Benutzer:Mediator/Tests/ELO: Unterschied zwischen den Versionen
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<!-- -------------------------------------------------------- --> | <!-- -------------------------------------------------------- --> | ||
<!-- --> | <!-- --> | ||
| + | |||
| + | === Beispiel 2 === | ||
| + | <!-- -------------------------------------------------------- -->{{#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;"> | ||
| + | <div><b>Tabelle:</b></div> | ||
| + | <!-- -------------------------------------------------------- --> | ||
| + | <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;">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;"> </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> </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> </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;"> </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> </td> | ||
| + | </tr> | ||
| + | <!-- -------------------------------------------------------- --> | ||
| + | <tr style="border-top: solid 1px Black; background-color: HoneyDew;"> | ||
| + | <!-- -------------------------------------------------------- --> | ||
| + | <td style="text-align: right; padding-right: 3px;">Differenz := </td> | ||
| + | <td style="text-align: right; padding-right: 3px; border-right: 1px solid Black;">{{#expr: ({{#var: mPlayer1ELOwertalt}} - {{#var: mPlayer2ELOwertalt}}) }}</td> | ||
| + | <td colspan="8"> </td> | ||
| + | </tr> | ||
| + | </table> | ||
| + | Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet. | ||
| + | </div> | ||
| + | <!-- ------------------------------------------------------------------------------ --> | ||
=== Beispiel 2 === | === Beispiel 2 === | ||
Version vom 19. April 2013, 16:31 Uhr
Inhaltsverzeichnis |
ELO: Erwartungswert
Im folgenden einige Beispiele für das Auswerten mathematischer Ausdrücke unter chessmail-wiki anhand verschiedener ELO-Berechnungen:
Partie: Spieler A vs. Spieler B
- bisherige ELO-Zahl Spieler A: ra := {{#vardefineecho: ra|2806}}
- bisherige ELO-Zahl Spieler B: rb := {{#vardefineecho: rb|2577}}
{{#vardefine: dif | {{#expr: ({{#var:rb}} - {{#var:ra}}) }} }} {{#vardefine: expo | {{#expr: ({{#var:dif}}/400) }} }} {{#vardefine: y1 | {{#expr: 10^{{#var:expo}} }} }} {{#vardefine: n | {{#expr: 1 + {{#var:y1}} }} }}
- Erwartungswert für Spieler A: ra:= {{#vardefineecho: erwa | {{#expr: {{#var:n}} }} }}
- Erwartungswert für Spieler B: rb:= {{#vardefineecho: erwb | {{#expr: 1 - {{#var: erwa}} }} }}
Spieler A (als Gewinner der Partie){{#vardefine: spa1 | 1 }} {{#vardefine:k|10}} {{#vardefine: nra| {{#expr: {{#var: ra}}+ {{#var: k}} * ({{#var: spa1}} - {{#var:erwa}}) }} }}
- neue (dynamisch berechnete) ELO-Zahl: {{#expr: {{#var:nra}} round0 }}
nF:
- {{#vardefineecho: mELOquotient400| 400 }} (const.)
- {{#vardefineecho: mELOquotient250| 250 }} (const.)
- {{#vardefineecho: k | 10}}
- player 1 (bisheriger ELO-Wert) {{#vardefineecho: mPlayer1ELOwertalt | 2806}} (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 }}
ELO:
- player 1 gewinnt: {{#vardefineecho: player1result | 1 }}
- neue Punkte für player 1: {{#vardefineecho: mPlayer1ELOwertneu |
{{#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}} }}
Beispiel 1
{{#vardefine: mELOquotient | {{#var: mELOquotient400}}}}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
Tabelle:
| Beispiele 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}}) }} | ||||||||
Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet.
Beispiel 2
{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
Tabelle:
| 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}}) }} | ||||||||
Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet.
Beispiel 2
{{#vardefine: mELOquotient | {{#var: mELOquotient250}}}}{{#vardefine: erwa | {{#expr: 1 / (1 + 10^( ({{#var: mPlayer2ELOwertalt}} - {{#var: mPlayer1ELOwertalt}}) / {{#var: mELOquotient}} ) ) }} }}
Tabelle:
| 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}}) }} | ||||||||
Hinweis: die einzelnen, neuen Berechnungswerte wurden entsprechend gerundet.
