After years of messing around, I finally decided to give it a shot. Still a work in progress, but I think they're reasonable for now and with the Gold Cup on the way and no WCQs for a while, I figured it was a good time to post them. Some oddities down on the list (Trinidad probably isn't that bad) but that's life. Each team has an offense rating and a defense rating. To get a predicted score for a (neutral site) match between two teams, simply multiply Team A's offense rating by Team B's defense rating to get Team A's predicted score, and vice versa. Each team's overall rating is based on their predicted record against a "league" of four teams of varying abilities. This is not necessarily the best way of combining the ratings but it'll do for now. You could also rank them "sequentially", so that each team would expect a positive record against all the teams below them...each team's sequential ranking is included in the "SEQ" column below. The relative ranking of teams depends on the competition. This ranking includes matches since 1/1/02, except for friendlies between teams from the same confederation (with a couple exceptions for teams that didn't score in official matches)--these may be added later at a low weighting but for now I'll do without them. Intercontinental friendlies are included because otherwise there just aren't enough matches between confederations. RK--rank Team--team Off--offense rating Def--defense rating Pct--Percentage of available points a team would be expected to win against the four-team league. SEQ--A team's rank if done "sequentially", as explained above Code: RK Team Off Def Pct. SEQ -- ---- --- --- ---- --- 1 Czech Republic 5.30 0.31 0.940 3 2 Brazil 4.95 0.28 0.936 2 3 Netherlands 4.42 0.23 0.931 1 4 Argentina 4.88 0.34 0.925 5 5 Portugal 4.73 0.33 0.921 7 6 Sweden 3.86 0.23 0.912 4 7 England 3.97 0.28 0.906 6 8 Spain 3.53 0.26 0.891 8 9 Turkey 3.62 0.33 0.878 10 10 Germany 3.91 0.41 0.872 13 11 France 3.12 0.28 0.863 9 12 Italy 3.20 0.32 0.855 11 13 Mexico 3.07 0.32 0.849 12 14 Uruguay 3.78 0.50 0.846 22 15 Ukraine 3.07 0.33 0.845 15 16 Slovakia 3.16 0.39 0.835 18 17 Paraguay 3.36 0.45 0.834 23 18 Denmark 3.19 0.40 0.834 21 19 Poland 3.41 0.46 0.833 24 20 Romania 3.50 0.49 0.831 25 21 Colombia 2.64 0.30 0.823 16 22 Russia 3.40 0.51 0.820 29 23 Croatia 2.75 0.34 0.819 19 24 United States 2.71 0.34 0.816 20 25 Ecuador 3.06 0.44 0.814 27 26 Greece 2.27 0.24 0.809 14 27 Cameroon 2.41 0.29 0.805 17 28 Peru 2.79 0.46 0.788 34 29 Morocco 2.31 0.34 0.782 28 30 Chile 2.26 0.32 0.781 26 31 Austria 3.11 0.59 0.779 39 32 Switzerland 2.81 0.51 0.776 37 33 Egypt 3.02 0.58 0.775 40 34 Nigeria 2.17 0.33 0.771 30 35 Senegal 2.23 0.35 0.771 31 36 Serbia/Mont 2.26 0.36 0.768 32 37 Ireland 2.29 0.38 0.767 33 38 Japan 2.29 0.38 0.767 35 39 Bolivia 2.79 0.58 0.756 44 40 Iran 2.80 0.58 0.755 45 41 Bulgaria 2.71 0.56 0.754 43 42 Venezuela 2.40 0.49 0.745 41 43 Ivory Coast 2.00 0.35 0.743 36 44 Finland 2.66 0.59 0.741 47 45 Hungary 2.74 0.62 0.741 49 46 Belgium 2.54 0.57 0.735 48 47 Tunisia 2.22 0.46 0.735 42 48 Norway 1.90 0.35 0.732 38 49 Costa Rica 2.52 0.58 0.731 50 50 South Korea 2.04 0.45 0.716 46 51 Latvia 2.14 0.49 0.714 51 52 Honduras 2.07 0.55 0.690 53 53 Wales 2.05 0.54 0.689 54 54 Macedonia 2.16 0.60 0.686 56 55 Georgia 2.53 0.75 0.685 59 56 Australia 2.31 0.68 0.681 58 57 Jamaica 1.84 0.50 0.674 55 58 Ghana 1.67 0.43 0.672 52 59 Israel 1.96 0.59 0.663 61 60 Oman 1.83 0.55 0.659 60 61 Scotland 1.71 0.50 0.658 57 62 Belarus 2.04 0.67 0.652 66 63 Slovenia 1.95 0.63 0.650 64 64 Albania 2.06 0.69 0.648 69 65 Libya 1.94 0.64 0.647 67 66 Togo 1.88 0.63 0.642 68 67 Bosnia/Herc 1.65 0.52 0.641 62 68 Cuba 1.91 0.65 0.639 70 69 Canada 1.68 0.54 0.638 65 70 South Africa 1.66 0.54 0.638 63 71 Zimbabwe 1.81 0.63 0.631 71 72 Gabon 1.92 0.73 0.618 79 73 Estonia 1.45 0.51 0.61 73 74 Guatemala 1.86 0.73 0.61 81 75 Iceland 2.02 0.82 0.609 83 76 Angola 1.48 0.53 0.609 74 77 Guinea 1.76 0.68 0.609 80 78 Jordan 1.46 0.53 0.606 75 79 Saudi Arabia 1.58 0.60 0.606 77 80 Sierra Leone 1.34 0.47 0.605 72 81 China 1.50 0.57 0.601 78 82 Lithuania 1.37 0.50 0.599 76 83 Mali 1.72 0.71 0.595 84 84 Congo-Kinshasa 1.57 0.63 0.594 82 85 Zambia 1.40 0.60 0.573 85 86 Algeria 1.51 0.68 0.570 86 87 Bahrain 1.77 0.84 0.568 87 88 Burkina