Why two competitors can play as many matches as they want

One of the major advantages of equTournaments and equRankings is that they give a lot of freedom to tournament officials and players in scheduling matches. In other words, any two competitors can play as many matches between each other as they would like to. In equRanking, victories and ties are not rewarded with points. So, if competitor A wins ten times over competitor B, then A will not simply be rewarded with 20 points, for example. In an equTournament, the match result represents the relative "strengths" of the opponents. If A and B played ten matches, then all ten results would indicate how "strong" A was in comparison to B and vice versa. So, if A beats B with a score 6:4 once or A beat B with the same score,(i.e., 6:4) ten times, their comparative "strengths" would remain the same, as evidenced by the rankings below.

On the surface, it looks like it does not matter how many times A wins over B with a score of 6:4, since the ranking remains the same, but in reality there is a difference. In fact, the more times A beats B with the same score, the more trustworthy that score becomes, the more trustworthy is the relationship of their "strenghts", and the more likely the difference in their ranking points will be closer to 1,000. So, how is it revealed in the ranking?

Consider three tennis players: A,B and C. In their first match A beats B 6:4. In a second match B beats C with a score of 7:6.

Some confusion arises after the third match, when A beats C with the same score 7:6, that B had beaten C. Now the difference in the ranking points between A and B is no longer 1000 points, B goes up 399 points in the ranking, almost half way closer to A than before.

Player B is unsure how she can beat C, but have a worse score against A than C had. If B and A had the same result against C, then they should be of the same strength, or that B should be closer to the 10,000 points mark, than to 9,000 points. Consequently, B decides to take on A again.

At the same time, C thinks that she is almost as good as A, but somehow lost to B. Therefore she does not agree that she should be in 3rd place, and she also thinks that more matches should be played.

The next day, A beats B again with the same score, 6:4. So, it seems that yesterdays result between the two players was not a fluke. The players have extra proof that A should have beaten B by a score of 6:4 and that the difference in points between A and B should be closer to 1,000 point. This is exaclty what happens in the equRanking. Player B losses 149 points. (see below)

It so happened that C was stuck in a traffic jam, and A and B played a third match, and again A beat B with the very same result, 6:4. The players substantiated the prior results again, that A and B should have a 1,000 point difference. Player B then goes down in the ranking again, C falls as well, but not as much as B. Now, C is in second place, and B in third. Although the difference in points between B and C is small.

What would happen if A beat B with a score of 6:4, a hundred times? Player A would have 10,000 points, C - 9,119 points and B - 9,007, almost at the 9,000 mark. The more matches A and B will play with a score of 6:4, the more the ranking will reflect a 1000 points difference between the two.

In the above example, there is one more thing worth mentioning. As the ranking of B gets closer to 9,000 points, the ranking of C gets closer to 9,120 points. What is so special about 9,120 points? It is an average of 9,620 and 8,620, where 9,620 represents the performance of C in her loss of 6:7 to A, and 8,620 represents the performance of C in her loss of 6:7 to B. It is another indication of how fair and precise the equRanking is.