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<h2>ELO: Erwartungswert</h2>
 
<h2>ELO: Erwartungswert</h2>
−
Im folgenden ein Beispiel für das Auswerten mathematischer Ausdrücke unter chessmail-wiki:
+
Im folgenden einige Beispiele für das Auswerten mathematischer Ausdrücke unter chessmail-wiki anhand verschiedener ELO-Berechnungen (Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet.):
−
 
+
[[Benutzer:Mediator/Test/ELO]]
−
<div style="border: 1px solid DimGray; padding: 3px;">
+
<!-- --------------------------- -->
 +
<div class="hidden" style="border: 1px solid DimGray; padding: 3px;">
 
Partie: '''Spieler A''' vs. '''Spieler B'''
 
Partie: '''Spieler A''' vs. '''Spieler B'''
 
* bisherige ELO-Zahl <u>Spieler A</u>: '''ra''' := <tt>{{#vardefineecho: ra|2806}}</tt>
 
* bisherige ELO-Zahl <u>Spieler A</u>: '''ra''' := <tt>{{#vardefineecho: ra|2806}}</tt>
Zeile 13: Zeile 14:
 
----
 
----
 
* Erwartungswert für Spieler A: '''ra''':= <tt>{{#vardefineecho: erwa | {{#expr: {{#var:n}} }} }}</tt>
 
* Erwartungswert für Spieler A: '''ra''':= <tt>{{#vardefineecho: erwa | {{#expr: {{#var:n}} }} }}</tt>
−
* Erwartungswert für Spieler B: '''rb''':= <tt>{{#vardefineecho: erwb | {{#expr: 1 - {{#var:erwa}} }} }}</tt>
+
* Erwartungswert für Spieler B: '''rb''':= <tt>{{#vardefineecho: erwb | {{#expr: 1 - {{#var: erwa}} }} }}</tt>
 
----
 
----
 
'''Spieler A (als Gewinner der Partie)'''{{#vardefine: spa1 | 1 }}
 
'''Spieler A (als Gewinner der Partie)'''{{#vardefine: spa1 | 1 }}
−
<span style="display:none">{{#vardefine: erwb | {{#expr: {{#var: spa1}} - {{#var:erwa}} }} }}</span>
+
<span style="display:none">{{#vardefine: erwb | {{#expr: {{#var: spa1}} - {{#var: erwa}} }} }}</span>
 
<span style="display:none">* k (CONST)</span>{{#vardefine:k|10}}
 
<span style="display:none">* k (CONST)</span>{{#vardefine:k|10}}
 
<span style="display:none">* neue Elo-Zahl von Spieler A:</span>{{#vardefine: nra| {{#expr: {{#var: ra}}+ {{#var: k}} * ({{#var: spa1}} - {{#var:erwa}}) }} }}
 
<span style="display:none">* neue Elo-Zahl von Spieler A:</span>{{#vardefine: nra| {{#expr: {{#var: ra}}+ {{#var: k}} * ({{#var: spa1}} - {{#var:erwa}}) }} }}
 
* '''neue (dynamisch berechnete) ELO-Zahl:''' <tt>{{#expr: {{#var:nra}} round0 }}</tt>
 
* '''neue (dynamisch berechnete) ELO-Zahl:''' <tt>{{#expr: {{#var:nra}} round0 }}</tt>
 
</div>
 
</div>
−
----
+
<!-- ----------------------------------------------------------------------- -->
 +
<div class="hidden">
 
----
 
----
 
nF:
 
nF:
 
----
 
----
−
* {{#vardefineecho: mELOquotient| 400 }} (const.)
+
* {{#vardefineecho: mELOquotient400| 400 }} (const.)
 +
* {{#vardefineecho: mELOquotient250| 250 }} (const.)
 
* {{#vardefineecho: k | 10}}
 
* {{#vardefineecho: k | 10}}
 
* player 1 (bisheriger ELO-Wert) {{#vardefineecho: mPlayer1ELOwertalt | 2806}} (var.)
 
* player 1 (bisheriger ELO-Wert) {{#vardefineecho: mPlayer1ELOwertalt | 2806}} (var.)
 
* player 2 (bisheriger ELO-Wert) {{#vardefineecho: mPlayer2ELOwertalt | 2577}} (var.)
 
