Tournament Analysis on the example of the WTC
I want to give you all an example how an event can be analysed and processed by Tournament Analysis. I will use the WTC in Herford for that. I use it out of several reasons. First many of you tried/did their own analysis and started discussions about it, at least it was so on the HE board. Second it was a really big tourney and should still be one of the five biggest even at the end of the year. As we have real actual data=results of the games played and final ranking and it is a team tourney we can show almost everything which complicates the analysis.
So how do we analyse a tourney?
If it and the results are on www.tourneykeeper.net. www.warscore.net, www.tabletopturniere.de, ranking.wfb-pol.org, the9thagerankings.com/#/events and on ecksen.ddns.net/eto/#/ than we copy paste it into a prepared file where the macros process it into the format we work with. If it is somewhere else (and we find it), we have to enter it in the right format per hand.
But what is the format we mostly work with? It is [(Number of participicants) – (Ranking reached) ] : [(Number of participicants) – 1 ]
And now I will explain it in English.At a small Tourney (6 participicants) with Place 1 SA, Place 2 VC, Place 3 SE, Place 4 ID, Place 5 KoE and Place 6 SA we will award the armies the following points:
Place 1 SA gets (6-1) : (6-1) =1
Place 2 VC gets (6-2) : (6-1) = 0,8
Place 3 SE gets (6-3) : (6-1) =0,6
Place 4 ID gets (6-4) : (6-1) = 0,4
Place 5 KoE gets (6-5) : (6-1) = 0,2
Place 6 SA gets (6-6) : (6-1) = 0
So as SA has both 1 and 0 points the mean would be 0,5 points.
What does what number mean? Which average number shows an army to be over performing and which number shows that the army is underperforming? Well, between 0,45 and 0,55 we consider armies to be balanced. Under 0,45 they underperform and over 0,55 they overperform.
So does in my example ID underperform? Well, I am sure we agree that one single army placement is a bit to few to say exactly how it really is. How much away the true value is assumed from the mean with a certain certainty (in our case 68 %) is measured with the certainty interval. It is calculate like that (here enter formula from arwaker).
With the certainty Interval we can see if the corridor of the assumed true value is inside the corridor of 0,45 – 0,55. It also explains why we don’t go for example for 0,475 - 0,525. How does the certainty Interval explain that? Well we need quite a real lot of tourney ranking results per army to get a certainty Interval which is under 0,05. Everything above would be broader then the corridor between 0,475 -0,525 and so allow us no interpretation.
That is one kind of analysis, but there are others, too. The more rounds are played on a tourney the more likely it is that an army shows it’s real strength. The more players are at a tourney the more likely it I that the pairing process brings players of equal skill to play each other. So naturally we have an additional calculation which takes the size and the length of a tourney into account. Later we compare both to see if tourney size and duration really have an influence and when which one. (Of course that only has a chance to have an effect if we have different tourneys with different size and duration.)
We also used to do some complex calculations to see what would be if every country had the same number of results (= we treated them equal in one analysis). But as that and analysis which tried to capture the competiveness of the different countries scenes proved to influence the Certanity interval in a way which made results uninterpretable, we dropped that.
The way we calculate the performance based on Ranking reached and the number of participicants naturally produces bigger differences between place 1 and place 2 depending on the number of participicants. That is different if we look at the actual games played. Those games always have a 20-0 / 0-20 matrix and so a 20-0 always brings 100 % or 1 and a 19-1 always brings 95% or 0,95. On that sort of analyse a totally balanced army would get an average of 10 points from it’s games. Here between 9.5 and 10.5 points average are the balance corridor. That kind of analyse can in theory potential produce more precise results than the ranking based, but we mostly get data for that analyse from big team tourneys and very few for smaller single tourneys. Later in this article I will go into more details how the difference between single and team tourneys influences our analysis.
What does that mean?
Well if we have the rankings reached by an army in a single tourney and the results of the matches it played, the result of an analysis based on ranking and the analysis of the actual played games natural will provide different numbers. But here again between 0,45 and 0,55 or between 9.5 and 10.5 points achieved on average (equalling 45 % - 55 %)… [Read More]