everyone gets to play a lot. So round robins are a good choice where, as with recreational sports, giving everyone a lot of opportunity to play is the main goal.

Spectacle

Round robin tournaments can be fun to play, but they’re often dull to watch. Late in the tournament, individual matches often mean nothing at all in terms of the tournament result, and early in the tournament the interesting results can seem so far away that it’s hard to get excited about a match – you don’t know whether it will be significant to the ultimate tournament result or not.

Everywhere, those who make money by selling the spectacle of competition are discovering that there’s money to be made by using a single-elimination format to create particularly compelling matches. Everything’s on the line when the loser goes home. And so, even where there’s good sense in using a round robin format to ensure that there will be a lot of games to sell during the “regular season”, knock-out post seasons are being tacked on to the season so that there are a few more really watchable games to sell.

This makes no sense from a fairness perspective. A double round robin, home and away, is clearly the fairer way to determine, for example, the best basketball team in the Big 10 conference. But the same commercial motives that have caused the big 10 to grow to 14 teams have caused it to reduce the importance of the regular season until it’s just a way of seeding an exciting knock-out tournament at the end. In another striking example, the National Hockey League, which played 1230 games in it’s five-month 2015-2016 season, tacked on another 91 games in two months of the Stanley Cup Playoffs.