Guild Wars 2

HabibLoew.2590:

We perform the same score calculation for each world and then plug those results into Glicko 2. This means that ratings change over time as a result of battle outcomes and that the rating for a given server reflects the history of that server’s performance.

The system and formula works well, but with free transfers in play, servers can change quickly and no longer be as strong as their rating indicates. HoD is the prime example. When the Titan Alliance fell apart, it took time for HoD to fall out of Tier 1. A possible solution is to take a page from the NASCAR Sprint Cup series. After the ratings are determined, baseline them by making the gap between each place 10 points (for example). This would make it easier for the places and match ups to change from week to week.

I’m assuming that the previous week rating is used as a starting value (r in this case) for the calculations.

Its for others to decide if the maths is good. I’m just a dumb nuker of stuff.

Personally, I’m impressed that an ArenaNet dev came out and explained how a mechanic works since that type of thing is anathema for most MMO companies. Kudos to you.

rather than set matches every week dictated by the ranking chart, will it be possible to have randomly picked 3 servers just go against each other every week and just keep their ratings instead… it might be fun or more interesting that way, because right now we are stuck with the same opponents for the 3rd week and it’s not the same as looking forward to playing with them the first week… just a random thought, thanks

My mind just blew up

Walay The Brave.6813:

rather than set matches every week dictated by the ranking chart, will it be possible to have randomly picked 3 servers just go against each other every week and just keep their ratings instead… it might be fun or more interesting that way, because right now we are stuck with the same opponents for the 3rd week and it’s not the same as looking forward to playing with them the first week… just a random thought, thanks

That would be a no. I understand where your coming from on that one. But other than the 2 servers your facing. There are maybe 3 other servers that stand a chance against you. Would be unfair to pretty much EVERYONE else lol.

Question – you are assuming that matches are independent, while they are not.
Example:

AvBvC

A gets 200000
B gets 2000
C gets 1000

We can clearly see that A is the winner, but BvC is down to margin of error. Both got dominated and there is no sure way to tell who would have won hypothetical BvC fight if A wasn’t present.

Is that formula on the graph page correct?

y = sin(x) – (0.5pi)(1*0.5)
is not the same as
y = (sin((x – 0.5) * Pi) + 1) * 0.5
is it?

Edit: Nevermind, browser was preventing the correct formula from loading.

Regrets of Sini.6083:

Question – you are assuming that matches are independent, while they are not.
Example:

AvBvC

A gets 200000
B gets 2000
C gets 1000

We can clearly see that A is the winner, but BvC is down to margin of error. Both got dominated and there is no sure way to tell who would have won hypothetical BvC fight if A wasn’t present.

not really.
since B got twice the points of C, then B would probably won a BvC match up.

Any system that doesn’t also take Participation Population into sampling VS. these Results, … just seems half baked to me. Maybe if there was a REAL odd-evening mechanic behind “Outmanned” this wouldn’t be the case but since there isn’t, Rank just looks arbitrary to me and I don’t feel any “Server Pride” when we blow another server out of the water

Do I understand it correct and do you calculate 6 scores :
1. A’s score from A vrs B
2. A’s score from A vrs C
3. B’s score from A vrs B
4. B’s score from B vrs C
5. C’s score from A vrs C
6. C’s score from B vrs C

This is rather odd, because from theory (I didn’t do the numbers) this would mean that A doesn’t care what B & C do: tie or not.

If A has 50% of the points, B 45% and C 5%, A will get the same ranking as when A has 50% of the points, B 25% and C 25%.

In other words: a server gets the same ranking boost for taking out the camps of the weakest enemy than they get from taking out a camp from the stronger enemy.

This would mean that the winning server shouldn’t be fightin the number 2, they should be fighting the number 3: the are weaker and taking a camp from them adds the same to their ranking.

I can not imagine that this is right, so please tell me where I am wrong

And, yes, like the previous poster said, I would certainly do ‘something’ with the population too. But that’s another discussion.

HabibLoew.2590:

wAGlickoScore = (sin((wAPercent – 0.5) * Pi) + 1) * 0.5

where wAScore and wBScore are the raw scores from the end of the match.

That last transform is easiest to visualize as a graph.

That’s also intresting… capturing points is less rewarding when you already have 90% of the points than when have 0% of the points. Basically, it rewards the big losers more heavily than the big winners for doing something.