Faso 1.60 0.76 0.562 88 89 New Zealand 1.90 0.95 0.560 90 90 Kenya 1.70 0.84 0.557 89 91 Uzbekistan 1.55 0.79 0.547 91 92 Iraq 1.78 0.96 0.540 95 93 Qatar 1.46 0.77 0.536 93 94 Congo-Brazza 1.22 0.64 0.529 92 95 Panama 1.28 0.69 0.527 94 96 Cape Verde Isl. 1.41 0.77 0.527 96 97 Armenia 1.44 0.80 0.527 97 98 Benin 1.89 1.14 0.517 100 99 Kuwait 1.59 0.95 0.512 99 100 Liechtenstein 1.51 0.94 0.501 101 101 Northern Ire 0.93 0.55 0.492 98 102 Rwanda 1.31 0.86 0.486 104 103 Uganda 1.16 0.75 0.484 103 104 Moldova 1.08 0.70 0.484 102 105 Guadeloupe 1.39 0.94 0.482 105 106 Trinidad/ 1.27 0.86 0.479 106 107 Cyprus 1.44 1.04 0.468 108 108 El Salvador 1.13 0.79 0.468 107 109 Martinique 1.44 1.07 0.462 110 110 Sudan 1.27 0.94 0.461 109 111 Gambia 1.42 1.09 0.454 112 112 Faroe Islands 1.45 1.12 0.454 113 113 Chad 1.55 1.20 0.453 114 114 Lebanon 1.08 0.84 0.445 115 115 United Arab Em 1.12 0.88 0.444 116 116 French Guyana 0.77 0.59 0.440 111 117 Syria 1.62 1.34 0.439 119 118 Azerbaijan 1.06 0.87 0.435 117 119 Haiti 1.06 0.88 0.433 120 120 Botswana 0.96 0.79 0.431 118 121 Malawi 1.53 1.34 0.424 121 122 Swaziland 1.51 1.35 0.419 122 123 Mauritius 1.40 1.27 0.415 123 124 North Korea 1.01 0.93 0.411 124 125 Turkmenistan 1.07 1.10 0.388 125 126 St. Lucia 1.67 1.71 0.386 126 127 St. Vincent 1.10 1.18 0.378 127 128 Thailand 1.26 1.39 0.370 128 129 Madagascar 0.82 0.93 0.366 129 130 Equatorial Gui 1.03 1.19 0.362 130 131 Liberia 0.84 1.05 0.347 132 132 Palestine 0.97 1.20 0.347 131 133 Tajikistan 0.62 0.79 0.344 134 134 Mozambique 1.01 1.28 0.341 133 135 Ethiopia 0.76 1.01 0.335 135 136 Burundi 0.97 1.31 0.329 136 137 Kazakhstan 0.66 0.98 0.316 137 138 Surinam 0.73 1.09 0.312 138 139 Andorra 0.60 0.96 0.303 147 140 Guinea-Bissau 0.76 1.20 0.302 144 141 Namibia 0.66 1.06 0.301 145 142 Yemen 1.14 1.72 0.301 140 143 Niger 0.81 1.27 0.300 142 144 Bermuda 1.18 1.81 0.298 141 145 Grenada 1.50 2.27 0.296 139 146 Malta 0.83 1.33 0.296 146 147 Indonesia 1.12 1.76 0.293 143 148 Barbados 0.80 1.38 0.282 149 149 Vietnam 0.91 1.57 0.278 148 150 Seychelles 0.75 1.45 0.260 151 151 Zanzibar 1.05 1.97 0.257 150 152 Singapore 0.74 1.47 0.256 152 153 Eritrea 0.49 1.06 0.254 159 154 Kyrgyzstan 0.73 1.48 0.253 153 155 Hong Kong 0.77 1.59 0.246 155 156 Myanmar 0.91 1.85 0.245 154 157 Tanzania 0.64 1.39 0.244 157 158 Central Afr Rep 0.52 1.18 0.243 160 159 Malaysia 0.80 1.71 0.239 156 160 Nicaragua 0.78 1.68 0.237 158 161 Mauritania 0.36 0.97 0.231 163 162 St. Kitts/Nevis 0.72 1.67 0.226 161 163 Vanuatu 0.45 1.22 0.220 162 164 Luxembourg 0.47 1.35 0.209 164 165 Maldives 0.69 1.98 0.189 165 166 Netherlands Ant 0.58 1.76 0.188 166 167 Solomon Islands 0.59 1.79 0.186 167 168 Lesotho 0.35 1.37 0.173 169 169 India 0.49 1.78 0.167 168 170 San Marino 0.30 1.36 0.163 173 171 Antigua 0.43 1.77 0.153 170 172 Sri Lanka 0.44 1.98 0.139 174 173 Dominican Rep 0.51 2.22 0.137 172 174 Fiji 0.55 2.34 0.136 171 175 Cayman Islands 0.36 1.91 0.129 176 176 Belize 0.25 1.61 0.124 181 177 Puerto Rico 0.54 2.57 0.122 175 178 Bangladesh 0.48 2.55 0.112 177 179 Tahiti 0.41 2.33 0.110 178 180 Guyana 0.44 2.57 0.104 179 181 Somalia 0.12 1.47 0.102 189 182 British Virgin 0.35 2.36 0.099 183 183 New Caledonia 0.57 3.49 0.087 180 184 Laos 0.49 3.23 0.084 182 185 Taiwan 0.42 3.09 0.079 185 186 Papua New Gui 0.54 3.59 0.079 184 187 Pakistan 0.37 2.92 0.077 186 188 Sao Tome + Pri 0.17 2.29 0.068 192 189 Dominica 0.34 3.21 0.064 187 190 Brunei 0.29 3.45 0.051 190 191 Nepal 0.37 3.88 0.051 188 192 Bhutan 0.14 3.31 0.034 198 193 Philippines 0.30 4.53 0.032 195 194 St. Martin 0.25 4.39 0.030 196 195 Aruba 0.45 6.02 0.026 193 196 Cambodia 0.37 5.51 0.026 194 197 East Timor 0.30 5.64 0.020 197 198 Montserrat 0.72 8.73 0.019 191 199 Turks+Caicos Is 0.00 3.29 0.018 209 200 Macao 0.15 4.92 0.016 201 201 Afghanistan 0.18 5.22 0.016 199 202 Anguilla 0.10 4.66 0.015 203 203 US Virgin Isl 0.20 6.87 0.009 202 204 Bahamas 0.25 7.77 0.007 200 205 Mongolia 0.14 7.66 0.004 204 206 Samoa 0.16 8.76 0.003 205 207 Cook Islands 0.06 9.05 0.001 207 208 Tonga 0.18 11.18 0.001 206 209 American Sam 0.08 19.87 0.000 208 210 Guam 0.00 19.88 0.000 210
What are the four teams in the hypothetical league? Seems to me there are a lot of holes in the explanation... I don't quite understand how you got the numbers.
