aleksey rehlov, creative mobile oÜ

Mathematical and psychological fundamentals

of competition systems in modern mobile games

Aleksey Rehlov | External Producer

Competition is a vital part of a mobile game

28-01-2016Mathematical and psychological fundamentals of

competition systems in modern mobile games2

Main competition system problems

• No competition feeling

• No motivation to participate

• Players don’t understand the rules

• It is too easy or too hard

• It is uncovered pay-to-win

• The participation takes too much time

• The system isn’t scalable

• It doesn’t increase KPI of the product



Why do these problems occur?

A competition system is designed or copied without understanding of its nature.



What is in-game competition?

In-game competition is a contest or rivalry between two or more players or in-game groups for resources, for prestige,

recognition, for awards, for group or social status, or for leadership and profit.

It arises whenever at least two parties strive for a goal which cannot be shared, where one's gain is the other's loss (a zero-

sum game).



Most common competition systems

• Scores based competition system

• Elo based competition system

• Groups based competition system



Scores based competition system



Main elements

• Place and Score

• Number of players

• Time length

• Time frames: multiple frames, one frame

• Tries model: time based, fixed number, non fixed number etc

• Scoring model: cumulative result, best result or mix

• Reward model: instant score based, final place based or mix

• Balance between chance and skill



Pros and Cons

• Easy to develop

• Easy to understand

• Works for a small amount of players

• Works well with a time limitation

• Can be used in almost any game

• Highly predictable

• Low competition level

• Low motivation

• Not very good for huge number of players

• Not friendly with late competitors

• Difficult to setup

• Often means pay-to-win

• Often consumes a lot of time



Issues with percentage

𝑃 =𝑃𝑜 ∙ 𝑛𝑜𝑁

Where:

• 𝑃 – final place in percentage;

• 𝑃𝑜 - base place in percentage;

• 𝑛𝑜 - base number of players;

• 𝑁 – final number of players.



0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1 2 3 4 5 6 7

Day of Competition

Final place in percentage

Issue with late participation

𝑆 = 𝑆𝑚𝑇 − 𝑡

𝑇• 𝑆 – result score;

• 𝑆𝑚 – max score;

• 𝑇 – total competition length;

• 𝑡 – missed competition length.

These issues can be softenedby score coefficient.



Issues with participation and rewards

How to soften these issues?

• Strong integration with the main game process;

• Adding easily accessible instant rewards;

• Adding the competition into the game cycle;

• Players notification about the competition and its rewards;

• Useful rewards for all types of players.



Elo based competition system



Main elements

• Place and Rating


• Matching System

• Elo Settings

• Team Elo Settings


• Reward model: instant rating based, final rating based or mix




Pros and Cons

• Easy to develop

• High competition level

• Best for 2 players

• Good for real-time competition

• Good for skill games

• Works for a large amount of players

• Works well with rating tables

• Bad for asynchronous competition

• Not working for a small number of players

• Bad for chance games

• Can be disappointing for donators

• Has a saturation point

• Elo Hell



Elo rating system

The mathematical expectation of scores amount which receives player A with player B:

𝐸𝑎 =1

1 + 10𝑅𝑏−𝑅𝑎400

Where: 𝑅𝑎 - player A rating, 𝑅𝑏 - player B rating.

The new rating of player A:𝑅′𝑎 = 𝑅𝑎 + 𝐾 ∙ (𝑆𝑎 − 𝐸𝑎)

Where: 𝐾 – K-factor, 𝑆𝑎 - actual score, 𝐸𝑎 - expected score.



Why do issues occur?

• No understanding how the elo rating works;

• Additional rating increase when player wins;

• Using in not 1 on 1 matches without modifications;

• Using in games with small skill and chance influence;

• Lack of players with close ratings;

• Dead players and players with too high rating;

• Using normal or even uniform distribution with logistic function.



Groups based competition system



Pros and Cons

• High competition level

• High motivation

• Works almost for any amount of players

• Good for asynchronous competitions

• Works well with a time limitation

• Can be used almost in any game

• Can separate gudgeons, dolphins and whale

• Highly predictable

• Friendly with late competitors

• Hard to develop

• Can be tricky to understand

• Difficult to setup

• Often consumes a lot of time



Main elements

• Group Model: number of levels, setup, promotion/demotion, time limitations

• Place and Score



• Scoring model: cumulative result, best result or mix

• Reward model: interim level and place based, final level and place based or mix




How to decrease the chance of problems?

• To have an expert of competition design in the team.

• To find a closest successful reference for the competition system, to conduct reverse engineering of it and to recreate it.

• Not to mix parts of different competition systems without thinking.

• To make all elements of the competition system as clear as possible.

• To design the competition system in concert with other parts of the game.

• To simulate all aspects of players behavior for an expected number of players in the competition and try to minimize all the negative effects by tweaking your competition system.

• To think about the competition system not as the last resort and before the game is almost done.



Next lecture on the same theme

How to create the right competition system for your game: methodology

November 10, DevGAMM Minsk 2016



Mathematical and psychological fundamentals of competition systems in modern mobile games

Questions?Aleksey Rehlov | External Producer

aleksey rehlov, creative mobile oÜ

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