But for the middle percentages, the graphs is pretty lineair: capturing points is more or less the same rewarding when you have 20% of the points than when have 60% of the points.

Tallis.5607:

Do I understand it correct and do you calculate 6 scores :
1. A’s score from A vrs B
2. A’s score from A vrs C
3. B’s score from A vrs B
4. B’s score from B vrs C
5. C’s score from A vrs C
6. C’s score from B vrs C

This is rather odd, because from theory (I didn’t do the numbers) this would mean that A doesn’t care what B & C do: tie or not.

If A has 50% of the points, B 45% and C 5%, A will get the same ranking as when A has 50% of the points, B 25% and C 25%.

In other words: a server gets the same ranking boost for taking out the camps of the weakest enemy than they get from taking out a camp from the stronger enemy.

This would mean that the winning server shouldn’t be fightin the number 2, they should be fighting the number 3: the are weaker and taking a camp from them adds the same to their ranking.

I can not imagine that this is right, so please tell me where I am wrong

And, yes, like the previous poster said, I would certainly do ‘something’ with the population too. But that’s another discussion.

attacking the third place person would make sense… if objectives were just pure score. as it is, keeps, towers, and especially supply camps also represent control and war-fighting abylity. if you fight the second place opponent, then you are not just limiting his score. you are also limiting their ability to fight back, which is inherently greater (and hence a greater threat) the the third place server.

HabibLoew.2590:

In standard Glicko 2 scores are represented as 0.0 for a loss, 0.5 for a draw, and 1.0 for a win. We use a slightly modified version that takes into account score differential. I’ll explain how using the wA vs. wB battle as an example. To calculate the Glicko 2 score for wA in the wA vs. wB matchup we do the following:

wAPercent = wAScore / (wAScore + wBScore)
wAGlickoScore = (sin((wAPercent – 0.5) * Pi) + 1) * 0.5

where wAScore and wBScore are the raw scores from the end of the match.

I am assuming the +1 in the above formula was indicative of wA winning the match?

While the Glicko/Glicko 2 system works well with 1v1 competition, I’ve never been a real fan of having it applied in 2+ competition. However, I like the way you guys have modified it and I think it’s not a bad system overall. (and to be fair, the algorithm itself is beyond my mathematical capabilities to understand, but it seems to always produce fairly decent results, regardless of what’s going on in that mathematical black box)

There is one aspect that I think is problematic, that maybe you guys could mull over. When a score is measured wA v wB, wA v wC, and wB v wC, the highest Glicko Score is awarded to a world based on how well they score relative to each opponent, in addition to the bonus for coming in first or second.

Assuming that each world wants to score as high as possible (at least in theory), the best results will be achieved by:

Primary:

A) Winning overall to get the +1 bonus.
B) Coming in at least second to get the .5 bonus.

These are good incentives that achieve what I suspect to be the intended results in of the system.

Secondary:

First Place:

A) Score as many points as possible.
B) Keep second place to as few points as possible.
iC) Keep third place to as few points as possible.

Second Place:

A) Score as many points as possible.
B) Keep First place to as few points as possible.
C) Keep third place to as few points as possible.

Third Place:

A) Score as many points as possible.
B) Keep First place to as few points as possible.
C) Keep Second place to as few points as possible.

The problematic part I see is with the incentives in italics above. Because the reward for the difference between each of the other worlds is constant regardless of which place the respective realms are in, it behooves a world to obtain points for themselves, and deny points from their enemies, in the most efficient way possible. Unfortunately, this system gives the first and second place worlds an incentive to attack the weaker third place world, since the point rewards are the same and the opposition likely weaker.

This is a long winded way of saying that I think that system should be modified to award less points to the score difference between 1st v 3rd, and 2nd v 3rd, to help provide incentive for the second place world to focus on the one in first place, and the first to focus on the second place, instead of just bouncing the third place into rubble.

So I dunno, maybe something like: GlickoScore = ((sin((wAPercent – 0.5) * Pi) + 1) * 0.5)*.9 if the percent score was versus the 3rd place world?

Tallis.5607:

In other words: a server gets the same ranking boost for taking out the camps of the weakest enemy than they get from taking out a camp from the stronger enemy.

This would mean that the winning server shouldn’t be fightin the number 2, they should be fighting the number 3: the are weaker and taking a camp from them adds the same to their ranking.

This was exactly my thought as well.

ilr.9675:

Any system that doesn’t also take Participation Population into sampling VS. these Results, … just seems half baked to me.