The four teams in the hypothetical league are: Team A--80th percentile offense and defense Team B--60th percentile offense and defense Team C--40th percentile offense and defense Team D--20th percentile offense and defense This gives a reasonable range of quality of opposition--but like I said, it's sort of arbitrary. Anyway, how I get the numbers: 1. Start off with a default set of ratings for each team (every team is rated with a 1 for offense and defense at the start--so every game would be predicted to end 1-1) 2. Compare the predicted score for each game with the actual score to get a "game probability". using the poisson distribution. For example, if Team A is expected to beat Team B 2.3-1.2 and the actual score was 2-1, then the game probability would be calculated like this: Chance of a team expected to score 2.3 goals scoring 2 goals: 0.265 (26.5%) Chance of a team expected to score 1.2 goals scoring 1 goal: 0.361 (36.1%) Game probability: (0.265*0.361)=0.096 3. Multiply all the game probabilities (weighted based on the competition, and some other stuff) together to get a "total probability". 4. Adjust the ratings until the total probability is maximized. I'm still messing with the weightings, and how to handle homefield advantage...but I felt it was worth posting now as a de facto Gold Cup prediction, and to get some feedback...
From what I understand that really doesn't affect the ranks too much. It's just you have to establish a "baseline" of sorts somewhere and so that's the baseline he chose to set. Correct, JG? A few questions (and obsercations): 1. Do you make any adjustments for home and road matches? Some clubs play far more often at home than others. 2. I assume step 4 uses some sort of iterative process to make closer and closer "guesses" as to what the probability maximizing numbers are, correct? 3. I do have some sample size concerns. Only going back three years concerns me a little, particularly when you throw out so many friendly matches (I do agree 100% though that the lack of inter-confederational matches necssitates the use of inter-federational friendlies). Have you tried to examine any sets of test data (say eliminating the 2005 matches and testing the systems accuracy on the 2005 results)? I'm thinking that a few more years with a gradual weighting system where results from longer ago are weighted less, but still counted. 4. (Just an observation) Someone might criticize the inherent assumption that the chances of Team A scoring 2 goals and Team B scoring 1 goal are not independent (that is they'd argue that how many goals Team A scores affects the probabilities of goals scored for Team B). Personally I think that would be blatant nitpickery and would not really have much effect on the overall validity on the system. 5. My opinion, and this goes with point 5, is that matches involving weaker teams probably need to have lesser weights, but I have yet to come up with a non clunky way to do this. Why? A few reasons: one is that weaker teams tend to play fewer matches meaning that whatever ratings they are assigned are likely to be less accurate. Another is that when a weak team faces a strong team, very often the strong team can win by whatever score it damn well feels like (eg. When Australia won 31-0, it could have stopped at any point it wanted to). Another reason is that when a strong team faces a weak team, even in matches that matter the strong team is more likely to send an understrength squad as it will likely be good enough to prevail. Maybe the solution is to look at each type of match and rate the overall average strength of teams for that type of match and adjust the weights for match type. 6. I prefer the sequential ranking because ultimately I think that's more in line with what people generally would want to know (IE, people are probably more interested in what Brazil would do against the Czechs than lower ranked teams). Your system though so knock yourself out, particularly since I realize the way you did it is a little easier. 7. Otherwise I really like the construction of your system. It seems like it could work extremely well. I think I might fiddle with it a little when I get a chance and see how it works with little tweaks here and there. It looks like excellent work on the face of it.
