Introduction
Welcome Wanderer!
Five months have elapsed since ‘A Geek Guide to Match&Tourneys Probabilities‘ article has been released. Since then we have witnessed two small changes in Gwent Masters Qualifiers format. First one was increasing the number of players in Day2 of Top64 qualifier from 8 to 16. The second one is very recent – first two rounds of Top16 stages are played as Single Elimination (SE) rather than Double (DE). To denote mixed approach we will use abbreviation SE+DE. Such change was based on results of a poll amongst Top 64 players.
In this article we will analyze in depth qualification probabilities as a function of a single game win probability (pW). This should not be confused with match (consisting of many games, like Bo3/Bo5) win probability. If you need a deeper introduction (methodology…), or would like to compare how random Bo3/Bo5 matches are, i refer you to the original article once again.
Top 64 Qualifier
Top 64 Gwent Qualifier consists of two stages now:
Day1: Swiss 6 rounds, Top16 qualifies for the second day
Day2: Top16 SE+DE, winners of winners and losers brackets qualify for Open
Swiss stage
Assumption: at least 4-2 score is needed for qualification. In the ideal scenario, when no one dropped the qualifiers, 9/15 players with 4-2 score would qualify. The external correction of multiplying by 9/15 is made, so that 1/4 chances are achieved for pW=0.5, as expected.
(DE + SE)16 Stage
Orange and Green lines are overlapping due to the simple fact, that SF loss and Final loss routes are same length now.
Top 16 Qualifier
The format is now identical with 2nd stage of Top64 Qualifier. Let’s just compare old DE with new DE+SE format then.
SE + DE format shortens and simplifies competition by a lot, while obviously making it more random. It should be noted that the more competitors ‘skill’ is diversed, the less appropriate SE+DE is. For pW=0.6 the difference is about 5%.
Comparison and total chances
Let’s compare total chances in Top16 and Top64 Qualifiers after revision.
Total(Season) label refers to chances during one season (Top16 + Top64), while Total(Open) includes full set of 4 Qualifiers during 2 seasons cycle. As could be seen, even small increase in pW rockets total chances in the long run: +0.05 => +20%. The observation that Top16 Qualifier gives 2x better chances than Top64 at pW=0.6 still holds
Time efficiency / skill rewarding
With Double Elimination Top16 phases lasting in the extreme cases about 15 hours, the topic of time efficiency got highlighted, so we would like to investigate it a bit in qualitative manner. In the old DE system, worst case number of Bo5 matches was equal to 7 during Top16. In DE+SE it is only 5 matches.
In Top64 Qualifier there are 6 Bo3 matches and again 5 Bo5 in playoffs. A Top16 player must be ready to play the total of 16 matches.
Let’s assess if the current system is efficient (skill rewarding). We will do it by comparison with naive system, where 15 Bo5 matches are played amongst Top64 players. This would be numerical experiment, where pairing is done in a stochastic way between players with similar number of points. We will check what are chances of claiming Top8 spot for various pW.
Graph above shows qualitatively how much information is lost. It is definitely a considerable amount. Chances of outstanding player with pW=0.6 are ~15% lower in the current system than in the reference one, in spite of playing one Qualifier in the limited field of Top16. Reference model could also help a bit to determine how many matches are needed in general to achieve low enough randomness of outcome.
I honestly thought these numbers would be higher, but I don’t see any blunder in computation so far. The number of matches seems to be about optimal – however it should probably be more dispersed in time, as many players suggest.
Conclusions and opinions
As Gwent Masters Season 2 comes to an end, concept works on the next one are ongoing. I hope this article will provide some strict, mathematical insight to the community.
Let’s go once again through the probabilities for an outstanding competitor (pW=0.6). In Top64 Swiss qualification chances are ~50%, which means a lot of frustration every second time. If passing through Day1, second day chances are about ~35%. Combining these, we have ~18% total chances. It translates to: no matter how good you are, don’t expect too much – just play and maybe the fortune will be with you.
Approaching Top16 Qualifier, the chances are obviously ~35%. This leads to ~47% combined in a season, and ~73% total to qualify for an Open (i’m lazy and read these values from graph just like you do). Consistency matters – particular Qualifiers are random, but in the long run any % of edge increases chances by a lot.
System composed of subsequent Qualifiers is considerably more random than corresponding League system with the same number of games. While League system is more skill rewarding mathematically, there are also of course other factors to think of in design process – these are beyond the scope of this article
Current time load seems to be optimal in general. However, particular Qualifiers used to be too intensive. Cutting the time will inevitably make qualification process less skill rewarding, so only more dispersed format could alleviate the problem.
The contemporary SE+DE circumvent does not do too much harm in terms of probabilities, but hardly could be viable in skill rewarding system. DE in fact was not much better – practical effect was similar, with nobody qualifying after losing R1 or R2.
The main problem is always the loss of information. Out of N matches, every one must be important and count somehow. No matter if in cup, league or other format.
Thanks for reading! Next article would be afterseason summary in the spirit of the last one. There is a bunch of very good scores on Pro Ladder now, so i am sure it will be exciting!
Written by: lerio2