You sir, get a +1.

My Brain….

who knew that such a game could be educational at the same time

Tallis.5607:

If A has 50% of the points, B 45% and C 5%, A will get the same ranking as when A has 50% of the points, B 25% and C 25%.

In other words: a server gets the same ranking boost for taking out the camps of the weakest enemy than they get from taking out a camp from the stronger enemy.

You’re ignoring the sine transform. It essentially applies “diminishing returns” to larger score differentials.

If A’s final rating in your example above was always the same, then there would be no need to evaluate two separate “matches”, the result would simply be based on A’s score, ignoring the other worlds’.

Math make Penguin’s head sore. Me say WvW rating should be based on which server has the most sticks to fight with. And all servers could be placed into a round robin ladder death match week after week.

On a side note, thanks so much for taking the time to explain these details to the community. But I’m kinda sad that I may never be smart enough to work for Anet. In two simple posts, Habib just put my Marketing degree to shame.

HabibLoew.2590:

wAGlickoScore = (sin((wAPercent – 0.5) * Pi) + 1) * 0.5

That last transform is easiest to visualize as a graph .

From what I understand the point of this transform is to apply diminishing returns to worlds that are dominating their opponents. It’s pretty clear on the graph, however, that there’s also similar a penalty to teams that are being dominated. Is this intended? It seems like if anything the worlds being dominated should be given a bit of a bonus for every last point they can manage to grab (not an overwhelming advantage of course, just something moderate).

110% the math tells the leader and second place to crush 3rd place. It’s the most logical decision.

Outnumbered buff is now where to be found. Our server has fought with it for hours sometimes, and still managed second. If we have the numbers it’s not uncommon for us to run the score up to 400 to even 600/15m. We clearly are stronger than our current two match ups, for the last 2 weeks. But our population fluctuates a lot. We know this and our pride is very high, because of it. But there needs to be a bonus for time spent fighting outnumbered. IMO

wildmanfrost.3986:

110% the math tells the leader and second place to crush 3rd place. It’s the most logical decision.

That will only come into play if/when the leader has already blown away second place. If second place is still close enough to win, the leader needs to keep them in check. Likewise, second place needs to take objectives from the leader if they want to have any hope of catching them. Beating the opponent is still the number one objective until it’s no longer an option (or guaranteed), and you aren’t going to beat any competitive opponents if you let them run wild.

Kreaven.3172:

Walay The Brave.6813:

rather than set matches every week dictated by the ranking chart, will it be possible to have randomly picked 3 servers just go against each other every week and just keep their ratings instead… it might be fun or more interesting that way, because right now we are stuck with the same opponents for the 3rd week and it’s not the same as looking forward to playing with them the first week… just a random thought, thanks

That would be a no. I understand where your coming from on that one. But other than the 2 servers your facing. There are maybe 3 other servers that stand a chance against you. Would be unfair to pretty much EVERYONE else lol.

It doesnt hurt in the NFL. Cleavand, for example, has no chance of beating anyone, yet they still have to play the superbowl champs. So, what you do is randomize the matchups so everyone plays everyone, and then at the end you have a win-loss record which is a better gauge of ranking. Some weeks will be fun, some wont, but every week will be a different experience.

All of this fancy math is great and all, but it leaves out the most important part of the equation, the human factor. Let’s face it, playing the same match-up for three weeks in a row is boring (unless it is relatively even). Especially if it is a lopsided match-up. Things are great as long as your server is winning, but being stuck in a tier hopelessly outmatched for three weeks takes it’s toll on a server’s WvWvW community. Players either transfer to a winning server or stop participating in WvWvW altogether and only diehards like me are left to carry on. In my opinion (I know, everybody has one) the current ranking system is not fluid enough. Servers advancing/dropping tiers happens way too slowly to keep match-ups balanced.

I’m trying to make heads of tails ( or whatever the saying is) from this formula, but I just can’t understand what the meaning is of:
the { and } in the glicko 2 formula to find out v and Delta.
Could you explain what they mean ? are they just normal ( and ) ?

EDIT: I tried using them as regular ( and ) but it didn’t work out :/

Uploaded it on a spreadshet, this is what I have right now:

https://docs.google.com/spreadsheet/ccc?key=0Ar3M4xnJRQqNdGc0ZTN5UjMwVzRWR2lzYXUtRnZqNFE

Lot of math going around and I’m recovering from a massive study session. What kind of weighting range does match score account for in the final grade. I mean is it worth grinding on WvW towards rollover or is that score basically negligible compared to the match result?