Pretty much...just a way of combining the offensive and defensive ratings into one number. Yes. Right now the home team's expected score is multiplied by 1.24 and the road team by 0.76. It would be nice to have different homefield advantages for each team--or at least for groups of teams--but that's difficult. Yes, although nothing particularly brilliant...I just adjust each team's ratings to a probability maximum in succession, and after a few times through the list it stabilizes...I suppose I could be hitting a local maximum, but anything more complicated is probably beyond my Excel skills. I'll probably end up adding the intraconfederation friendlies at some point because it will add more data for teams with few matches. I actually hadn't thought of testing on the 2005 results, but that's a good idea. I do a thing where I weight matches involving teams of similar ability more than matches between teams of widely differing abilities, but the implementation is sort of arbitrary for now. Hadn't thought of discounting matches involving weaker teams in general. Yeah...it depends on what question you want to answer. I figured I'd hedge and include both rankings. Thanks...like I said above I'd been messing around with rating ideas for a long time, but had never been quite sure if was doable enough to be worth the time...the fact that you seemed to have come up with a reasonable system partially inspired me to give it a real shot.
New ratings, post Gold Cup. I added the intracontinental friendlies and messed around with some of the weightings a bit so some teams that haven't played may have noticeable changes in their ratings. Code: RK Team Off Def Pct SEQ -- -------------- ----- ----- ----- --- 1 Czech Republic 5.41 0.30 0.942 2 2 Brazil 4.94 0.29 0.933 3 3 Netherlands 4.34 0.24 0.925 1 4 Argentina 4.70 0.34 0.916 7 5 England 4.15 0.28 0.909 5 6 Sweden 4.02 0.28 0.904 6 7 Spain 3.74 0.24 0.902 4 8 Portugal 4.22 0.37 0.892 9 9 Germany 3.99 0.43 0.868 14 10 Turkey 3.45 0.33 0.864 10 11 France 3.09 0.27 0.860 8 12 Denmark 3.62 0.39 0.859 12 13 Italy 3.07 0.31 0.848 11 14 Uruguay 3.75 0.49 0.842 21 15 Mexico 3.11 0.34 0.841 15 16 Ukraine 2.93 0.32 0.835 13 17 Romania 3.59 0.48 0.834 23 18 Paraguay 3.28 0.44 0.825 22 19 United States 2.85 0.34 0.824 17 20 Croatia 2.83 0.35 0.818 19 21 Poland 3.31 0.49 0.813 29 22 Cameroon 2.47 0.30 0.806 18 23 Colombia 2.61 0.33 0.806 20 24 Ecuador 3.03 0.45 0.804 30 25 Greece 2.31 0.26 0.804 16 26 Russia 3.24 0.54 0.796 35 27 Slovakia 2.73 0.41 0.794 28 28 Austria 3.23 0.57 0.789 38 29 Ireland 2.44 0.35 0.787 24 30 Peru 2.83 0.48 0.781 36 31 Nigeria 2.34 0.34 0.780 25 32 Chile 2.25 0.33 0.775 26 33 Morocco 2.24 0.33 0.773 27 34 Switzerland 2.77 0.51 0.767 39 35 Senegal 2.29 0.37 0.766 31 36 Serbia/Mont 2.34 0.38 0.765 34 37 Japan 2.26 0.37 0.762 33 38 Egypt 2.80 0.55 0.760 41 39 Iran 3.02 0.62 0.759 42 40 Bulgaria 2.66 0.51 0.757 40 41 Ivory Coast 2.19 0.37 0.754 37 42 Norway 2.06 0.33 0.752 32 43 Bolivia 2.80 0.58 0.751 44 44 Belgium 2.66 0.57 0.742 45 45 Costa Rica 2.63 0.56 0.741 46 46 Finland 2.55 0.56 0.732 49 47 Venezuela 2.23 0.46 0.730 43 48 Hungary 2.68 0.64 0.724 52 49 Tunisia 2.09 0.45 0.716 47 50 Honduras 2.29 0.53 0.716 50 51 Israel 2.46 0.59 0.715 53 52 Belarus 2.54 0.62 0.715 54 53 South Korea 2.09 0.46 0.714 48 54 Wales 2.15 0.50 0.709 51 55 Jamaica 2.09 0.54 0.688 55 56 Macedonia 2.12 0.62 0.669 57 57 Libya 2.01 0.59 