### Eternal ranking for Berlin 2000-01-21 to 2023-03-31

**Color legend:**

Shows the color coding of the different player classes. Just click on the buttons to show/hide a certain type in the tables below!

- Human player
- Group
- Automated forecast
- Reference method
- Sleepy

# Explanation of table columns:

**“> Median:**

How many points above or below the median is a player on average in a weekend? The higher, the better; can also be negative.

\(p_t\) := own points on played days

\(median_t\) := median on these days

\(p_{med} = \frac{ \sum_t [ { p_t – median_t } ] } { participations }\)

**“Ind. SD”:**

The individual standard deviation. Whereby this is not a standard deviation in the true sense. Instead, for each tournament weekend, the differences between the scores of all players with a score > median and the respective weekend median were calculated. From these differences, a mean was calculated for each weekend (“upper SD”). The individual SD (\(SD_{ind}\)) of a player is in turn the mean of all upper SD of the tournaments in which he participated. Each player “fights” against his individual standard deviation – the higher it is, the larger his mean distance to the median should be (\(p_{med}\)).

\(p_s\) := points of the players who have a score above the weekend median

\(p_a\) := scores of all players

\(SD_{upper} = \frac{ \sum_s [ p_s – median(p_a) ] } { players }\)

\(SD_{ind} = \frac{ \sum_t SD_{upper} } { participations } = \frac{ \sum_t \frac{ \sum_s [ p_s – median(p_s) ] } { players } }{ participations }\)

**“Points”:**

The perpetual score, which was calculated using the following formula:

\(p_{eternal} = k \cdot 1000 \cdot \frac{ p_{med} }{ SD_{ind} }\)

Thus, it is the ratio of points above the median to the individual standard deviation. This is multiplied by 1000 to get nicer values and last but not least it is multiplied by the factor \(k\).

\(k\) is zero for less than 25 participations, meaning the player does not appear in the list and 1 for 100 participations and more. Between 25 and 99 participations it is determined by a root function:

\(k = \sqrt{ \frac{ participations } { 100 } }\)

**“Max”:**

The maximum number of points a player has scored in his entire career in a weekend.

**“Medium”:**

The average score

**“Wins”:**

Number of weekend victories

**“Top3 (%)”:**

How often was a player on a podium? (in percent)