… hopefull that makes sense

any rating based on a world setup…. which presumes that WORLD wil have the same team next week …. when a transfer is allowed every week, will be hosed.

I point to the fact that just the weekly limit of transfers has minimized a large portion of unequal distribution of play.

Now imagine a sports team where;
1. the players were ALWAYS anonymous
2. allowed to SWITCH SIDES every week

Clearly this would not be a scenario where long-term team score would maintain any validity.

It is exploitable to any team that had a forums, and a mind to do so. They can just decide to bail to a low rated server same day every week, and slaughter the low rateds they are matched against.

Luckily the rewards for ‘winning’ in wvw arent that great; they dont gain much by cheating.

Id like to know the math behind outmanned buff. Because sometimes i see a server with a ton of people in a border but no outmanned buff. How many more does a server have to have to trigger the buff?

Whats total player count in a borderland? Is there a cap per server or per borderland period?

Is is ‘mathematically’ possible to have the same match-up 2 weeks in a row?

I am sure the math behind the rating is interesting and all that. Unfortunately however, the model is incorrect and does not work for edge cases. For example, just look at HoD and ET. For many match ups they have been match against very 1 sided fights.

A good model will need to be able to take into account drastic increase/decrease in server WvW strength and adjust accordingly, instead of allowing the server to raise/fall tier by tier, causing uneven match ups.

I posted this a couple of days ago, but I haven’t received any feedback, could someone tell me what I am doing wrong ?

https://docs.google.com/spreadsheet/ccc?key=0Ar3M4xnJRQqNdGc0ZTN5UjMwVzRWR2lzYXUtRnZqNFE#gid=0

I like the logic behind this math, that if a world does not do great for one week, it will not just go to the bottom of the ladder.

However, I do have a major concern about the long term use of this formula. I believe that as time goes by, the match ups will be the same for very long periods.

After applying the Glicko 2 formula, the sum of the rating of the three Worlds remains the same. Therefore, for the first division or tier 1 of the ranking (I don’t know how you call it), everytime there is a switch between two Worlds, the global sum of the ratings increases. On the other end of the ranking, the same happens for the last “division” where the sum of the ratings reduces.

Therefore, I’m afraid that in a few months, the rankings will barely change every week as the rating differences will be greater and greater. Even if a World is doing great in a division for 2 or 3 weeks in a row, it might not be able to climb to the next division.

To forum users: Could you please tell me if I’m wrong?
To Anet: Do you have anything planned to counter this?

PD: Sorry for any mistakes in this post, English is not my mother tongue.

HabibLoew.2590

Check out the match up history for ET and HoD
http://mos.millenium.org/matchups#history

Now tell me these are good matchups
It doesn’t matter how good your math is if you have made bad asumptions (<- stupid filter should have two s’s)
In this case a server is not a single entity but a collection of them
All of which can freely transfer to another server and your calculation has no accounting for this

Hi Habib,

It seems that one of the main advantages of the Glicko rating system is that ratings can be adjusted quickly because of the large step differences between loss (0), draw (0.5) and win (1). However, the wAPercent function serves to centralize values around 0.5. While the wAGlickoScore transformation does help mitigate this around edge values in [0,1], it is linear in neighborhoods of 0.5. This seems to split matches into two possible directions of motion:

1) A blowout where one server wins heavily and causes all three servers to be adjusted strongly due to being at the “edge” of the wAGlickoScore transform (see HoD and ET)

2) A convergence as all servers have fairly close to the same score and are normalized near the 0.5 mean value.

Ultimately, this seems to result in a stratification between tiers; within-bracket matchups converge to the median glicko rating (unless there is a blowout) while between-bracket scores diverge. This seems unhealthy for overall matchups as people seem to prefer playing different opponents (even if the matches will be more uneven) rather than the same matchups over and over.

Because of these circumstances, has your team given consideration to increasing the volatility in waGlickoScore or changing how waPercent is calculated to create a more uniform distribution in [0,1] ?

zastari.1730:

…However, the wAPercent function serves to centralize values around 0.5. While the wAGlickoScore transformation does help mitigate this around edge values in [0,1], it is linear in neighborhoods of 0.5. This seems to split matches into two possible directions of motion:

1) A blowout where one server wins heavily and causes all three servers to be adjusted strongly due to being at the “edge” of the wAGlickoScore transform (see HoD and ET)

2) A convergence as all servers have fairly close to the same score and are normalized near the 0.5 mean value.

