Gwent for Geeks: Efficient Laddering

Posted by lerio2 May 25, 2020 in Uncategorized

Introduction

Welcome, Wanderer! After a month break we arrive back with “Gwent for Geeks” cycle. This time we will investigate how to play efficiently on pro ladder. We won’t here tell you anything on deck preparation or improving your gameplay. Instead we would try to answer the question: when to play to be efficent? Is playing early in the season a good idea, or rather you should go for a late climb? Or maybe playing uniformly all season is the way to go? We will build a simple model to answer these questions! Have a good reading!

What is Pro Ladder?

Arriving at the Pro Ladder a new player often lacks a lot of information on how it works, so we will pursue here short introduction. To achieve Pro Ladder player status you need to climb up to rank 0 and accept the rules in your settings. Players on the Pro Ladder are ordered with respect to MMR (Matchmaking Ranking). Higher MMR means higher position. MMR is a simple sum of 4 best faction results – fMMRs (fMMR = faction MMR). As the name suggest, matchmaking ranking is used for pairing players starting pro ladder lobby. However, what is important for pairing is the current fMMR of the faction you play, not the total one! 

Faction MMRs

Faction MMR is adjusted every time you win/lose/draw a game on Pro Ladder with a particular faction. Matchmaking is always done based on your current fMMR, but for rankings the peak result counts. The peak is simply the highest score you achieved during the season. There is a threshold of 25 games needed for the peak to be 100% included in the total MMR. For example, if you played 20 games, only 20/25 = 80% of your peak will be included in your ladder score (MMR). While going for 25 games on every faction before further grind is not a necessary habit, pro players often do it – achieving 25 games on 4 main factions is called placements

Rating changes and rating system

There is no official information on rating system used in Gwent when it comes to matchmaking and rating changes after each game. However, there is common agreement between pro players, based on observations and studies, (thanks to Team Aretuza and Team Leviathan for this information) that ratings change according to ELO system with K=15. At the Pro Ladder season start rating change in each game would be in the range of 7-8 points, as the rating differences between players are very small. However, later in the season it is possible to get +3 points/lose -12 points against much lower rated player.

Ladder model and its assumptions

We will go here into the details of the model which would subsequently be used for the ladder simulation. The model could be used for various studies – if you would like to see something particular or have a good idea for a study – do not hesitate to hit me up on Discord!

The origins of this study root back to the Season of the Elf, when Xiwer was fighting for Top16 position, but unfortunately ended up on 17th position.

Assumptions

1) Player skills are rated (0-10); skill difference determines chances of winning a game, e.g. 10 vs 0 has 100% chances of winning the game, 10 vs 5: 75% and so on.

2) MMR=fMMR – we go one dimension with a single faction

3) fMMR after each game changes in accordance with K=15 ELO system.

4) Pairing is not random but also not deterministic – rating difference is minimized in a stochastic way

5) Season is composed of N timeslots. During a timeslot player may play or not. There is ‘activity’ variable associated which each player, which stands for probability of playing in every single timeslot.

6) We assume Gaussian distribution of the skills at the start. (μ=5, σ=1.5)

7) It is possible to add/remove players at any timeslot. The graphs will show results for open ladder – each timestep the number of players increase.

8) We trace achievements of four players using different strategies (skill=10)

  • Xiwer plays at the start and stops at 1/3 of the season
  • Ximer plays in the middle (1/3 to 2/3) of the season
  • Wixer plays at the very end (2/3 to end) of the season
  • Mixer plays uniformly (randomly) during whole season so that it roughly sums up to 1/3 of timeslots.

 

9) Parameters.

  • Timeslots: 240
  • Activities of other players: 50%
  • Number of trials (independent season runs for each player): 100
  • Added players: 10 per timeslot, μ=3.5, σ=1.2

Results

Conclusions

The instant conclusion from the charts shown above is that Wixer (player grinding only in the very last third of season) is in clearly superior position in every aspect: highest average winrate, highest peak MMR score, averagely weakest and highest rated opponents. The final third of the season is the most important one. If you are going to challenge top spots, or want to remain in Top500 with least possible effort – make sure to save time for the last week of the season.

On the contrary, Xiwer’s way is obviously the hardest and least efficient. The cause of this effect is obviously underestimated opponents average fMMR. Xiwer plays against better opponents, who at the same time have lowest average rating.

Ximer is the man of the middle. His opponents are significantly higher rated than Xiwer’s, but not with too much lower skill. Mixer is slightly weaker than Ximer in all stats. The only exception is winrate, where Mixer is clearly weakest out of all players. It is hard for us to attribute it to anything; in fact Mixer’s opponent were averagely less skillful than Xiwer’s.

How does this model transfer to reality? It explains a lot Tailbot’s and Kolemoen’s attitude towards laddering – never spamming games early in the season and grinding hardly only in the very last week. However, it has to be said, that playing last days of the season in practice is not as easy as in theory. Players usually exhibit highest focus and play most serious decks in spite of being ‘averagely less skillful’.

See you on ladder!

lerio2

Patreon

Writing in-depth Gwent articles is fun, but time consuming. If you like ‘Alphabet’ or ‘Gwent for Geeks’ cycle or other articles, and fancy to support my efforts – here is the way to go: https://www.patreon.com/lerio2

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