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<blockquote data-quote="Brigantine" data-source="post: 958223" data-attributes="member: 73940"><p>The model I made mostly focuses on who wins games, I didn't put too much thought into bonus points and win margins. But since the projections of who progresses from pools depends on it, I'll show what's happening in the model here. Even though a few things seem not-quite-right.</p><p></p><p><strong><span style="font-size: 18px">Japan vs Russia:</span></strong></p><p></p><p>Japan win 99.7%, draw <0.1%, Russia win 0.3%</p><p>Table Points Japan \ Table Points Russia</p><ul> <li data-xf-list-type="ul"><strong>99.2%</strong> 5 TP Japan \ Russia 0 TP <strong>99.2%</strong>, __________ 2 TP <0.1%</li> <li data-xf-list-type="ul">_0.4% 4 TP Japan \ Russia 0 TP _0.2%, 1 TP 0.2%</li> <li data-xf-list-type="ul"><0.1% 2 TP Japan \ Russia _____________________ 2 TP <0.1% <br /> </li> <li data-xf-list-type="ul">_0.3% 1 TP Japan \ Russia _________________________________ 4 TP 0.2%, 5 TP <0.1%<br /> </li> <li data-xf-list-type="ul"><0.1% 0 TP Japan \ Russia _________________________________ 4 TP <0.1%<br /> </li> <li data-xf-list-type="ul">_</li> <li data-xf-list-type="ul">100% TB Russia Total: ___ 0 TP <strong>99.4%</strong>, 1 TP 0.2%, 2 TP __0.1%, 4 TP 0.3%, 5 TP <0.1%</li> </ul><p><strong><span style="font-size: 18px"></span></strong></p><p><strong><span style="font-size: 18px">Australia vs Fiji:</span></strong></p><p></p><p>Australia win 81%, draw 1.6%, Fiji win 17%</p><p>Table Points Australia \ Table Points Fiji</p><ul> <li data-xf-list-type="ul"><strong>63%</strong> 5 TP Australia \ Fiji 0 TP <strong>60%</strong>, 1 TP 1.2%, 2 TP _1.4%</li> <li data-xf-list-type="ul">19% 4 TP Australia \ Fiji 0 TP 8.5%, 1 TP 10%, 2 TP _0.2%</li> <li data-xf-list-type="ul">0.3% 3 TP Australia \ Fiji ___________________ 2 TP <0.1%, 3 TP 0.3%</li> <li data-xf-list-type="ul">2.5% 2 TP Australia \ Fiji ___________________ 2 TP _1.2%, 3 TP 0.1%, 4 TP 0.3%, 5 TP 1.0%<br /> </li> <li data-xf-list-type="ul">11% 1 TP Australia \ Fiji _________________________________________ 4 TP 9.5%, 5 TP 1.0%</li> <li data-xf-list-type="ul">5.0% 0 TP Australia \ Fiji ________________________________________ 4 TP 3.5%, 5 TP 1.8%</li> <li data-xf-list-type="ul">_</li> <li data-xf-list-type="ul">100% TP Fiji Total: _____ 0 TP <strong>69%</strong>, 1 TP 11%, 2 TP _3.0%, 3 TP 0.4%, 4 TP _13%, 5 TP 4.0%</li> </ul><p><strong><span style="font-size: 18px">France vs Argentina:</span></strong></p><p></p><p>France win 67%, draw 2.5%, Argentina win 31%</p><p>Table Points France \ Table Points Argentina</p><ul> <li data-xf-list-type="ul">39% 5 TP France \ Argentina 0 TP 35%, 1 TP 2.0%, 2 TP _2.0%<br /> </li> <li data-xf-list-type="ul"><strong>28%</strong> 4 TP France \ Argentina 0 TP 12%, 1 TP _<strong>15%</strong>, 2 TP _0.4%<br /> </li> <li data-xf-list-type="ul">0.4% 3 TP France \ Argentina ___________________ 2 TP <0.1%, 3 TP _0.3%<br /> </li> <li data-xf-list-type="ul">4.0% 2 TP France \ Argentina ___________________ 2 TP _1.8%, 3 TP <0.1%, 4 TP 0.5%, 5 TP 1.8%<br /> </li> <li data-xf-list-type="ul">16% 1 TP France \ Argentina __________________________________________ 4 TP 15%, 5 TP 1.4%<br /> </li> <li data-xf-list-type="ul">13% 0 TP France \ Argentina __________________________________________ 4 TP 7.0%, 5 TP 6.0%</li> <li data-xf-list-type="ul">_</li> <li data-xf-list-type="ul">100% TP Argentina Total: ___ 0 TP 47%, 1 TP <strong>17%</strong>, 2 TP _4.5%, 3 TP _0.4%, 4 TP 22%, 5 TP 9.0%</li> </ul><p><strong><span style="font-size: 18px">New Zealand vs South Africa:</span></strong></p><p></p><p>New