Documentation

Introduction to equTournaments and equRankings

The traditional tournament designs, like the round-robin or elimination systems, where invented at a time when the word "computer" did not exist yet. They had to rely on very simple ranking methods.

For instance, the simple accumulation of points is still the most common ranking method used in round-robin tournaments. All possible results are reduced to three basic outcomes: a win, tie or loss. Each outcome is rewarded by a fixed number of points, such as two points for a victory, one point for a tie, and zero for a loss. So the total number of points that a player accumulates depends exclusively on the number of victories, ties and losses.

The first significant innovation in tournament design dates back to the 1950s when Anton Hoesslinger introduced a ranking system called Ingo. He rejected the idea of rewarding a victory by a fixed number of points. Instead, Hoesslinger felt that the number of points rewarded should depend on the strength of the opponent. The principle is simple: The better player you beat, the more points you should get.

The first practical success for Hoesslinger's ideas came in the 1960s only, when a system called Elo, named after Arpad Elo, who made important improvements to the Ingo system, was introduced in the US Chess Federation. Computing the Elo algorithm requires the use of a basic calculator, as did Ingo. But while they were a great improvement over older ranking systems, neither system takes into account the points spread between the winner and the loser of a match.

Compared to this, equTournament and equRanking constitute a major step forward, moving from the era of the simple calculator to today's ubiquitous and mobile computing power.

equTournament and equRanking are a tournament and ranking system based on a set of equations carefully designed to produce the most accurate information possible about the performance of the competitors. It considers all available and important information, not just the strength of the opponent, but also the points spread of the results and/or the proportion of points won and lost.

Like all other tournament and ranking systems, equTournament and equRanking consist of two components:

It is important to remember that "ranking" is a general term that can refer to either:

For example, the ATP tour ranking in tennis consists of a rank-ordered list showing who is number one in the world, who is number two, and so on. To produce this list, a set of rules is needed, rules that clearly define what kind of tournaments are part of ATP tour ranking system, how many points the competitors are rewarded for winning a match at different stages of these tournaments, and so on. Practically all world sports associations have their own world ranking systems of which the world ranking list is a part.

The first major feature of equTournaments and equRankings is that they produce a very precise and informative ranking, that exactly:

equTournaments ranking is very different from any of the traditional ranking systems. It is far more informative and useful to players, coaches and audiences alike.

Here is an example to show how it works. Consider an ice-hockey tournament and two participating teams, the Penguins and the Seals. In traditional ranking, when one team - the Penguins, say - has more points than the other team - the Seals - this just means that the Penguins were able to accumulate more points than the Seals, nothing more.

Very often, the fact that one team has more points than the other does not even imply that the first team is necessarily the better one. Indeed, the Penguins could have accumulated those points simply by playing against weaker teams than those that the Seals played. For example, if the Penguins had 3 victories against the 3 weakest teams in the league they would have 6 points. Meanwhile, the Seals could have 2 ties and one victory against the top three teams, which would give them only 4 points, 2 less then Penguins. But does that really mean that they are the weaker team?

By contrast, in the equTournament ranking if the Penguins have more points than the Seals, this always means that the Penguins really are a better team than the Seals. On top of that, the point difference between them provides extremely useful information about precisely how much better the Penguins are than the Seals. Here is a typical equTournaments ranking:

Note first that the equTournaments ranking uses 4-digit numbers. This is because we discovered through many experiments that only numbers of 4 digits or more are able to convey the exact information we are looking for. Second, in equRanking, the leader always has 10,000 points, and all other teams are ranked relative to the leader.

Now, notice that in this particular equTournaments ranking the Penguins and the Seals have 200 points difference between them. This 200-point difference is a precise measure of how much better the Penguins are as compared to the Seals. The 200 points stand for 2 goals. What the difference basically means is that if the two teams play exactly as well as they have until now, the Penguins should beat the Seals in their next match by exactly a two-point difference.

So if in their next match the Penguins do in fact win against the Seals with a score of 4:2 why should this change their ranking and the point difference between them? Both teams did exactly as expected according to their rankings before the game so this ranking should remain unchanged after. And that's exactly what equRanking does: if the teams perform precisely as predicted, the difference between them in the ranking remains unchanged.

Results like these that do not change the ranking we call a real tie or equtie. In the example of the Penguins and the Seals all results such as 2:0, 3:1, 4:2, 5:3, etc., are equties, at this stage of the tournament or season. Even the score 110-108 is considered as equtie because the point-spread in this score is equal to two, and at the start of the tournament we decided to measure all results by the difference in the score, what is typical for ice-hockey. But this is not the only option. equTournament ranking is able to measure results in many different ways. It could be a point-spread, proportion of scored goals, or weighted mix of both.

An equtie is different from a traditional tie such as 0:0, 1:1, 2:2, etc. An equtie is far more informative than a traditional tie because it shows very precisely for each outcome whether it is a real achievement, an under-achievement, or on a par with previous matches for each team. If either of the teams does better than its equtie then it is achieving an improvement over its previous performance. We call this an equwin. For example, a victory of 3:0, 6:2, or 5:2, is an equwin for the Penguins at this stage of the tournament.

But suppose the Penguins beat the Seals with a difference of 1 goal only, say, 4:3. In the traditional ranking system the Penguins would still get another 2 points for the win and the Seals would get nothing, so that the distance in the ranking between them would increase. By contrast, in the equTournament ranking system such a victory would have the opposite effect. Since the Penguins won by less than 2 goals, they actually did worse than they had previously done and so they obviously don't deserve the 200-point lead they had over the Seals. So in equRanking the difference between them will actually decrease.

Since the 4:3 victory is in fact an under-achievement for the Penguins compared to their previous record, we call it an equloss.

The second major characteristic of equTournaments and equRankings is the flexibility of their ranking and scheduling components. In the traditional tournament design, the ranking and scheduling systems are inextricably connected to each other. For example, a round-robin ranking system works with one scheduling scheme only: it only makes sense if all participants play against every other participant.

It is much the same for the elimination ranking system, the most popular system for tournaments with large numbers of participants. It only works with one scheduling scheme: it starts with a draw to decide who plays against whom in the first round and after that, it is governed by strict elimination rules. As a result it is impossible, for example, for a match to be played between the runner-up and the competitor who lost to the champion in the quarterfinals.

equTournament and equRanking solve problems like these. The ranking and scheduling components of equTournament and equRanking are almost entirely independent of one another. The ranking only requires a simple and obvious condition of connectivity in the scheduling component to work properly. As a result, in equTournaments and in equRankings the ranking component can coexist with countless scheduling schemes. They give tournament officials the freedom to use whatever scheduling scheme best fits their particular needs, as well as the needs of the other major stakeholders in any competition: the fans, the media, sports associations, the competitors and their coaches.

See also: benefits for competitors, coaches, parents, fans, officials, associations.