arena-simulation

Simulation insights :

Current rules

There is a big disadvantage for early attackers. The later you attack, the better

Frozen trophies

Frozen trophies aims at reducing are anihilating the late attacker advantage.

Divergence, or Panda effect, is the result of many player attacking the same target, which can start a day with a good trophy count and then gets downed under zero in a day.

The simulation shows divergences for Defender frozen trophies.

The simulation shows divergences also for Defender and Attaker frozen trophies

The simulation shows no divergence for Defender frozen trophies + average defense trophies 30 (Defenses of the day are averaged then multiplied by 30.)

Reduce defense losses by a factor

Simulation shows no reduction of late attacker advantage.

Match oponent with similar battle count

Simulation shows similar results whatever the hour you attack. Grouping your attacks works much better than spreading them according to simulation.

Simulation for AoW:legion arena

Do your own sim :

Clone me,
Install node.js,
Choose the scenarios by editing some values at the top of index.js
Start the simulation from the command line with

node index.js
Simulation is slow (1h for 3 seasons on my computer), run it in background
Multiple scenarios can run in parallel (launch scenario 1, edit file for scenario 2, launch scenario 2 ..). It does not impact significatively the simulation time.

Check already made simulations (the .csv files)

Original code for frozen trophy simulation by Kitsune, additional scenarios by Toto

Assumptions and simplifications in the simulation:

All player start at 2500 (simplification)
Only 5 heros, with RPS effect
Match result are based on Hero RPS effect and power
Matchmaking selects random players and the best expected result is then chosen and fought. (This might be an extremely effective, thus unrealistic, way to pick an opponent in a match list, it should be quite true for the top players)
Players always choose the best match in their match list, match list is limited in size (not 100)
There is no revenge (simplification)
3 attacker profiles :
- 30 % buy battle pass and will do 40 attacks daily, (not realist, but fair for each simulated bp players, and easier to compare)
- 10 % are inactive (less than 15 attacks per day),
- 60 % (other players) do between 15 and 30, The repartition of number of attacks in each profile is a bell curve, the number of attack is calculated for each player, it does not change during the simulation Number of attacks increases accross the seasons (linear increase)
The % of battle pass users is the same for all power levels (simplification)
Timezones attacks are segregated (simplification). All player from a same timezone attack before the players from the next timezone
Attacks are in random order within a timezone
to initiaite panda effects, some noise is added at the beginning of day 5 with 100 players (id 0 to 99) getting +1000 trophies, and 100 (id 100 to 199) getting -1000.

Possible simulation scenarios :

You can mix scenarios.

Timezone

Players will play at different times by timezone

const TIMEZONE_ORDER = true;

TIMEZONE_COUNT = 8;

The result filenames contain the number of Timezones used TZ<count>.

You can have time zone 0 attack all day while other attack in order

const SCENARIO_ONE_TZ_PLAYS_ALL_DAY = true;

You can have one time zone where players plays about 1/3 of the day

const SCENARIO_ONE_TZ_PLAYS_8h = true;

if you set true for all day and 8h players in TZ 0 will play all day
Minimize defensive loss

Adapt the result of a defensive loss by a chosen factor

const SCENARIO_MINIMISE_DEF_LOSS = true;

const SCENARIO_MINIMISE_DEF_LOSS_FACTOR = 0;

The result filenames are prefixed with MDL<factor>-.
Constrain possible matched opponents based on the relative attack count for the day

PLayers are matched with opponents having the same battle count (+/- SCENARIO_PROGRESSION_CONSTRAINT_ON_MATCHMAKING_DIFFERENCE ), if possible. The scope of matchable enlarges when the match list is too small.

const SCENARIO_PROGRESSION_CONSTRAINT_ON_MATCHMAKING = true;

const SCENARIO_PROGRESSION_CONSTRAINT_ON_MATCHMAKING_DIFFERENCE = 0;

The result filenames are prefixed with PCOM<Diff>-.
Frozen trophies for defender

Defender's trophies are frozen for the day, attacker picks his opponent and gets a result based on his trophies and defender's frozen trophies.

const SCENARIO_FROZEN_DEF_TROPHIES = true;

Attacker's trophies are frozen for the day, attacker picks his opponent and gets a result based on his frozen trophies and defender's trophies.

```const SCENARIO_FROZEN_OFF_TROPHIES = true;``

You can set none, either or both frozen def and frozen off. The result filenames are prefixed with FrozenDefs- or FrozenOffsas approriate.

Another possibility is to test frozen def trophies with averaged defense results

Defense of the day = SCENARIO_AVERAGE_DEF_FACTOR * sum(Defenses_points) / defense_count

const SCENARIO_FROZEN_DEF_TROPHIES = true; const SCENARIO_AVERAGE_DEF = true; ```const SCENARIO_AVERAGE_DEF_FACTOR = 30;``

The later mode produces an additional csv file with each daily average made (defenses_count, defenses_points, defense_average) to check how much unfair average are made on player getting low defense counts.

New mode suggested by peter G, Semi frozen with live defensive gains and losses, and locked offensives gains and losses. Player are matched and battle results are calculated with their live trophies. The offensive wins are then added at reset.

const SCENARIO_SEMI_FROZEN = true;

This mode is not compatible with other FROZEN Trophies modes, and will be simulated only if they are all on false.
Count of players and seasons to simulate

Simulate up to 100 000 players (or more, but a new players.json init file will be needed), and any number of season.

const PLAYER_COUNT = 100000;

const SEASONS_TO_SIM = 3;

The result filenames are suffixed with the number of players and the season players<player-count>-Season<season>.

You may run multiple simulations in parallel (just edit the const to run different scenarios), for a reasonable amount of simulations that should not slow down the simulations. You may mix scenarios as well, (eg. PCOM and MDL)

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