ALGORITEM OCENJEVANJA ELO

The Algoritem ocenjevanja Elo je pogosto uporabljen ocenjevalni algoritem, ki se uporablja za razvrščanje igralcev v številnih tekmovalnih igrah.

Igralci z višjimi ocenami ELO imajo večjo verjetnost zmage v igri kot igralci z nižjimi ocenami ELO.
Po vsaki igri se posodobi ELO rating igralcev.
Če igralec z višjo oceno ELO zmaga, se le nekaj točk prenese od igralca z nižjo oceno.
Če pa zmaga igralec z nižjo oceno, so prenesene točke od igralca z višjo oceno veliko večje.

Pristop: Za rešitev težave sledite spodnji zamisli:

P1: Verjetnost zmage igralca z ratingom 2 P2: Verjetnost zmage igralca z ratingom 1.
P1 = (1,0 / (1,0 + pow(10 ((ocena1 - ocena2) / 400))));
P2 = (1,0 / (1,0 + pow(10 ((ocena2 - ocena1) / 400))));

Očitno je P1 + P2 = 1. Ocena igralca je posodobljena z uporabo spodnje formule:-
ocena1 = ocena1 + K*(dejanska ocena - pričakovana ocena);
V večini iger je 'dejanski rezultat' 0 ali 1, kar pomeni, da igralec zmaga ali izgubi. K je konstanta. Če je vrednost K nižja, se ocena spremeni za majhen delež, če pa je vrednost K višja, so spremembe ocene pomembne. Različne organizacije določijo različno vrednost K.

primer:

podniz java

Recimo, da na chess.com poteka tekma v živo med dvema igralcema
ocena1 = 1200 ocena2 = 1000;
P1 = (1,0 / (1,0 + pow(10 ((1000-1200) / 400)))) = 0,76
P2 = (1,0 / (1,0 + pow(10 ((1200-1000) / 400)))) = 0,24
In predpostavimo konstanto K=30;
PRIMER-1:
Recimo, da igralec 1 zmaga: ocena1 = ocena1 + k*(dejansko - pričakovano) = 1200+30(1 - 0,76) = 1207,2;
ocena2 = ocena2 + k*(dejansko - pričakovano) = 1000+30(0 - 0,24) = 992,8;
Primer-2:
Recimo, da igralec 2 zmaga: ocena1 = ocena1 + k*(dejansko - pričakovano) = 1200+30(0 - 0,76) = 1177,2;
ocena2 = ocena2 + k*(dejansko - pričakovano) = 1000+30(1 - 0,24) = 1022,8;

Za rešitev težave sledite spodnjim korakom:

Izračunajte verjetnost zmage igralcev A in B z uporabo zgornje formule
Če zmaga igralec A ali igralec B, se ocene ustrezno posodobijo z uporabo formul:
- ocena1 = ocena1 + K*(dejanski rezultat - pričakovan rezultat)
- ocena2 = ocena2 + K*(dejanska ocena - pričakovana ocena)
- Pri čemer je dejanski rezultat 0 ali 1
Natisnite posodobljene ocene

Spodaj je izvedba zgornjega pristopa:

CPP

#include    using namespace std; // Function to calculate the Probability float Probability(int rating1 int rating2) {  // Calculate and return the expected score  return 1.0 / (1 + pow(10 (rating1 - rating2) / 400.0)); } // Function to calculate Elo rating // K is a constant. // outcome determines the outcome: 1 for Player A win 0 for Player B win 0.5 for draw. void EloRating(float Ra float Rb int K float outcome) {  // Calculate the Winning Probability of Player B  float Pb = Probability(Ra Rb);  // Calculate the Winning Probability of Player A  float Pa = Probability(Rb Ra);  // Update the Elo Ratings  Ra = Ra + K * (outcome - Pa);  Rb = Rb + K * ((1 - outcome) - Pb);  // Print updated ratings  cout << 'Updated Ratings:-n';  cout << 'Ra = ' << Ra << ' Rb = ' << Rb << endl; } // Driver code int main() {  // Current ELO ratings  float Ra = 1200 Rb = 1000;  // K is a constant  int K = 30;  // Outcome: 1 for Player A win 0 for Player B win 0.5 for draw  float outcome = 1;  // Function call  EloRating(Ra Rb K outcome);  return 0; }

