OK, this will be a very long post, so some of you may want to read just the bold text.
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First, the rating on August 29 (pre-USO) will be
1. LD: 4609
2. MS: 4452
3. AM: 3907
4. KC: 3179
Maria's 18th result is 72 points so if she gets less than that at USO, this result will become her 17th and will start to count.
Post-USO rating will be:
1. MS: 4360 + USO (but at least
4432)
2. LD: 4153 + USO -> needs at least
279 at USO
3. AM: 3653 + USO -> needs at least
779 at USO
4. KC: 3179 + USO -> needs at least
1253 at USO
At USO
Kim can get at most 650+(4+16+30+70+86+150+200)=1206, i.e. she
can't get to #1 no matter what.
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One can calculate all possible mathematical ranges of points that a player can get by getting into, say, QF, or winning the title. That would mean considering possibilities that MS, LD, or AM play finals with some qualifier outside of top 100. The results would be quite unrealistic and will take a longer time to compute. Instead, I will assume that all seeds win their first two matches, after that anything can happen. Thus, none of the above 3 players will see some low ranked player in 3rd round or after that. Whoever they beat, they will get at least 30 quality points.
OK, here it goes:
Maria loses in 1st or 2nd round: gets <72 points, finishes with 4432 after USO
Maria gets in 3rd: 76 or 92 points
Maria in 4th: 140-156
Maria in QF: 258-298
Maria in SF: 418-528
Maria in F: 612-802
Maria wins T: 836-1196
Lindsay gets in 3rd: 78 or 92 points
Lindsay gets in QF: 244-298
Lindsay gets in SF: 420-514
Lindsay gets in F: 614-810
Lindsay wins T: 838-1114 (if MS does not reach F), 958-1154 (if MS reaches F)
Amelie gets in 3rd: 88 or 92 points
Amelie gets in F: 624-764 (if LD does not reach SF); 794-878 (if LD reaches SF)
Amelie wins T: 848-1068 (if plays neither LD in SF, nor MS in F), 1018-1182(if plays LD in SF but not MS in F)
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To remind, Lindsay needs at least 279, Amelie needs at least 779. Thus,
1.
To have a shot at #1 Lindsay has to reach at least QF, Amelie needs F if she beats LD in SF, otherwise she needs to win the title.
AMELIE
1. If Amelie gets into F without beating Lindsay in SF, she will have at most 764 points, not enough for #1. She will need the title.
If Amelie gets into F by beating Lindsay in SF, she will have at most 878 points. This is enough to pass Maria, if she stumbles early. However, Lindsay, by reaching SF, will have at least 420, i.e. she would have passed Maria, too. The difference between earned points will be 878-420=458 which is not enough for Amelie to compensate for 500 points differential between her and Lindsay (3653 vs 4153). Thus, final may be enough for Amelie to pass Maria but no matter what else happens final will never be enough to get #1.
Amelie MUST win the title to have a chance at #1.
2. If Lindsay doesn't reach SF then Amelie's title will give her at least 848. With Lindsay having at most 298 for QF, Amelie will pass her in the rankings.
If Lindsay does reach SF and loses to Amelie who then wins the title, then Lindsay will have at most 514, Amelie will have at least 1018. Again, the difference is larger than 500, so
Amelie will pass Lindsay if she wins the title.
As far as passing Maria goes, if Amelie wins title with just 848 points then Maria will need just 142 points to keep #1. Maria can get these points by reaching 4th round. If Amelie wins the title with 1182 points then Maria will need 476 points to guarantee that Amelie's title will not make her #1. At this point, only the final makes sure that Maria gets these 476 points.
To summarize,
Amelie MUST win the title to have a chance at #1.
If Maria doesn't reach 4th round, Amelie is #1. If Maria reaches final, Maria is #1. If Amelie wins the title while Maria is stopped in 4th, QF, or SF, then #1 depends on quality points earned in the process.
LINDSAY
1.
If Maria loses in 1st or 2nd round, or reaches 3rd round with 76 points, then QF may or may not be enough for Lindsay, SF will be enough, no matter what.
2.
If Maria reaches the 3rd round with 92 points (it depends on whether Randriantefy beats Gambale in the 1st round), then she'll have 4452.
Then, Lindsay will need 299, i.e. QF is insufficient for her no matter what and she
will need SF.
3.
If Maria gets into 4th round, then SF will be enough for Lindsay, no matter what.
4.
If Maria gets into QF, then SF may or may not be enough for Lindsay, F will be enough, no matter what.
5.
If Maria gets into SF, then F may or may not be enough for Lindsay, title will be enough, no matter what.
6.
If Maria gets into F, then title may or may not be enough for Lindsay. For instance, if Maria gets 802 points for getting into F, Lindsay will need 1009 points for the title while her total may be as low as 958.
OK, I guess that's about it.