## How is the ladder calculated?

**The Elo points**

The valuation system developed by professor Arpad Elo around 1960 has been divised according to scientific methods and the statistics and the probability theory. Within the ESL, points are meausred by this "

**Elo point**" theory and this allows players of different strengths to gain different amounts of points against differently skilled opposisition. Therefore, they are adapted for each match, and player's points will be adapted according to their league standings and ratings. Basisally, the point scheme is an expectation of profit. If two teams of equal points play, then there will be a very small points difference. However, if a higher ranked team plays a lower ranked team, the higher ranked team will be expected to win and will therefore get less points by doing so. This case is reversed if the lower ranked clan defeats the higher clan; then the lower team will gain a lot of points and the higher team will lose alot of points. Also, the match score is taken into consideration and a team who wins by a large margin will get more points than a team who win by only a small margin (taking that both teams have an equal amount of points.) This way, if a high ranked team does not meet the expectation of the Elo scheme and only wins by a small margin over a team who is ranked much lower, the high ranked team may even lose points! The longer the ladder runs, the more precisely the evaluation of a team is. From only five matches the "Elo" system can predict logical values, and a probable outcome, for a match. Elo Ladders are rarely reset, therefore the system keeps a record of all your matches to improve its prediction. This system allows a team to enter the league at any time and to find their correct rank very quickly. Before a match comes to the Elo calculation, it is prepared by a league-specific calculation module, in order to break down.

Currently, there are the following calculation modules:

**default**: Standard calculation. There is two rounds and in each case a valuation is given for each participant. A proportional distribution be given for the scoreand it will be rationalised. With zero scores (e.g. 24-0) and also negative scores, both sides are raised, or lowered, evenly until both sides are in positives ranges (e.g 0:3 will become 1:4 & 1:-3 becomes 3:1).

__Example:__Match A vs B

Round 1: 50:20 (71%:29%)

Round 2: 90:130 (41%:59%)

Total: 112%:88% final result: 56%:44%

Team A win, although team B did win Round 1. Therefore, the final persentage is decreased and Team A will gain less points.

**default_noshift**: Similar to "default", but the result is not raised with "zero" results. This module is used when there is to be "100% victories" e.g. (e.g. 2:0, 2:1).

**winloss**: Two Rounds are played, but for each round only a "victory" or "defeat" is registered (100%, and/or 0% victory). Both rounds are then added together, so that the end result canonly be 100%:0%, 50%:50% or 0%:100%.

**BestOfThree**: Apart from the two normal rounds, there is an optional third round, which is played, if the first two rounds were drawn. Therefore, there is always a match winner.

**tfc**: Like "default", only with "zero" results +10 added on both sides.

**cs**: (CO Rules) Similar to "default", only in each case the Attacker's points (Terrorist wins on de_maps or Counter-Terrorists on cs_maps) are counted. The Defender's points are irrelevant for the calculation and are there fore statistic purposes only.

**oneround**: The same as "default" except only one round is played instead of two.

**oneround_winloss**: The mixture out "winloss" and "oneround." One round is played, in which there can only be a winner and a loser.

**oneround_noshift**: The mixture out "oneround" and "default_noshift." One round is played, in which "zero" scores will not raise the point score.

The "

**Elo formula**" Generally:

**Rnew = Result old + C1 * (W - E)**

W = The percentage points of the result of the match (e.g.: 100% = won, 50% = undecided, 0% = lost)

Rold = Old Ranking (Elo points)

Rnew = New Ranking

E = Expected percentage points (calculated beforehand)

C1 = Constant one (at present: 50)

The prediction of percentage points are calculated as shown below:

**E = 1 / (1+10^ (-(R-Rother)/C2))**

R = Ranking of the own team

Rother = Ranking of the opponent

C2 = Constant one (at present: 400)

The same calculation is then accomplished once more from the view of the other player, in order to compute his/her new score.

__Example:__

Match result: 3:6

Persentages: 33%:66%

old Elo points: 1000:1000

new Elo points:

**992**(-8) :

**1008**(+8)

Expectation of profit:

E = 1/(1+10^(-(1000-1000)/400)) = 0.5

new points for team1: Rnew = 1000 + 50 * (0,33 - 0,5) = 1000 - 8 =

**992**(rounded)

new points for team2: Rnew = 1000 + 50 * (0,66 - 0,5) = 1000 + 8 =

**1008**(rounded)

### More questions and answers in this subject area

What is a ladder?

How do I leave a Ladder?

What does the "What if Machine" diagram show on challenge?

How does the Auto-Challenger work?

Why there is no "Default-Win"

Match Modules

All questions & answers