0.665 56 58 Slovenia 1.90 0.57 0.657 60 59 South Africa 1.89 0.57 0.657 59 60 Latvia 1.90 0.57 0.656 61 61 Georgia 2.29 0.78 0.646 71 62 Australia 1.95 0.64 0.644 64 63 Ghana 1.57 0.47 0.642 58 64 Cuba 1.93 0.63 0.642 65 65 Togo 1.84 0.59 0.641 62 66 Oman 1.84 0.60 0.639 63 67 Zimbabwe 1.85 0.61 0.638 66 68 Mali 1.89 0.64 0.636 69 69 Canada 1.71 0.56 0.632 67 70 Albania 1.91 0.66 0.630 74 71 Scotland 1.56 0.52 0.623 68 72 Gabon 1.91 0.70 0.620 76 73 Guinea 1.89 0.70 0.618 77 74 Bosnia/Herce 1.57 0.54 0.617 72 75 Guatemala 1.84 0.69 0.613 79 76 Jordan 1.48 0.51 0.611 73 77 Sierra Leone 1.39 0.47 0.609 70 78 Angola 1.49 0.54 0.604 75 79 Congo-Kinshasa 1.69 0.65 0.602 81 80 China 1.50 0.56 0.600 78 81 Saudi Arabia 1.56 0.59 0.600 80 82 Iceland 1.90 0.77 0.600 83 83 Zambia 1.49 0.58 0.591 82 84 Lithuania 1.53 0.63 0.584 84 85 Kenya 1.78 0.77 0.584 86 86 Panama 1.44 0.61 0.573 85 87 Iraq 1.82 0.86 0.565 89 88 Estonia 1.39 0.62 0.564 87 89 Burkina Faso 1.55 0.72 0.562 88 90 Bahrain 1.81 0.87 0.561 90 91 Uzbekistan 1.63 0.81 0.549 91 92 Algeria 1.43 0.72 0.540 93 93 Congo-Brazza 1.34 0.67 0.537 92 94 New Zealand 1.60 0.85 0.534 95 95 Qatar 1.44 0.76 0.532 94 96 Armenia 1.45 0.81 0.520 97 97 Cyprus 1.59 0.90 0.519 99 98 Cape Verde Isl. 1.38 0.77 0.518 96 99 Kuwait 1.51 0.89 0.509 100 100 Moldova 1.08 0.61 0.504 98 101 Guadeloupe 1.43 0.89 0.497 101 102 Trinidad/Tobago 1.36 0.87 0.491 102 103 Benin 1.64 1.06 0.491 104 104 Uganda 1.16 0.74 0.485 103 105 Rwanda 1.27 0.86 0.474 106 106 Syria 1.60 1.14 0.468 111 107 El Salvador 1.15 0.80 0.466 107 108 Gambia 1.30 0.93 0.465 110 109 Northern Ire 0.89 0.60 0.464 105 110 Sudan 1.30 0.93 0.463 112 111 Haiti 1.16 0.84 0.459 113 112 Botswana 1.00 0.72 0.458 109 113 Malawi 1.56 1.18 0.455 114 114 Martinique 1.46 1.11 0.453 115 115 Faroe Islands 1.56 1.19 0.453 116 116 French Guyana 0.77 0.54 0.450 108 117 Liechtenstein 1.33 1.04 0.447 118 118 Azerbaijan 1.10 0.84 0.446 117 119 United Arab Em 1.21 0.96 0.439 119 120 Mauritius 1.29 1.04 0.439 120 121 Kazakhstan 1.27 1.13 0.416 122 122 Chad 1.42 1.26 0.416 123 123 North Korea 1.05 0.93 0.416 121 124 Equatoria Gui 1.25 1.14 0.410 124 125 St. Vincent 1.18 1.08 0.408 126 126 Lebanon 1.05 0.97 0.408 125 127 Thailand 1.29 1.31 0.384 127 128 Turkmenistan 1.07 1.12 0.378 128 129 Mozambique 1.04 1.10 0.377 129 130 Liberia 0.88 0.94 0.375 130 131 Swaziland 1.32 1.44 0.370 131 132 Malta 1.10 1.25 0.362 132 133 Ethiopia 0.89 1.04 0.357 133 134 Madagascar 0.92 1.07 0.357 134 135 Guinea-Bissau 0.96 1.14 0.352 135 136 Tajikistan 0.62 0.76 0.350 137 137 Burundi 0.96 1.17 0.347 136 138 Barbados 1.03 1.27 0.343 138 139 St. Lucia 1.31 1.63 0.338 139 140 Nigeria 0.85 1.15 0.327 140 141 Palestine 0.81 1.14 0.319 141 142 Indonesia 1.15 1.64 0.309 142 143 Namibia 0.76 1.15 0.305 144 144 Kyrgystan 0.90 1.36 0.303 143 145 Andorra 0.57 0.96 0.293 147 146 Grenada 1.36 2.09 0.291 145 147 Surinam 0.73 1.23 0.285 148 148 Zanzibar 1.13 1.88 0.276 146 149 Yemen 1.02 1.72 0.275 149 150 Lesotho 0.73 1.30 0.275 150 151 Eritrea 0.51 1.01 0.268 157 152 Hong Kong 0.83 1.53 0.264 151 153 Seychelles 0.69 1.31 0.263 154 154 Singapore 0.81 1.53 0.258 153 155 Tanzania 0.76 1.45 0.258 156 156 St. Kitts/Nevis 0.82 1.56 0.257 155 157 Bermuda 1.03 1.94 0.253 152 158 Nicaragua 0.82 1.62 0.251 158 159 Mauritania 0.41 0.97 0.245 163 160 Malaysia 0.78 1.61 0.243 160 161 Vietnam 0.89 1.79 0.243 159 162 Central Afr Rep 0.51 1.16 0.240 