* player 2 (bisheriger ELO-Wert) {{#vardefineecho: mPlayer2ELOwertalt | 2577}} (var.)
 +
* player 1 gewinnt: {{#vardefineecho: player1result | 1 }}
 +
* player 1 remis: {{#vardefineecho: player1result | 0.5 }}
 +
* player 1 verliert: {{#vardefineecho: player1result | 0 }}
 +
* player 1 {{#vardefineecho: player1result | 1 }}
 +
----
 +
</div>
 +
<!-- ----------------------------------------------------------------------------- -->
 +
<div class="hidden">
 
----
 
----
−
Player1:
+
'''ELO''':  
−
* erwa: {{#vardefineecho: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) round3}} }}
+
* player 1 gewinnt: {{#vardefineecho: player1result | 1 }}
−
* ELO: {{#vardefineecho: mPlayer1ELOwertneu | {{#expr: {{#var: nra}} round0 }} }} (gen.)
+
** neue Punkte für player 1: {{#vardefineecho: mPlayer1ELOwertneu |  
−
* ELO: {{#vardefineecho: mPlayer1ELOwertneu | {{#expr: {{#var: ra}}+ {{#var: k}} * ({{#var: spa1}} - {{#var:erwa}}) round0 }} }}  (gen., gerundet)
+
{{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} (gen., gerundet)
 +
** Differenz 1: {{#expr: {{#var: mPlayer1ELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }}
 +
* player 1 remis: {{#vardefineecho: player1result | 0.5}}
 +
** neue Punkte für player 1: {{#vardefine: player1result | 1 }}{{#vardefineecho: mPlayer1ELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} (gen., gerundet)
 +
** Differenz: {{#expr: {{#var: mPlayer1ELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }}
 +
* player 1 verliert: {{#vardefineecho: player1result | 0}}
 +
** neue Punkte für player 1: {{#vardefineecho: mPlayer1ELOwertneu |
 +
{{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}  (gen., gerundet)
 +
** Differenz: {{#expr: {{#var: mPlayer1ELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }}
 
