Existence and connectivity

Connectivity is a very simple, but also a very important concept for managing an equTournament or equRanking effectively. A ranking's existence and credibility depend on how well the competitors are connected. What this means will be explained in this guided tour.

Please create a new tennis tournament of the ALPHA type, enter a match of 6:4 for A vs. B, and submit it by clicking the box in the fourth column.

In an equRanking, every match result represents the relative "strengths" of the opponents. When you click the Update Ranking button the equRanking translates all of the results into ranking points, creating the ranking that reflects the performances of the competitors as precisely as possible.

To make it easy to read, an equRanking is scaled in such a way that a 1,000 point difference in ranking points represents the proportion of won/lost games of 60% to 40%. This representation holds only in 0:0 irrelevant sports like tennis, volleyball and squash, and is different in 0:0 relevant sports like football, ice-hockey and basketball. Since competitor A and competitor B had exactly this proportion of won/lost games in their match (i.e., 60% to 40%), then the difference in their ranking points should be 1,000 points. Please click the Update Ranking button to confirm this.

Please submit a second match of 7:5 for B vs. C. Since the strength of A can be measured in relation to the strength of B, and the strength of C can be measured in relation to the strength of B, then it should be possible to compute the ranking list of all three players. Please click the Update Ranking button again.

Now please submit a third match of 6:3 for D vs. E.

It is possible to measure the "strengths" of D and E in relation to each other, but it is not possible to measure their strengths in relation to A, B or C because neither D nor E has had any opponent in common with either A, B or C. Therefore, it is impossible to compute the complete ranking list and more matches need to be played. This is exactly the message you will receive if you try to upgrade the ranking at this point. Please click the Update Ranking button and the following message box will appear.

The second line in this message box explains why the program was unable to compute the ranking. The message says that participants are not connected. The best way to show what this means is use a graph to represent the matches. So far, we have used a table representation of the tournament matches, where the first two columns contain the names of the opponents and the third column contains the score. But tournament results can also be represented graphically, where the participants are represented by nodes and matches are represented by arcs.

In the graphical representation of the aforementioned tournament matches we see that the participants are divided into two disconnected groups: A-B-C and D-E. Since there was not a single match between participants from both groups, then we don't have any information about how strong these two groups are in relation to each other. For example, both D and E can be significantly better players then A, B and C but we cannot know whether this is the case until at least one of them plays at least of the other group of players.

In short, the ability to compute the ranking depends on whether all the nodes(participants) are connected by arcs(matches). If there exists a chain which connects all the nodes then it is possible to measure the relative "strengths" of all the competitors and an overall ranking will be possible. If such a chain does not exist, then it is impossible to compute the ranking and more matches will need to be played. To determine which matches should be played, you can use the Suggest Singles dialog.
Please go to: Main Menu > Tools > Suggest Singles.

To connect both groups there must be at least one match between players from each group. If you decide that in the next match, C should play against E, simply double-click on C and then double-click on E in the Suggest Singles dialog box. Their names will appear in the tournament window.

This match will connect both groups. Please submit a result of 2:6 for C vs. E. Now, from the graphic representation of this tournament we can see that all participants are connected, and that it becomes possible to compute the ranking. We call this Connectivity.

Please click the Update Ranking button to see the current ranking.

Connectivity is a very handy and easy to understand concept when it is presented visually. It is also an indispensable requirement for the possibility of creating a ranking. When you run a competition and you need to get the initial ranking as soon as possible, all you have to do it is to make sure that all competitors get connected as soon as possible. It is always possible to produce the initial ranking after two rounds of matches. For example, assume that there 8 competitors in the competition. In the graph below the dark-coloured arcs represent matches of the first round and the light-coloured arcs represent matches of the second round.

You may find that a "list-like" graphic representation makes it easier to visualize the initial two rounds of the tournament. Below is an example for a tournament with an odd number of participants.

In each graph you can clearly see how the Connectivity required for generating a complete ranking is only achieved in the second round of matches. But while Connectivity is necessary for making a ranking possible, two rounds of matches may not be enough to produce a credible ranking. To produce a more credible ranking more matches need to be played and Connectivity is a major tool to understand what makes a ranking more credible.