162 163 Myanmar 0.91 2.01 0.225 161 164 Netherlands Ant 0.65 1.58 0.219 164 165 Luxembourg 0.67 1.64 0.215 165 166 San Marino 0.43 1.36 0.193 166 167 India 0.53 1.71 0.177 167 168 Antigua 0.49 1.77 0.164 169 169 Solomon Islands 0.63 2.13 0.162 168 170 Sri Lanka 0.46 1.87 0.148 172 171 Vanuatu 0.35 1.62 0.146 174 172 Belize 0.30 1.51 0.143 175 173 Maldives 0.56 2.23 0.141 171 174 Puerto Rico 0.64 2.57 0.134 170 175 Guyana 0.60 2.48 0.132 173 176 Cayman Islands 0.33 1.88 0.121 177 177 Somalia 0.15 1.39 0.114 188 178 Pakistan 0.41 2.34 0.106 179 179 Tahiti 0.43 2.44 0.106 178 180 Dominican Rep 0.40 2.33 0.106 180 181 Bangladesh 0.44 2.65 0.096 182 182 Dominica 0.61 3.25 0.096 176 183 Fiji 0.46 2.75 0.094 181 184 Sao Tome/Prin 0.22 1.95 0.091 186 185 Laos 0.45 3.24 0.075 183 186 Taiwan 0.43 3.35 0.068 185 187 British VI 0.27 2.69 0.067 189 188 Papua New Gui 0.54 4.17 0.059 184 189 New Caledonia 0.42 3.80 0.055 187 190 Nepal 0.36 3.68 0.051 190 191 Brunei 0.28 3.67 0.042 191 192 Bahamas 0.25 4.37 0.027 195 193 Philippines 0.22 4.23 0.026 196 194 Aruba 0.40 5.61 0.024 193 195 St. Martin 0.14 3.90 0.024 198 196 Bhutan 0.12 3.76 0.023 199 197 Cambodia 0.31 5.27 0.022 194 198 Turks+Caicos Is 0.00 3.01 0.019 209 199 Afghanistan 0.13 5.04 0.012 201 200 Montserrat 0.69 9.42 0.012 192 201 East Timor 0.24 6.16 0.011 197 202 Macao 0.19 5.83 0.011 200 203 US Virgin Isl 0.11 6.88 0.004 202 204 Anguilla 0.09 6.98 0.004 204 205 Mongolia 0.08 7.20 0.003 206 206 Samoa 0.12 9.19 0.001 203 207 Cook Islands 0.06 10.38 0.000 207 208 Tonga 0.16 13.88 0.000 205 209 Guam 0.00 20.08 0.000 210 210 American Samoa 0.08 26.66 0.000 208
What would happen if you selected a team's last "x" games instead of automatically weighting older games less heavily? Is that statistically more arbitrary? Also, are there any rules/guidelines for how you weight older games or is that down to professional judgment?
JG -- I fit the model that I think is equivalent to yours, weighting all games equally, and including all results from 1/1/02 through 4/10/06. I fit separate effects for home-field and neutral-field, taken to be identical for all countries. For the most part, the results appear similar to what you found last summer ... is this a surprise, or would you expect your weightings to have only a minor effect? One difference I noticed is that Ireland is #11 (up from #24) and Sweden #14 (down from #6) ... hopefully, this isn't too much a result of Ireland's recent 3-0 win over the Swedes (can't say I've checked). Below are team ratings, in "Seq" order, on the log scale to make offense and defense comparable. The Czech strength looks offense-skewed; the Dutch strength (surprisingly to me) defense-skewed; and of course, Brazil looks just plain strong. Code: COUNTRY Rk Off. Def. Brazil 1 1.26 -1.18 Netherlands 2 1.02 -1.39 Spain 3 1.04 -1.25 Czechia 4 1.33 -0.96 France 5 0.92 -1.35 Argentina 6 1.20 -0.90 Italy 7 0.91 -1.10 England 8 1.04 -0.89 Portugal 9 1.02 -0.88 Romania 10 0.98 -0.86 Ireland 11 0.65 -1.17 UnitedStates 12 0.78 -1.02 Germany 13 1.13 -0.66 Sweden 14 1.03 -0.75 Mexico 15 0.77 -1.00 Denmark 16 0.95 -0.76 Yugoslavia 17 0.90 -0.78 Croatia 18 0.69 -0.97 Turkey 19 0.86 -0.75 Greece 20 0.55 -1.05 Uruguay 21 0.99 -0.51 Colombia 22 0.54 -0.96 Paraguay 23 0.61 -0.87 Poland 24 0.86 -0.54 Switzerland 25 0.81 -0.58 Nigeria 26 0.58 -0.80 SerbiaandMontenegro 27 0.62 -0.75 Cameroon 28 0.61 -0.75 Morocco 29 0.50 -0.86 Bulgaria 30 0.74 -0.60 Slovakia 31 0.70 -0.62 Norway 32 0.50 -0.82 Japan 33 0.59 -0.72 Peru 34 0.83 -0.48 SouthKorea 35 0.43 -0.87 Russia 36 0.75 -0.53 Belgium 37 0.73 -0.54 Wales 38 0.47 -0.77 Australia 39 0.65 -0.58 Senegal 40 0.59 -0.63 Egypt 41 0.70 -0.51 Chile 42 0.44 -0.76 Ukraine 43 0.33 -0.83 Israel 44 0.75 -0.39 Belarus 45 0.79 -0.35 Iran 46 0.61 -0.52 Finland 47 0.64 -0.49 Ecuador 48 0.50 -0.63 Venezuela 49 0.58 -0.52 Tunisia 50 0.43 -0.64 Austria 51 0.69 -0.38 CostaRica 52 0.70 -0.34 Hungary 53 0.56 -0.41 Honduras 54 0.53 -0.40 BosniaandHerzegovina 55 0.34 -0.54 Bolivia 56 0.56 -0.28 China 57 0.29 -0.51 Macedonia 58 0.47 -0.33 Canada 59 0.37 -0.43 Guinea 60 0.36 -0.43 Slovenia 61 0.31 -0.45 Jamaica 62 0.34 -0.42 Mali 63 0.26 -0.44 Scotland 64 0.33 -0.36 Oman 65 0.27 -0.40 Ghana 66 0.22 -0.42 Guatemala 67 0.41 -0.22 Latvia 68 0.34 -0.25 Iceland 69 0.43 -0.13 SaudiArabia 70 0.17 -0.39 SouthAfrica 71 0.28 -0.27 Angola 72 0.24 -0.30 Iraq 73 0.40 -0.13 SierraLeone 74 -0.04 -0.55 Lithuania 75 0.17 -0.33 Estonia 76 0.14 -0.35 Togo 77 0.23 -0.22 Jordan 78 0.04 -0.40 Cuba 79 0.17 -0.25 Georgia 80 0.43 0.00 Albania 81 0.24 -0.17 Libya 82 0.24 -0.17 Bahrain 83 0.30 -0.06 Uzbekistan 84 0.25 -0.09 Cyprus 85 0.26 -0.08 Zambia 86 0.01 -0.28 NewZealand 87 0.32 0.03 Zimbabwe 88 0.17 -0.11 BurkinaFaso 89 0.14 -0.13 Algeria 90 0.04 -0.22 Armenia 91 0.09 -0.17 Qatar 92 0.14 -0.12 Gambia 93 0.15 -0.10 Moldova 94 -0.14 -0.37 Panama 95 0.04 -0.19 Guadeloupe 96 0.19 -0.03 Gabon 97 0.13 -0.07 NorthernIreland 98 -0.15 -0.33 Kuwait 99 0.16 0.00 Kenya 100 0.14 -0.02 Syria 101 0.32 0.16 NorthKorea 102 -0.09 -0.24 UnitedArabEmirates 103 0.11 0.00 Haiti 104 0.13 0.09 Martinique 105 0.21 0.17 TrinidadandTobago 106 -0.07 -0.11 Uganda 107 -0.09 -0.11 Congo 108 -0.20 -0.13 FaroeIslands 109 0.07 0.17 Malawi 110 0.11 0.24 ElSalvador 111 -0.24 -0.07 CapeVerde 112 -0.05 0.11 Azerbaijan 113 -0.26 -0.08 Liechtenstein 114 -0.15 0.04 Botswana 115 -0.31 -0.12 Sudan 116 -0.06 0.15 Kazakhstan 117 -0.10 0.12 Lebanon 118 -0.09 0.16 Ethiopia 119 -0.11 0.14 Chad 120 0.00 0.28 Benin 121 -0.06 0.24 Rwanda 122 -0.06 0.24 Barbados 123 -0.22 0.13 FrenchGuiana 124 -0.37 0.01 Palestine 125 -0.27 0.15 Thailand 126 0.01 0.44 Grenada 127 0.22 0.66 Turkmenistan 128 -0.18 0.28 Mauritius 129 -0.24 0.27 Malta 130 -0.16 0.38 SaintLucia 131 -0.01 0.54 Madagascar 132 -0.26 0.29 Mozambique 133 -0.40 0.19 Belize 134 -0.12 0.52 CentralAfricanRepublic 135 -0.37 0.27 Tajikistan 136 -0.60 0.05 Niger 137 -0.37 0.30 Surinam 138 -0.53 0.17 EquatorialGuinea 139 -0.42 0.28 Guyana 140 -0.16 0.54 Vietnam 141 -0.19 0.54 Liberia 142 -0.47 0.27 Indonesia 143 -0.16 0.62 Reunion 144 -0.50 0.29 Singapore 145 -0.41 0.39 Bermuda 146 -0.07 0.73 NetherlandsAntilles 147 -0.41 0.40 Burundi 148 -0.47 0.41 Malaysia 149 -0.48 0.39 Swaziland 150 -0.23 0.66 Andorra 151 -0.84 0.05 Yemen 152 -0.15 0.74 HongKong 153 -0.36 0.58 SaintKittsandNevis 154 -0.35 0.62 Myanmar 155 -0.35 0.62 Kyrgyzstan 156 -0.74 0.31 Namibia 157 -0.67 0.40 Maldives 158 -0.44 0.64 Lesotho 159 -0.69 0.40 AntiguaandBarbuda 160 -0.51 0.61 Eritrea 161 -0.74 0.42 Nicaragua 162 -0.70 0.47 Luxembourg 163 -0.73 0.45 Tanzania 164 -0.66 0.53 Seychelles 165 -0.82 0.39 India 166 -0.62 0.60 SolomonIslands 167 -0.51 0.76 Zanzibar 168 -0.63 0.67 Vanuatu 169 -0.99 0.31 Mauritania 170 -0.96 0.36 Fiji 171 -0.70 0.73 PuertoRico 172 -0.75 1.00 NewCaledonia 173 -0.66 1.10 DominicanRepublic 