----
 
----
−
 
+
</div>
−
 
+
<!-- -------------------------------------------------------- -->
−
Literatur:
+
<!-- -------------------------------------------------------- -->{{#vardefine: mELOquotient | {{#var: mELOquotient400}}}}<!--
−
* http://de.wikipedia.org/wiki/Elo-Zahl#Berechnung
+
-->{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
−
* http://www.mathe-lexikon.at/statistik/lagemasse/mittelwert/geometrisches-mittel.html
+
<!-- -------------------------------------------------------- -->
 +
<div style="border: 1px Gainsboro solid; padding: 4px; background-color: #EEEEEE; margin-bottom: 3px;">
 +
<!-- -------------------------------------------------------- -->
 +
<table style="padding-left: 3px; border: 1px solid black; width: 100%; border-collapse: collapse;">
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: solid 1px Black; background-color: Black; color: Snow;">
 +
<!-- -------------------------------------------------------- -->
 +
<td colspan="10" style="padding-left: 3px;">1.Beispiel zur ELO-Berechnung (<b>historisch</b>, <span style="color: PaleTurquoise;">q := {{#var: mELOquotient}}</span>)</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px Black solid; background-color: LightGray; color: Black;">
 +
<!-- -------------------------------------------------------- -->
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Spieler/ELO</td>
 +
<td style="border-right: 1px solid Black;">&nbsp;</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Sieg</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Remis</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Niederlage</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: solid 1px Black; background-color: Gainsboro;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px; border-right: 1px dotted Black;">Name</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">(alt)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">Erwartungswert</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO:(neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px dotted LightGrey; background-color: LemonChiffon;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler A</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#var: mPlayer1ELOwertalt}}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#expr: {{#var: erwa}} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 1 }}{{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; padding-right: 3px;">&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="background-color: LightCyan;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler B</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#var: mPlayer2ELOwertalt}}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: (1 - {{#var: erwa}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-top: solid 1px Black; background-color: HoneyDew;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="text-align: right; padding-right: 3px;">Differenz :=&nbsp;</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}</td>
 +
<td colspan="8">&nbsp;</td>
 +
</tr>
 +
</table>
 +
</div>
 +
<!-- -------------------------------------------------------- -->
 +
<!--                                                          -->
 +
<!-- -------------------------------------------------------- -->{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}<!--
 +
-->{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
 +
<!-- -------------------------------------------------------- -->
 +
<div style="border: 1px Gainsboro solid; padding: 4px; background-color: #EEEEEE; margin-bottom: 5px;">
 +
<!-- -------------------------------------------------------- -->{{#vardefineecho: mPlayer1ELOwertalt|2269}}{{#vardefineecho: mPlayer2ELOwertalt|2330}}
 +
<table style="padding-left: 3px; border: 1px solid black; width: 100%; border-collapse: collapse;">
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px Black solid; background-color: Black; color: Snow;">
 +
<!-- 2269 2330 -------------------------------------------------------- -->
 +
<td colspan="10" style="padding-left: 3px;">2.Beispiel zur ELO-Berechnung (<b>chessmail</b>, <span style="color: PaleTurquoise;">q := {{#var: mELOquotient}}</span>)</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px Black solid; background-color: Gainsboro;">
 +
<!-- -------------------------------------------------------- -->
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Spieler/ELO</td>
 +
<td style="border-right: 1px solid Black;">&nbsp;</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Sieg</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Remis</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Niederlage</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: solid 1px Black; background-color: Gainsboro;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px; border-right: 1px dotted Black;">Name</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">(alt)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">Erwartungswert</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO:(neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px dotted LightGrey; background-color: LemonChiffon;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler A</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#var: mPlayer1ELOwertalt}}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#expr: {{#var: erwa}} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 1 }}{{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; padding-right: 3px;">&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="background-color: LightCyan;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler B</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#var: mPlayer2ELOwertalt}}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: (1 - {{#var: erwa}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-top: solid 1px Black; background-color: HoneyDew;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="text-align: right; padding-right: 3px;">Differenz :=&nbsp;</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}</td>
 +
<td colspan="8">&nbsp;</td>
 +
</tr>
 +
</table>
 +
</div>
 +
<!-- ------------------------------------------------------------------------------ -->
 +
<!-- -------------------------------------------------------- -->{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}{{#vardefine: mPlayer1ELOwertalt | 2806}}{{#vardefine: mPlayer2ELOwertalt | 2209}}{{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}<!--
 +
-->{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
 +
<!-- -------------------------------------------------------- -->
 +
<div style="border: 1px Gainsboro solid; padding: 4px; background-color: #EEEEEE; margin-bottom: 5px;">
 +
<!-- -------------------------------------------------------- -->
 +
<table style="padding-left: 3px; border: 1px solid black; width: 100%; border-collapse: collapse;">
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px Black solid; background-color: Black; color: Snow;">
 +
<!-- -------------------------------------------------------- -->
 +
<td colspan="10" style="padding-left: 3px;">3.Beispiel zur ELO-Berechnung (<b>chessmail</b>, <span style="color: PaleTurquoise;">q := {{#var: mELOquotient}}</span>)</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px Black solid; background-color: Gainsboro;">
 +
<!-- -------------------------------------------------------- -->
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Spieler/ELO</td>
 +
<td style="border-right: 1px solid Black;">&nbsp;</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Sieg</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Remis</td>
 +
<td colspan="2" style="padding-left: 3px; border-right: 1px solid Black;">Niederlage</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: solid 1px Black; background-color: Gainsboro;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px; border-right: 1px dotted Black;">Name</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">(alt)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid Black;">Erwartungswert</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO:(neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px dotted Black;">ELO (neu)</td>
 +
<td style="padding-left: 3px; text-align: left; border-right: 1px solid  Black;">Dif.</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-bottom: 1px dotted LightGrey; background-color: LemonChiffon;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler A</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{mNumForm|{{#var: mPlayer1ELOwertalt}}}}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#expr: {{#var: erwa}} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 1 }}{{mNumForm|{{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{mNumForm |  {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; border-right: 1px dotted Black; padding-right: 3px;">{{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }}</td>
 +
<td style="text-align: right; border-right: 1px solid Black; padding-right: 3px;">{{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}</td>
 +
<td style="text-align: right; padding-right: 3px;">&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="background-color: LightCyan;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="padding-left: 9px;">Spieler B</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">
 +
{{mNumForm | {{#var: mPlayer2ELOwertalt}}}}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: (1 - {{#var: erwa}}) }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{mNumForm |  {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{mNumForm |  {{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">üüü{{mNumForm |  {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{mNumForm |  {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px dotted Black;">{{mNumForm |  {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }} }}</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}</td>
 +
<td>&nbsp;</td>
 +
</tr>
 +
<!-- -------------------------------------------------------- -->
 +
<tr style="border-top: solid 1px Black; background-color: HoneyDew;">
 +
<!-- -------------------------------------------------------- -->
 +
<td style="text-align: right; padding-right: 3px;">Differenz :=&nbsp;</td>
 +
<td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}</td>
 +
<td colspan="8">&nbsp;</td>
 +
</tr>
 +
</table>
 +
</div>

