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Condition

## Impact on the match simulation

In the context of the match simulation, a player's condition affects their in-game performance via a fixed function. A fixed amount of the player's rating is weighted by their condition rating.
Logic:
• Given an Elo rating and a condition then the player's rating in the game is:
$GameRating = (PositionRating-1200)+(1200 * condition)$
Example:
• A player has an Elo rating of 2000 and
• A condition of 100%:
$GameRating(100\%)=(2000-1200)+(1200*100\%)=2000$
• A condition of 80%:
$GameRating(80\%)=(2000-1200)+(1200*80\%)=1760$
• A condition of 50%:
$GameRating(50\%)=(2000-1200)+(1200*50\%)=1400$

## Relationship between fitness and condition

During a match, a player's condition decreases, meaning they get tired and their performance worsens. The rate at which a player loses condition is dependent on their fitness, however, the rate at which they recover is independent of fitness.
When decreasing a player's 0-100 condition, using the below formula we convert the number to an Elo value, a domain that is easier to operate over mathematically.
$Elo(x) = -\frac{ln(\frac{1}{x-0.15}-1)+0.0015*1700}{0.0015}$
​We decrease the condition, then convert it back to a condition value (0-100) using the below formula
$Condition(x) = \frac{1}{1+e^{- 0.0015(x-1700)}}+0.15$
Players recover whilst they're not playing in a game.