Ultimately, this seems to result in a stratification between tiers…

I was wondering if the rating system made it difficult for the top rated server of one tier to get rated higher than the bottom rated server in the tier above (e.g., Blackgate and Stormbluff Isle).

Would Blackgate be hurt because the other servers in its tier have lower ratings than SBI’s competitors?

I love fighting those guys and I’m not eager to see them go. But on the other hand, we’re on track to go four weeks without a membership change in the top two tiers.

I think WvW scoring should be dictated by numbers of players and nothing else would matter, really.
Applying a different score to a camp/fort/keep or whatever just on the base of the number of players involved on that Borderland during the 15 minutes period time.
Let the 90 people zerg rush over a 15 players borderland and let them have only 1/6 of the scoring during that tally! What? you don t like it? That will not be a punishment on higher populated server, it would be just as fair as it can get a proper confrontation.
The real problem would be the huge mole of data that should be crossed by server counting out access in relation of capping objectives maybe…or maybe not ^^

I agree with the people who find the repeated matchups boring. What do you guys think about having a ‘jumble’ week every fourth week or so? If the algorithm was adjusted some, points could be correctly assigned based on the relative ratings going in to that week, then back to tiers the next. Some weeks us lower ranked servers might get killed by SoS or someone, and SoS would be a little bored, but I would like the variety and the challenge.

Habib Loew.6239:

Just a quick clarification. The formulas

wAPercent = wAScore / (wAScore + wBScore)
wAGlickoScore = (sin((wAPercent – 0.5) * Pi) + 1) * 0.5

make no assumptions about winners or losers. The first simply calculates a relative score percentage between the two teams involved. This is a number between 0.0 and 1.0. The second transforms the relative percentage into a Glicko 2 score using a sine wave which has the effect of making large score differentials have a less than linear impact on the Glicko 2 score (see the linked graph). The result is still in the range 0.0 to 1.0. Effectively this means that as score differentials get larger and larger the actual Glicko 2 score for a team approaches 0.0 or 1.0 more and more slowly.

We perform these operations pairwise on all the teams, so we are calculating 6 matches (two for each team) which fits the Glicko 2’s one-way nature. This is because the rating changes are asymmetric.

Because the ratings of two teams matter when calculating the results of a match (a lower rated team beating a higher rated team results in more change than a higher rated team beating a lower rated team) if two teams are very close in score then there is generally very little change in their ratings. Again, I encourage you to read the Glicko 2 website for a more thorough explanation of that part of the process.

Looking at that sine transform (instead of a 1:1 45° line), I get the following impression:
1) Anything lower than 0.5 is attenuated even further. Anything higher than 0.5 is amplified.
2) Anything in the middle moving up gets to move up faster. If moving down, it gets to drop down faster as well.
3) Once you’re really high or really low, there’s inertia that makes you stick to where you are. Anything really low will have a really hard time getting back up. Anything really high won’t drop appreciably unless pushed by a large amount.

Perhaps I’m missing something (because I’m not taking into account what the rest of the Glicko math does), but that’s not promoting dynamic changes at the extremes, but rather pushing the scores faster to one end and then helping them to stay there.

If I’m correct, the exact opposite would achieve dynamism at the edges. A curve that moves fast up at 0, then slows down in the middle, and accelerates again near 1. (Two exponentials which meet at 0.5, for example). Result: If you’re at the very top, you get slided down more easily. If you’re at the very bottom you can climb up more easily. If you’re in the middle you find it harder to get to an extreme, although movement is not hindered.

Am I missing something or does that sine wave really represent your intentions?

I agree with all those that think it’s boring to always be against the same servers for 3 weeks in a row. Why can’t it be mixed to provide more fun in seeing new enemies to match up with? Why not keep the precious formula for ranking teams, but instead of moving up or down (which happens to slowly or at all) and have all the #1 winners from the week move to the #1 winner bracket, all the 2nd place servers fight each other in the #2 bracket and same for #3. That way each week it would shuffle around enough to keep it interesting. I’m not saying that facing Jade Quarry would result in a win for our server, but the current system greatly reduces that from ever happening. Sometimes fighting a better server helps us learn something new, and the next time we fight it could be a different story. Just a thought, but from a casual WvW player’s point of view, I will no doubt get tired of it, if I see the same servers again and again.