174 -0.82 0.94 SanMarino 175 -1.31 0.51 SriLanka 176 -1.22 0.66 Tahiti 177 -0.96 0.97 Bangladesh 178 -1.25 0.80 Dominica 179 -0.87 1.20 Taiwan 180 -1.02 1.06 Laos 181 -0.87 1.35 Pakistan 182 -1.33 0.96 Somalia 183 -1.69 0.79 CaymanIslands 184 -1.60 0.92 PapuaNewGuinea 185 -1.03 1.56 Nepal 186 -1.14 1.50 Aruba 187 -0.82 1.88 SaoTomeePrincipe 188 -1.63 1.12 Djibouti 189 -1.21 1.63 Montserrat 190 -0.75 2.13 Brunei 191 -1.73 1.18 BritishVirginIslands 192 -1.54 1.38 Philippines 193 -1.46 1.60 Afghanistan 194 -1.30 1.79 Cambodia 195 -1.40 1.73 SaintMartin 196 -1.71 1.52 Bahamas 197 -1.62 1.65 Macao 198 -1.72 1.64 Bhutan 199 -2.30 1.45 USVirginIslands 200 -2.05 1.95 Anguilla 201 -2.25 1.86 Tonga 202 -1.88 2.23 Mongolia 203 -2.12 2.05 WesternSamoa 204 -2.11 2.27 CookIslands 205 -3.67 2.06 EasternSamoa 206 -2.80 3.01 Guam 207 -4.43 2.74 Comoros 208 -14.70 1.38 Tuvalu 209 -14.97 1.82 FederatedStatesofMicronesia 210 -15.86 3.44
Ignoring that one game, Ireland is #14 and Sweden #11 ... so the good news is that the model seems to behave reasonably; the bad news is that I still don't know why we've gotten different rankings for these two teams. (have you been including bandy scores in the ratings? )
One team I strongly disagree on: HOLLAND They were absolutely hopeless on their last three encounters! At home against: Macedonia 0-0 Italy 1-3 Ecuador 1-0 Most likely that I will bet against this team from start to finish.
Seems like a hard part of developing these rating systems is figuring out how to separate hiccups from genuine downturns. That Italy game you reference is their only loss since Euro 2004, and apart from Macedonia, the only opponents who've tied them are England, Germany, and Sweden. I think it's possible they just had a couple of bad days.
Sorry I didn't catch this thread until now...I've been absolutely swamped recently. Thanks for the update. I don't think my weightings should have much effect, IIRC they didn't move any teams more than a few places either way. I find it a little odd that T&T is persistently rated so low.
Apparently their terrible results from early in the cycle are hard to shake off ... most notable are losses to #135 St. Lucia, #152 St. Kitt's & Nevis, and #182 Taiwan. If you include only their results from the past year, they come out at #57 instead of #106. In that time frame, they've played 15 games, which is enough to suggest that they really are stronger. Here are the 32 finalists, using up-to-date results and adding a couple of corrections ... the US is the highest-rated team that isn't favored to advance beyond the group stage. Code: Gp Team Rk Off Def F Brazil 1 1.26 -1.17 C Netherlands 2 1.00 -1.37 E Czechia 3 1.33 -0.95 G France 4 0.93 -1.32 H Spain 5 1.03 -1.19 C Argentina 6 1.19 -0.87 E Italy 7 0.88 -1.07 B England 8 1.05 -0.85 D Portugal 9 1.00 -0.85 A Germany 11 1.17 -0.62 D Mexico 12 0.78 -0.98 B Sweden 13 1.01 -0.73 E UnitedStates 15 0.75 -0.96 F Croatia 18 0.67 -0.95 C CotedIvoire 20 0.79 -0.77 B Paraguay 23 0.67 -0.76 A Poland 24 0.87 -0.54 C SerbiaandMontenegro 29 0.61 -0.75 G Switzerland 32 0.79 -0.53 F Japan 34 0.60 -0.70 G SouthKorea 38 0.40 -0.83 F Australia 43 0.69 -0.52 H Ukraine 44 0.33 -0.83 D Iran 45 0.68 -0.47 A Ecuador 46 0.52 -0.62 H Tunisia 50 0.45 -0.63 A CostaRica 53 0.68 -0.34 E Ghana 69 0.18 -0.39 H SaudiArabia 74 0.17 -0.35 D Angola 77 0.19 -0.31 G Togo 79 0.24 -0.21 B TrinidadandTobago 106 -0.06 -0.08