#### Introduction

Ranked system in Gwent: The Witcher Card Game is a modified ELO system, where peak scores rather than current ELO (or using Gwent terms – MMR) determine the position on ladder. Starting factional MMR (fMMR) for is equal to 2400 for each one of 6 factions.

While it is obvious that in temporary (rather than peak) MMR system a player with 50% winrate would achive no more than his starting rank on average, with Peak System the situation is less clear. In this article we try to answer basic question: what Total MMR is achieved during ‘ladder random walk’ where the probability to win each game is equal to 50% with draws excluded.

#### Methodology

There is a consensus amongst pro players that ELO system with **K=15** resembles MMR system used in Gwent very well. Then **net fMMR gain/loss** for every game against player at the same fMMR is equal to **7.5**.

For the sake of simplicity we assume winrate does not depend on rating and every game is played against an opponent at the exact same fMMR level. Obviously the average peak MMR would depend on the number of games played with each faction.

While many statistical quantities could be derived from subsequent simulation, we go straight for total MMR scores. Those are calculated in exact same way as in Gwent: only Top4 factional scores are included. Three scenarios were considered:

a) 6 factions played; 100 games per faction (all-around grind)

b) 6 factions; 25 games (extended placements)

c) 4 factions; 25 games (minimal placements)

Monte Carlo simulation with 100k players sample. Cases b) and c) were derived from a).

#### Results

All-around grind: **9901 MMR** (**2475** per faction)

Extended placements: **9744 MMR** (**2436**)

Minimal placements: **9706 MMR** (**2427**)

#### Conclusions

The first and most important conclusion: in the Peak System the total fMMR score of a random walker (or ladder monkey if you prefer more spicy wording) is already **~100MMR higher than the base line (9600)** after minimal placements. Choosing more than 4 factions (extended placements) gives a slight boost: **~38** MMR on average. Even for a random walker the grind has some impact as could be seen from comparison of *All-around grind* with both *Placements* scores.

Now its time to juxtapose these estimated values with Top500 cutoff reality. Let’s use 480-500 place results from Gwent Masters Website for the most recent season at the moment I type this paragraph.

Cutoff depends mostly on season length and also fluctuates with Gwent popularity. Let’s asumme 10k MMR is the cutoff value for the sake of comparison. Obviously, this level is absolutely out of reach for minimal and extented placements. All-around grind could lead close to 10k, with most ~~monkeys~~ players finishing below cutoff, but a few actually passing it!

It is worth noting that all-around grind is not even the optimal monkey strategy. The correct one would be always choosing the Top4 faction which is closest to the peak. This is a topic for another article though…

Thanks for reading and be sure to get more than 9.7k MMR in placements every next time! ðŸ˜‰