November tests and IRB rankings

[ZeFrenchy]

Hey guys. I had some free time, so I built up a table to figure out the possible ranking changes this November. I'll explain how I did it and how to use it.

What the numbers below mean: The numbers below are (negative) 1/10 of the rating difference taking the home advantage handicap and capped to a magnitude of 1, which is how the IRB rankings are calculated.

How to obtain them: Take, for instance, the game between France and Australia. Australia's rating is 86.37, and France's is 86.06 (the actual ranking plus 3 pts for home advantage handicap). The difference is 0.31, so 1/10th of it is 0.03.

How to use these numbers: The numbers below represent the ratings change if a match is drawn. If a team wins a game, you have to add 1 to the number below, whereas if they lose, you substract 1. If the difference is more than 15 points, you multiply them by 1.5. Thus, if France wins by more than 15 points, we gain 1.5*(1+0.03)=1.55 points. In any case, the points that are won by a side are lost by the opponent (zero-sum). The explanation is taken from the IRB website.

[TABLE="class: grid, width: 700"]
<colgroup><col><col><col><col><col><col><col></colgroup><tbody>[TR]
[TD]Ranking[/TD]
[TD]Country[/TD]
[TD]Rating[/TD]
[TD]Match 1[/TD]
[TD]Match 2[/TD]
[TD]Match 3[/TD]
[TD]Match 4[/TD]
[/TR]
[TR]
[TD="align: right"]1[/TD]
[TD]New Zealand[/TD]
[TD="align: right"]92,91[/TD]
[TD="align: right"]-1,00[/TD]
[TD="align: right"]-1,00[/TD]
[TD="align: right"]-0,76[/TD]
[TD="align: right"]-0,68[/TD]
[/TR]
[TR]
[TD="align: right"]2[/TD]
[TD]Australia[/TD]
[TD="align: right"]86,37[/TD]
[TD="align: right"]-0,03[/TD]
[TD="align: right"]-0,03[/TD]
[TD="align: right"]-0,73[/TD]
[TD="align: right"]-0,11[/TD]
[/TR]
[TR]
[TD="align: right"]3[/TD]
[TD]South Africa[/TD]
[TD="align: right"]84,69[/TD]
[TD="align: right"]-0,18[/TD]
[TD="align: right"]-0,37[/TD]
[TD="align: right"]0,14[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]4[/TD]
[TD]England[/TD]
[TD="align: right"]83,09[/TD]
[TD="align: right"]-1,00[/TD]
[TD="align: right"]0,03[/TD]
[TD="align: right"]-0,14[/TD]
[TD="align: right"]0,68[/TD]
[/TR]
[TR]
[TD="align: right"]5[/TD]
[TD]France[/TD]
[TD="align: right"]83,03[/TD]
[TD="align: right"]0,03[/TD]
[TD="align: right"]-0,74[/TD]
[TD="align: right"]-0,98[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]6[/TD]
[TD]Wales[/TD]
[TD="align: right"]82,26[/TD]
[TD="align: right"]-0,66[/TD]
[TD="align: right"]-0,90[/TD]
[TD="align: right"]0,76[/TD]
[TD="align: right"]0,11[/TD]
[/TR]
[TR]
[TD="align: right"]7[/TD]
[TD]Ireland[/TD]
[TD="align: right"]79,85[/TD]
[TD="align: right"]0,18[/TD]
[TD]NA[/TD]
[TD="align: right"]-0,42[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]8[/TD]
[TD]Argentina[/TD]
[TD="align: right"]78,63[/TD]
[TD="align: right"]0,66[/TD]
[TD="align: right"]0,74[/TD]
[TD="align: right"]0,42[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]9[/TD]
[TD]Scotland[/TD]
[TD="align: right"]77,97[/TD]
[TD="align: right"]1,00[/TD]
[TD="align: right"]0,37[/TD]
[TD="align: right"]-0,62[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]10[/TD]
[TD]Samoa[/TD]
[TD="align: right"]76,23[/TD]
[TD="align: right"]-0,39[/TD]
[TD="align: right"]0,90[/TD]
[TD="align: right"]0,98[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]11[/TD]
[TD]Italy[/TD]
[TD="align: right"]76,03[/TD]
[TD="align: right"]-0,42[/TD]
[TD="align: right"]1,00[/TD]
[TD="align: right"]0,73[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]12[/TD]
[TD]Tonga[/TD]
[TD="align: right"]74,79[/TD]
[TD="align: right"]0,42[/TD]
[TD="align: right"]-0,82[/TD]
[TD="align: right"]0,62[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]13[/TD]
[TD]Canada[/TD]
[TD="align: right"]72,3[/TD]
[TD="align: right"]0,39[/TD]
[TD="align: right"]-1,00[/TD]
[TD] [/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]14[/TD]
[TD]Fiji[/TD]
[TD="align: right"]70,6[/TD]
[TD="align: right"]1,00[/TD]
[TD]NA[/TD]
[TD="align: right"]0,04[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]15[/TD]
[TD]Georgia[/TD]
[TD="align: right"]67,95[/TD]
[TD]NA[/TD]
[TD="align: right"]-0,30[/TD]
[TD="align: right"]-0,04[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]16[/TD]
[TD]Japan[/TD]
[TD="align: right"]67,93[/TD]
[TD="align: right"]-0,04[/TD]
[TD="align: right"]0,30[/TD]
[TD]NA[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]17[/TD]
[TD]USA[/TD]
[TD="align: right"]66,61[/TD]
[TD="align: right"]-0,46[/TD]
[TD="align: right"]0,82[/TD]
[TD="align: right"]0,09[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]18[/TD]
[TD]Romania[/TD]
[TD="align: right"]64,54[/TD]
[TD="align: right"]0,04[/TD]
[TD]NA[/TD]
[TD="align: right"]-0,09[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="align: right"]19[/TD]
[TD]Russia[/TD]
[TD="align: right"]62,05[/TD]
[TD="align: right"]0,46[/TD]
[TD="align: right"]1,00[/TD]
[TD]NA[/TD]
[TD] [/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]