Aktuelle Version vom 28. Juni 2013, 21:20 Uhr

ELO: Erwartungswert

Im folgenden einige Beispiele für das Auswerten mathematischer Ausdrücke unter chessmail-wiki anhand verschiedener ELO-Berechnungen (Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet.): Benutzer:Mediator/Test/ELO

{{#vardefine: mELOquotient | {{#var: mELOquotient400}}}}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}

1.Beispiel zur ELO-Berechnung (historisch, q := {{#var: mELOquotient}})
Spieler/ELO   Sieg Remis Niederlage  
Name (alt) Erwartungswert ELO:(neu) Dif. ELO (neu) Dif. ELO (neu) Dif.  
Spieler A {{#var: mPlayer1ELOwertalt}} {{#expr: {{#var: erwa}} }} {{#vardefine: player1result | 1 }}{{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}  
Spieler B {{#var: mPlayer2ELOwertalt}} {{#expr: (1 - {{#var: erwa}}) }} {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }} {{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }} {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}} }} {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }} {{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}  
Differenz :=  {{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}  

{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}

{{#vardefineecho: mPlayer1ELOwertalt|2269}}{{#vardefineecho: mPlayer2ELOwertalt|2330}}

2.Beispiel zur ELO-Berechnung (chessmail, q := {{#var: mELOquotient}})
Spieler/ELO   Sieg Remis Niederlage  
Name (alt) Erwartungswert ELO:(neu) Dif. ELO (neu) Dif. ELO (neu) Dif.  
Spieler A {{#var: mPlayer1ELOwertalt}} {{#expr: {{#var: erwa}} }} {{#vardefine: player1result | 1 }}{{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}  
Spieler B {{#var: mPlayer2ELOwertalt}} {{#expr: (1 - {{#var: erwa}}) }} {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }} {{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }} {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}} }} {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }} {{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}  
Differenz :=  {{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}  

{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}{{#vardefine: mPlayer1ELOwertalt | 2806}}{{#vardefine: mPlayer2ELOwertalt | 2209}}{{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}

3.Beispiel zur ELO-Berechnung (chessmail, q := {{#var: mELOquotient}})
Spieler/ELO   Sieg Remis Niederlage  
Name (alt) Erwartungswert ELO:(neu) Dif. ELO (neu) Dif. ELO (neu) Dif.  
Spieler A {{#number_format: {{#var: mPlayer1ELOwertalt}} |0|,|.}} {{#expr: {{#var: erwa}} }} {{#vardefine: player1result | 1 }}{{#number_format: {{#vardefineecho: mPlayer1SiegELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} |0|,|.}} {{#vardefineecho: mPlayer1SiegDif| {{#expr: {{#var: mPlayer1SiegELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0.5 }}{{#vardefineecho: mPlayer1RemisELOwertneu | {{#number_format: {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} |0|,|.}} }} {{#vardefineecho: mPlayer1RemisDif | {{#expr: {{#var: mPlayer1RemisELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }} {{#vardefine: player1result | 0 }}{{#vardefineecho: mPlayer1NiederlELOwertneu | {{#expr: {{#var: mPlayer1ELOwertalt}} + 10 * ({{#var: player1result}} - {{#var: erwa}}) round0 }} }} {{#vardefineecho: mPlayer1NiederlDif | {{#expr: {{#var: mPlayer1NiederlELOwertneu}} - {{#var: mPlayer1ELOwertalt}} }} }}  
Spieler B

{{#number_format: {{#var: mPlayer2ELOwertalt}} |0|,|.}}

{{#expr: (1 - {{#var: erwa}}) }} {{#number_format: {{#expr: {{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1SiegDif}} }} |0|,|.}} {{#number_format: {{#expr: ((-1)*{{#var: mPlayer1SiegDif}}) }} |0|,|.}} üüü{{#number_format: {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} |0|,|.}} {{#number_format: {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1RemisDif}}) }} |0|,|.}} {{#number_format: {{#expr: ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1NiederlDif}}) }} |0|,|.}} {{#expr: ((-1)*{{#var: mPlayer1NiederlDif}}) }}  
Differenz :=  {{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}  
Abgerufen von „https://cm-wiki.novasign.ch/index.php?title=Benutzer:Mediator/Tests/ELO&oldid=95389“