Zealand win 59%, draw 2.5%, South Africa win 39%</p><p>Table Points New Zealand \ Table Points South Africa</p><ul> <li data-xf-list-type="ul">29% 5 TP New Zealand \ South Africa 0 TP 25%, 1 TP 2.0%, 2 TP 2.0%<br /> </li> <li data-xf-list-type="ul"><strong>29%</strong> 4 TP New Zealand \ South Africa 0 TP <strong>12%</strong>, 1 TP _17%, 2 TP 0.5%<br /> </li> <li data-xf-list-type="ul">0.4% 3 TP New Zealand \ South Africa ___________________ 2 TP 0.1%, 3 TP _0.3%<br /> </li> <li data-xf-list-type="ul">4.0% 2 TP New Zealand \ South Africa ___________________ 2 TP 2.0%, 3 TP <0.1%, 4 TP 0.4%, 5 TP 1.6%<br /> </li> <li data-xf-list-type="ul">19% 1 TP New Zealand \ South Africa _________________________________________ 4 TP 17%, 5 TP 1.8%<br /> </li> <li data-xf-list-type="ul">18% 0 TP New Zealand \ South Africa _________________________________________ 4 TP 9.0%, 5 TP 9.0%<br /> </li> <li data-xf-list-type="ul">_</li> <li data-xf-list-type="ul">100% TP South Africa Total: ________ 0 TP <strong>37%</strong>, 1 TP _19%, 2 TP 4.5%, 3 TP 0.4%, 4 TP 26%, 5 TP 13%</li> </ul><p></p><p>Italy vs Namibia etc. - I might edit these in later</p><p></p><p>[technical fine-print follows]</p><p><span style="font-size: 10px">On a related note, I've been thinking for a while what I should do with Rankings Points changes after RWC games start. I don't want to use the 2x weighting used in the rankings because then mid-RWC issued projections would go haywire and be inconsistent. I thought about not updating the RP at all, but that would cause problems too.</span></p><p><span style="font-size: 10px">And now I've decided. I'll keep my own table of teams and their RP, and update each team's RP (the average of the probability distribution) as calculated by a Bayesian update, i.e. I'll average the team's RP in all the scenarios which predicted the correct outcome in terms of the table points awarded to both teams. </span></p><p><span style="font-size: 10px">(or as a contingency if a very unlikely <1.0% outcome occurs, I'll calculate it just on a win/draw/loss basis. Unless that was also unlikely at <=0.2% in which case I'll default to exchanging 3.00 RP or 4.50 RP for a 15+ point winning margin. In the case of a <=0.2% draw, I'll split the difference between a 4-1 win and a 1-4 loss)</span></p><p><span style="font-size: 10px">This means that that two teams after playing each other won't gain/lose the same amount of RP, but hopefully projections from one week to the next will be consistent, e.g. if a team wins a 50:50 must-win game, their chances beyond that game should double.</span></p></blockquote><p></p>
[QUOTE="Brigantine, post: 958223, member: 73940"] The model I made mostly focuses on who wins games, I didn't put too much thought into bonus points and win margins. But since the projections of who progresses from pools depends on it, I'll show what's happening in the model here. Even though a few things seem not-quite-right. [B][SIZE=5]Japan vs Russia:[/SIZE][/B] Japan win 99.7%, draw <0.1%, Russia win 0.3% Table Points Japan \ Table Points Russia [LIST] [*][B]99.2%[/B] 5 TP Japan \ Russia 0 TP [B]99.2%[/B], __________ 2 TP <0.1% [*]_0.4% 4 TP Japan \ Russia 0 TP _0.2%, 1 TP 0.2% [*]<0.1% 2 TP Japan \ Russia _____________________ 2 TP <0.1% [*]_0.3% 1 TP Japan \ Russia _________________________________ 4 TP 0.2%, 5 TP <0.1% [*]<0.1% 0 TP Japan \ Russia _________________________________ 4 TP <0.1% [*]_ [*]100% TB Russia Total: ___ 0 TP [B]99.4%[/B], 1 TP 0.2%, 2 TP __0.1%, 4 TP 0.3%, 5 TP <0.1% [/LIST] [B][SIZE=5] Australia vs Fiji:[/SIZE][/B] Australia win 81%, draw 1.6%, Fiji win 