Now go do your math. The 4th place is up for grabs. Example: if France win all three games by 15 points or less, we will get 1.31 points (1.03 from Australia, 0.26 from Argentina and 0.02 from Samoa), making a total of 84.34. If England lose againt the All Blacks and win the rest, all by 15 or less, they will get 0.57 points (0 from Fiji, 1.03 from Australia, 0.86 from South Africa and -0.32 from NZ), making a total of 83.66 and thus losing the fourth spot.

The 8th spot is also interesting and, imo, is a lot more important than tha fourth one. A 9th place in the rankings makes it sure that you will have 2 tier 1 nations in tour pool, whereas an 8th spot makes it a 25% chance.

 

[Feicarsinn]

Without meaning to be a dick, I'm not sure this model works. In your given example at the end you say that France would gain 0.26 points from beating Argentina in their second test. But the difference between France and Argentina's ranking will vary after the first test. For example, if France lose heavily and Argentina win comfortably, the gap will be significantly closer meaning that a French win would give them more than a 0.26 boost.

I'm not certain that constructing models such as these are very practical without the aid of a computer programme tbh. It reminds me somewhat of calculating the behaviour of a non linear pendulum, which while seaming relatively straightforward, quickly becomes impossible.

 

[dullonien]

Wales should be looking to win 3 out of 4. If that happens, all by 15 points or less, Wales will gain: (-0.66+1=0.33) + (-0.9+1=0.1) - (0.76-1=0.24) + (0.11+1=1.11) = 1.3, giving us a final standing of 83.56.

So if we do win 3, and in order to get 4th spot, we need England to also lose against SA/Aus as well as against NZ, and France to lose to Austrailia. I think we'll then sneak in above both. Although, if Aus lose all three matches, they would drop quite considerable, but not sure how much.

Without meaning to be a dick, I'm not sure this model works. In your given example at the end you say that France would gain 0.26 points from beating Argentina in their second test. But the difference between France and Argentina's ranking will vary after the first test. For example, if France lose heavily and Argentina win comfortably, the gap will be significantly closer meaning that a French win would give them more than a 0.26 boost.

I'm not certain that constructing models such as these are very practical without the aid of a computer programme tbh. It reminds me somewhat of calculating the behaviour of a non linear pendulum, which while seaming relatively straightforward, quickly becomes impossible.

Ah, of course. Everything goes out the window after the first game.

Edit. Wtf is happening. The forum insists on splitting Feic's post into 2 in my quote. Every time I edit it and remove the [/QUOTE]

between the two paragraphs, it automatically puts it back in after I save the edit!

 

[ZeFrenchy]

Without meaning to be a dick, I'm not sure this model works. In your given example at the end you say that France would gain 0.26 points from beating Argentina in their second test. But the difference between France and Argentina's ranking will vary after the first test. For example, if France lose heavily and Argentina win comfortably, the gap will be significantly closer meaning that a French win would give them more than a 0.26 boost.

I'm not certain that constructing models such as these are very practical without the aid of a computer programme tbh. It reminds me somewhat of calculating the behaviour of a non linear pendulum, which while seaming relatively straightforward, quickly becomes impossible.

Dammit! You're right. In any case, it's a good enough approximation. The maximum number of rating points any side can win is 3 (for instance if Italy or Scotland beat the All Blacks by more than 15 points), so that will mean 0.3 points more (or less) on the line for the next games, and that effect in the following game would be 0.03 points. Most of the games have a lot less on stake, so unless there is a huge upset, I think it can be useful.
You're right though, so the disclaimer should be made: if the results after a particular calculation are too close (I'd say less than 0.3 points or so), they should be taken carefully.