Well, in addition to it being painfully slow for matchups to change, this glicko 2 style rating system is based on the end of week score, and Anet STILL hasn’t told us where all of THOSE points are coming from, even!

https://forum-en.gw2archive.eu/forum/pvp/wuvwuv/Clarification-needed-please-Dolyak-points/first

This whole time we’ve been playing a competitive game for points, without actually knowing where all of those points come from, how we get all of our points, or how the points are tallied.

I’m a bit confused why people are suggesting population should be considered. If your server isn’t performing as well as another due to population, that is a pity. However, it doesn’t mean the server should get a handicap in terms of rankings. That doesn’t make sense.

Ilesyt.7084:

I’m trying to make heads of tails ( or whatever the saying is) from this formula, but I just can’t understand what the meaning is of:
the { and } in the glicko 2 formula to find out v and Delta.
Could you explain what they mean ? are they just normal ( and ) ?

EDIT: I tried using them as regular ( and ) but it didn’t work out :/

Uploaded it on a spreadshet, this is what I have right now:

https://docs.google.com/spreadsheet/ccc?key=0Ar3M4xnJRQqNdGc0ZTN5UjMwVzRWR2lzYXUtRnZqNFE

I’ve found the error. When you calculate E vs Vabbi, RoS or FoW, you are using the next expression:

1/(1+((EXP)))(MU-MUj)))

(MU-MUj) has to be inside the exponencial, in your equation it’s out. Use this expression:

1/(1+(EXP*(MU-MUj))))

Try it out.

Edit: Also, when you caltucate v you got to do the inverse, I mean elevate to -1.

Lakland.8102:

I agree with all those that think it’s boring to always be against the same servers for 3 weeks in a row. Why can’t it be mixed to provide more fun in seeing new enemies to match up with? Why not keep the precious formula for ranking teams, but instead of moving up or down (which happens to slowly or at all) and have all the #1 winners from the week move to the #1 winner bracket, all the 2nd place servers fight each other in the #2 bracket and same for #3. That way each week it would shuffle around enough to keep it interesting. I’m not saying that facing Jade Quarry would result in a win for our server, but the current system greatly reduces that from ever happening. Sometimes fighting a better server helps us learn something new, and the next time we fight it could be a different story. Just a thought, but from a casual WvW player’s point of view, I will no doubt get tired of it, if I see the same servers again and again.

This horrible idea gets brought up everytime there is a discussion about this. In the VAST VAST majority of cases, the server moving up would get completely crushed, and the server moving down would destroy everything in sight.

The gap between each individual tier is huge, and this idea will just lead to completely boring matches. You will not learn anything from getting spawncamped.

Habib Loew.6239:

Just a quick clarification. The formulas

wAPercent = wAScore / (wAScore + wBScore)
wAGlickoScore = (sin((wAPercent – 0.5) * Pi) + 1) * 0.5

make no assumptions about winners or losers. The first simply calculates a relative score percentage between the two teams involved. This is a number between 0.0 and 1.0. The second transforms the relative percentage into a Glicko 2 score using a sine wave which has the effect of making large score differentials have a less than linear impact on the Glicko 2 score (see the linked graph). The result is still in the range 0.0 to 1.0. Effectively this means that as score differentials get larger and larger the actual Glicko 2 score for a team approaches 0.0 or 1.0 more and more slowly.

We perform these operations pairwise on all the teams, so we are calculating 6 matches (two for each team) which fits the Glicko 2’s one-way nature. This is because the rating changes are asymmetric.

Because the ratings of two teams matter when calculating the results of a match (a lower rated team beating a higher rated team results in more change than a higher rated team beating a lower rated team) if two teams are very close in score then there is generally very little change in their ratings. Again, I encourage you to read the Glicko 2 website for a more thorough explanation of that part of the process.

Could someone explain why they are using a sin function? Having been on SF in T8 I can say that is really hard to get more points when you already have everything. If you want to solve the T8/9 problem you should consider getting rid of the sin function or using something like tangent or sinh.

Imo no amount of math manipulation to try and set the matchups is going to work.

They are going to have to come up with some sort of manual matchmaking (matchmaking within a bubble around your server, seasons, manual manipulation, etc.).