17% Table Points Australia \ Table Points Fiji [LIST] [*][B]63%[/B] 5 TP Australia \ Fiji 0 TP [B]60%[/B], 1 TP 1.2%, 2 TP _1.4% [*]19% 4 TP Australia \ Fiji 0 TP 8.5%, 1 TP 10%, 2 TP _0.2% [*]0.3% 3 TP Australia \ Fiji ___________________ 2 TP <0.1%, 3 TP 0.3% [*]2.5% 2 TP Australia \ Fiji ___________________ 2 TP _1.2%, 3 TP 0.1%, 4 TP 0.3%, 5 TP 1.0% [*]11% 1 TP Australia \ Fiji _________________________________________ 4 TP 9.5%, 5 TP 1.0% [*]5.0% 0 TP Australia \ Fiji ________________________________________ 4 TP 3.5%, 5 TP 1.8% [*]_ [*]100% TP Fiji Total: _____ 0 TP [B]69%[/B], 1 TP 11%, 2 TP _3.0%, 3 TP 0.4%, 4 TP _13%, 5 TP 4.0% [/LIST] [B][SIZE=5]France vs Argentina:[/SIZE][/B] France win 67%, draw 2.5%, Argentina win 31% Table Points France \ Table Points Argentina [LIST] [*]39% 5 TP France \ Argentina 0 TP 35%, 1 TP 2.0%, 2 TP _2.0% [*][B]28%[/B] 4 TP France \ Argentina 0 TP 12%, 1 TP _[B]15%[/B], 2 TP _0.4% [*]0.4% 3 TP France \ Argentina ___________________ 2 TP <0.1%, 3 TP _0.3% [*]4.0% 2 TP France \ Argentina ___________________ 2 TP _1.8%, 3 TP <0.1%, 4 TP 0.5%, 5 TP 1.8% [*]16% 1 TP France \ Argentina __________________________________________ 4 TP 15%, 5 TP 1.4% [*]13% 0 TP France \ Argentina __________________________________________ 4 TP 7.0%, 5 TP 6.0% [*]_ [*]100% TP Argentina Total: ___ 0 TP 47%, 1 TP [B]17%[/B], 2 TP _4.5%, 3 TP _0.4%, 4 TP 22%, 5 TP 9.0% [/LIST] [B][SIZE=5]New Zealand vs South Africa:[/SIZE][/B] New Zealand win 59%, draw 2.5%, South Africa win 39% Table Points New Zealand \ Table Points South Africa [LIST] [*]29% 5 TP New Zealand \ South Africa 0 TP 25%, 1 TP 2.0%, 2 TP 2.0% [*][B]29%[/B] 4 TP New Zealand \ South Africa 0 TP [B]12%[/B], 1 TP _17%, 2 TP 0.5% [*]0.4% 3 TP New Zealand \ South Africa ___________________ 2 TP 0.1%, 3 TP _0.3% [*]4.0% 2 TP New Zealand \ South Africa ___________________ 2 TP 2.0%, 3 TP <0.1%, 4 TP 0.4%, 5 TP 1.6% [*]19% 1 TP New Zealand \ South Africa _________________________________________ 4 TP 17%, 5 TP 1.8% [*]18% 0 TP New Zealand \ South Africa _________________________________________ 4 TP 9.0%, 5 TP 9.0% [*]_ [*]100% TP South Africa Total: ________ 0 TP [B]37%[/B], 1 TP _19%, 2 TP 4.5%, 3 TP 0.4%, 4 TP 26%, 5 TP 13% [/LIST] Italy vs Namibia etc. - I might edit these in later [technical fine-print follows] [SIZE=2]On a related note, I've been thinking for a while what I should do with Rankings Points changes after RWC games start. I don't want to use the 2x weighting used in the rankings because then mid-RWC issued projections would go haywire and be inconsistent. I thought about not updating the RP at all, but that would cause problems too. And now I've decided. I'll keep my own table of teams and their RP, and update each team's RP (the average of the probability distribution) as calculated by a Bayesian update, i.e. I'll average the team's RP in all the scenarios which predicted the correct outcome in terms of the table points awarded to both teams. (or as a contingency if a very unlikely <1.0% outcome occurs, I'll calculate it just on a win/draw/loss basis. Unless that was also unlikely at <=0.2% in which case I'll default to exchanging 3.00 RP or 4.50 RP for a 15+ point winning margin. In the case of a <=0.2% draw, I'll split the difference between a 4-1 win and a 1-4 loss) This means that that two teams after playing each other won't gain/lose the same amount of RP, but hopefully projections from one week to the next will be consistent, e.g. if a team wins a 50:50 must-win game, their chances beyond that game should double.[/SIZE] [/QUOTE]
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