 

[dullonien]

+rep for the effort in any case. It is still useful to get some approximations.

Edit. Is there a mistake in the match 3 column. Shouldn't SA be -0.14 and England be +0.14?

 

[ZeFrenchy]

+rep for the effort in any case. It is still useful to get some approximations.

Edit. Is there a mistake in the match 3 column. Shouldn't SA be -0.14 and England be +0.14?

Well thank you. I admit some frustration after reading Feic's post.

As for the England-South Africa, it's not a mistake. England have a handicap because of playing at home, so their effective rating is 86.09, which is 1.4 points higher than SA. That means that a draw would make England lose points (without considering the results of the previous games, etc)

 

[Feicarsinn]

Dammit! You're right. In any case, it's a good enough approximation. The maximum number of rating points any side can win is 3 (for instance if Italy or Scotland beat the All Blacks by more than 15 points), so that will mean 0.3 points more (or less) on the line for the next games, and that effect in the following game would be 0.03 points. Most of the games have a lot less on stake, so unless there is a huge upset, I think it can be useful.
You're right though, so the disclaimer should be made: if the results after a particular calculation are too close (I'd say less than 0.3 points or so), they should be taken carefully.

No worries, I spend quite a lot of my time working things that behave like the rankings system. Usually though you can neglect higher power effects (or in this case derivations from current rankings) if they're a lot smaller than your first term (or potential ranking points earned for the first game.) I'll have a think over it later, but I have an idea that might make it possible to make quite accurate predictions.

 

[dullonien]

Well thank you. I admit some frustration after reading Feic's post.

As for the England-South Africa, it's not a mistake. England have a handicap because of playing at home, so their effective rating is 86.09, which is 1.4 points higher than SA. That means that a draw would make England lose points (without considering the results of the previous games, etc)

Ahhhh, I understand now.

 

[rusty_lock]

This site has always worked really well for me.

http://www.lassen.co.nz/pagmisc.php#hrh

 

[SelimNiai]

This is all far to complicated for my tiny brain to compute

 

[LittleGuy]

I wouldn't spend too much time on this guys, the IRB is releasing a full mathematical scenario on possible bandings on Thursday.

 

[Kiwi_Bloke_In_Perth]

Hi there at least you guys will get to see all the matches. I live in Aus and Foxtel has NO coverage of the All Black's NH tests and I pay 105 bucks a month for HD as well. So annoyed. Luckily I do have Setanta as well so I get to see AB's vs Wales and England . I will have to see the other two matches by aheemmm other means.

 

[ZeFrenchy]

Update. The table below doesn't include the AB-Scotland game, but if the AB win, the ratings will be unchanged. SA overtakes OZ at second place, and France take the 4th spot.

For next week, if England beat Australia, they will overtake them. So, a French win would mean Australia to leave the top 4...


[TABLE="class: grid, width: 606"]
<tbody>[TR]
[TD]Ranking[/TD]
[TD]Country[/TD]
[TD]Rating[/TD]
[TD]Match 2[/TD]
[TD]Match 3[/TD]
[TD]Match 4[/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]New Zealand[/TD]
[TD]92,91[/TD]
[TD]-1,00[/TD]
[TD]-0,93[/TD]
[TD]-0,68[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]South Africa[/TD]
[TD]85,51[/TD]
[TD]-0,45[/TD]
[TD]0,06[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]Australia[/TD]
[TD]84,82[/TD]
[TD]0,13[/TD]
[TD]-0,52[/TD]
[TD]-0,12[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]France[/TD]
[TD]84,58[/TD]
[TD]-0,73[/TD]
[TD]-1,00[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]England[/TD]
[TD]83,09[/TD]
[TD]-0,13[/TD]
[TD]-0,06[/TD]
[TD]0,68[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]Wales[/TD]
[TD]80,60[/TD]
[TD]-0,65[/TD]
[TD]0,93[/TD]
[TD]0,12[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]Argentina[/TD]
[TD]80,29[/TD]
[TD]0,73[/TD]
[TD]0,17[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]Ireland[/TD]
[TD]79,03[/TD]
[TD]NA[/TD]
[TD]-0,17[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]Scotland[/TD]
[TD]77,97[/TD]
[TD]0,45[/TD]
[TD]-0,68[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]10[/TD]
[TD]Samoa[/TD]
[TD]77,15[/TD]
[TD]0,65[/TD]
[TD]1,00[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD]Italy[/TD]
[TD]76,61[/TD]
[TD]1,00[/TD]
[TD]0,52[/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]