Java

import java.lang.Math; public class EloRating {  // Function to calculate the Probability  public static double Probability(int rating1 int rating2) {  // Calculate and return the expected score  return 1.0 / (1 + Math.pow(10 (rating1 - rating2) / 400.0));  }  // Function to calculate Elo rating  // K is a constant.  // outcome determines the outcome: 1 for Player A win 0 for Player B win 0.5 for draw.  public static void EloRating(double Ra double Rb int K double outcome) {  // Calculate the Winning Probability of Player B  double Pb = Probability(Ra Rb);  // Calculate the Winning Probability of Player A  double Pa = Probability(Rb Ra);  // Update the Elo Ratings  Ra = Ra + K * (outcome - Pa);  Rb = Rb + K * ((1 - outcome) - Pb);  // Print updated ratings  System.out.println('Updated Ratings:-');  System.out.println('Ra = ' + Ra + ' Rb = ' + Rb);  }  public static void main(String[] args) {  // Current ELO ratings  double Ra = 1200 Rb = 1000;  // K is a constant  int K = 30;  // Outcome: 1 for Player A win 0 for Player B win 0.5 for draw  double outcome = 1;  // Function call  EloRating(Ra Rb K outcome);  } }

Python

import math # Function to calculate the Probability def probability(rating1 rating2): # Calculate and return the expected score return 1.0 / (1 + math.pow(10 (rating1 - rating2) / 400.0)) # Function to calculate Elo rating # K is a constant. # outcome determines the outcome: 1 for Player A win 0 for Player B win 0.5 for draw. def elo_rating(Ra Rb K outcome): # Calculate the Winning Probability of Player B Pb = probability(Ra Rb) # Calculate the Winning Probability of Player A Pa = probability(Rb Ra) # Update the Elo Ratings Ra = Ra + K * (outcome - Pa) Rb = Rb + K * ((1 - outcome) - Pb) # Print updated ratings print('Updated Ratings:-') print(f'Ra = {Ra} Rb = {Rb}') # Current ELO ratings Ra = 1200 Rb = 1000 # K is a constant K = 30 # Outcome: 1 for Player A win 0 for Player B win 0.5 for draw outcome = 1 # Function call elo_rating(Ra Rb K outcome)

using System; class EloRating {  // Function to calculate the Probability  public static double Probability(int rating1 int rating2)  {  // Calculate and return the expected score  return 1.0 / (1 + Math.Pow(10 (rating1 - rating2) / 400.0));  }  // Function to calculate Elo rating  // K is a constant.  // outcome determines the outcome: 1 for Player A win 0 for Player B win 0.5 for draw.  public static void CalculateEloRating(ref double Ra ref double Rb int K double outcome)  {  // Calculate the Winning Probability of Player B  double Pb = Probability((int)Ra (int)Rb);  // Calculate the Winning Probability of Player A  double Pa = Probability((int)Rb (int)Ra);  // Update the Elo Ratings  Ra = Ra + K * (outcome - Pa);  Rb = Rb + K * ((1 - outcome) - Pb);  }  static void Main()  {  // Current ELO ratings  double Ra = 1200 Rb = 1000;  // K is a constant  int K = 30;  // Outcome: 1 for Player A win 0 for Player B win 0.5 for draw  double outcome = 1;  // Function call  CalculateEloRating(ref Ra ref Rb K outcome);  // Print updated ratings  Console.WriteLine('Updated Ratings:-');  Console.WriteLine($'Ra = {Ra} Rb = {Rb}');  } }

JavaScript

// Function to calculate the Probability function probability(rating1 rating2) {  // Calculate and return the expected score  return 1 / (1 + Math.pow(10 (rating1 - rating2) / 400)); } // Function to calculate Elo rating // K is a constant. // outcome determines the outcome: 1 for Player A win 0 for Player B win 0.5 for draw. function eloRating(Ra Rb K outcome) {  // Calculate the Winning Probability of Player B  let Pb = probability(Ra Rb);  // Calculate the Winning Probability of Player A  let Pa = probability(Rb Ra);  // Update the Elo Ratings  Ra = Ra + K * (outcome - Pa);  Rb = Rb + K * ((1 - outcome) - Pb);  // Print updated ratings  console.log('Updated Ratings:-');  console.log(`Ra = ${Ra} Rb = ${Rb}`); } // Current ELO ratings let Ra = 1200 Rb = 1000; // K is a constant let K = 30; // Outcome: 1 for Player A win 0 for Player B win 0.5 for draw let outcome = 1; // Function call eloRating(Ra Rb K outcome);

Izhod

Updated Ratings:- Ra = 1207.21 Rb = 992.792

Časovna zapletenost: Časovna kompleksnost algoritma je odvisna predvsem od kompleksnosti funkcije pow, katere kompleksnost je odvisna od arhitekture računalnika. Na x86 je to delovanje v konstantnem času: -O(1)
Pomožni prostor: O(1)