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Rn<\/strong> is the new rating.<\/p>\n <\/div>\n <\/div>\n <\/li>\n \n \n
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Ro <\/strong>is the prematch rating.<\/p>\n <\/div>\n <\/div>\n <\/li>\n \n \n
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K <\/strong>is the weight constant for the tournament played. (For example, Eloratings.net<\/strong> uses 60 for World Cup finals, 50 for continental championship, 40 for World Cup and continental qualifiers, and 30 for other tournaments, with just 20 for friendly matches. It also needs to be adjusted for goal difference).<\/p>\n <\/div>\n <\/div>\n <\/li>\n \n \n
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W <\/strong>is the result of the game (a team get 1 for a win, 0.5 for a draw, and 0 for a loss).<\/p>\n <\/div>\n <\/div>\n <\/li>\n \n \n
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We <\/strong>is the win expectancy.<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n\n Calculating Win Expectancy\n <\/h3>\n \n\n \n As you can see, in order to calculate the Elo Rating, you first need to calculate the Win expectancy. To do this, use the following formula:<\/strong><\/p>\n\n\n We = 1 \/ (10(-dr\/400) + 1)<\/strong><\/p>\n\n\n dr <\/strong>is the difference in ratings<\/strong> plus 100 points for a home team.<\/p>\n\n\n The following chart shows some examples of what a win expectancy<\/strong> looks like for difference in ratings from 0 to 800 points.<\/p>\n\n\n
Ratings Difference<\/th> Higher Rated team<\/th> Lower Rated team<\/th><\/tr><\/thead> 0<\/td> 0.5<\/td> 0.5<\/td><\/tr> 10<\/td> 0.514<\/td> 0.486<\/td><\/tr> 20<\/td> 0.529<\/td> 0.471<\/td><\/tr> 30<\/td> 0.543<\/td> 0.457<\/td><\/tr> 40<\/td> 0.557<\/td> 0.443<\/td><\/tr> 50<\/td> 0.571<\/td> 0.429<\/td><\/tr> 60<\/td> 0.585<\/td> 0.415<\/td><\/tr> 70<\/td> 0.599<\/td> 0.401<\/td><\/tr> 80<\/td> 0.613<\/td> 0.387<\/td><\/tr> 90<\/td> 0.627<\/td> 0.373<\/td><\/tr> 100<\/td> 0.64<\/td> 0.36<\/td><\/tr> 110<\/td> 0.653<\/td> 0.347<\/td><\/tr> 120<\/td> 0.666<\/td> 0.334<\/td><\/tr> 130<\/td> 0.679<\/td> 0.321<\/td><\/tr> 140<\/td> 0.691<\/td> 0.309<\/td><\/tr> 150<\/td> 0.703<\/td> 0.297<\/td><\/tr> 160<\/td> 0.715<\/td> 0.285<\/td><\/tr> 170<\/td> 0.727<\/td> 0.273<\/td><\/tr> 180<\/td> 0.738<\/td> 0.262<\/td><\/tr> 190<\/td> 0.749<\/td> 0.251<\/td><\/tr> 200<\/td> 0.76<\/td> 0.24<\/td><\/tr> 210<\/td> 0.77<\/td> 0.23<\/td><\/tr> 220<\/td> 0.78<\/td> 0.22<\/td><\/tr> 230<\/td> 0.79<\/td> 0.21<\/td><\/tr> 240<\/td> 0.799<\/td> 0.201<\/td><\/tr> 250<\/td> 0.808<\/td> 0.192<\/td><\/tr> 260<\/td> 0.817<\/td> 0.183<\/td><\/tr> 270<\/td> 0.826<\/td> 0.174<\/td><\/tr> 280<\/td> 0.834<\/td> 0.166<\/td><\/tr> 290<\/td> 0.841<\/td> 0.159<\/td><\/tr> 300<\/td> 0.849<\/td> 0.151<\/td><\/tr> 325<\/td> 0.867<\/td> 0.133<\/td><\/tr> 350<\/td> 0.882<\/td> 0.118<\/td><\/tr> 375<\/td> 0.896<\/td> 0.104<\/td><\/tr> 400<\/td> 0.909<\/td> 0.091<\/td><\/tr> 425<\/td> 0.92<\/td> 0.08<\/td><\/tr> 450<\/td> 0.93<\/td> 0.07<\/td><\/tr> 475<\/td> 0.939<\/td> 0.061<\/td><\/tr> 500<\/td> 0.947<\/td> 0.053<\/td><\/tr> 525<\/td> 0.954<\/td> 0.046<\/td><\/tr> 550<\/td> 0.96<\/td> 0.04<\/td><\/tr> 575<\/td> 0.965<\/td> 0.035<\/td><\/tr> 600<\/td> 0.969<\/td> 0.031<\/td><\/tr> 625<\/td> 0.973<\/td> 0.027<\/td><\/tr> 650<\/td> 0.977<\/td> 0.023<\/td><\/tr> 675<\/td> 0.98<\/td> 0.02<\/td><\/tr> 700<\/td> 0.983<\/td> 0.017<\/td><\/tr> 725<\/td> 0.985<\/td> 0.015<\/td><\/tr> 750<\/td> 0.987<\/td> 0.013<\/td><\/tr> 775<\/td> 0.989<\/td> 0.011<\/td><\/tr> 800<\/td> 0.99<\/td> 0.01<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n Adjusting for goal difference\n <\/h3>\n \n\n \n K <\/strong>is a number you need to adjust goal difference in the game.<\/p>\n\n\n
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2 goals increase it by 50%<\/p>\n <\/div>\n <\/div>\n <\/li>\n
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3 goals increase it by 75%<\/p>\n <\/div>\n <\/div>\n <\/li>\n
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4 or more increases it by 3\/4 + (Goal difference \u2013 3)\/8<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n Example\n <\/h3>\n \n\n \n Let us look at a hypothetical example<\/strong>. Belgium is the current Elo leader (April 2020), with 2084 points.England is currently at 12th place, with 1956 points.<\/p>\n\n\n If the two were to meet for a friendly, in Belgium, we can calculate their respective win expectancies before the match, as well as how the match result would affect their respective Elo ratings.<\/p>\n\n
\n First, let\u2019s calculate their win expectancy, using the formula We = 1 \/ (10(-dr\/400) + 1):<\/strong><\/p>\n\n\n The ratings difference is 2084 \u2013 1956 +100= 228.<\/p>\n\n
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Win expectancy for Home team Belgium = 1 \/ (10(-228\/400)+ 1) = 0,789<\/strong><\/p>\n <\/div>\n <\/div>\n <\/li>\n \n \n
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