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For some time I have written down detailed information about my match history:
http://www.lysator.liu.se/~john/history.html
The original purpose was to try to calculate the league offsets. Then came the division modifiers and made life harder, but I think I can make some interesting observations anyway. I have selected some games from this match history the following way:
1: Remove all games from before my promotion to gold, and also the first games after promotion. The reason is to make sure that my points are stable and have converged to my MMR.
2: Remove all games where my opponent only has a few games played.
3: Remove all games where my point gain/loss is not equal to my opponents point loss/gain. I assume that if they are not equal, it indicates that either mine or my opponents points are not in sync with MMR.
For the games I am left with I calculate my and my opponents "real scores", ie points with bonus pool removed. This is the "MR" column in the match history. Then I take the difference between my and my opponents "real score". If the match is even and we are in the same league, the difference should be close to 0, disregarding division offsets. If I am favored the difference should be positive.
Here is an example. This is the differences from all games where my opponents were gold and very slightly favored. This means a -10 point loss or a +14 point gain for me:
-59 -70 20 -60 -57 23 -67 -70 26 26
Interesting, don't you think? There are clearly two groups, and I bet my left arm that this is due to the division modifiers. Here is a picture to visualize it better:
![[image loading]](http://www.lysator.liu.se/~john/chart1.png)
The mean value for the negative group is -64 and 24 for the positive group. The difference between the two is 88 which should be the division offset, but the data points are few.
The next example is: Opponent gold and -11 point loss or +13 point gain:
44 48 52 -2 -25 -32 -22 -19 -37 -17 -29 -33 -33 -30 -26 -42 -27 28
Link to chart
Again, two groups except for the two outliers -2 and 28. Removing those gives the means 48 and -29. The difference is 77.
Strangely enough there are almost no matches which are exactly even (12 points loss/gain), so the next example is opponent gold and -13 point loss or +11 point gain:
19 35 27 97 20 13 32
Group means: 24 and 97. Difference: 73. We can see that the groups become more positive as I become more favored, which make sense.
Link to chart
Opponent silver and -11 point loss or +13 point gain:
-156 -199 -167 -96 -141 -149 -80 -139
Removing -199 gives group means -150 and -88. Difference: 62
Now it gets interesting. Switching to silver league shifts the two groups in the -11/+13 case by 124 and 136 points. This should be an indication of the league offset between silver and gold.
Link to chart
Again, no silver matches with +-12 point gain/loss. Coincidence? Opponent silver and -13 point loss or +11 point gain:
-100 -91 -99 -94 -100 -110 -98 -93 -34 -112 -105 -154 -93 -98 -27
Removing -154 gives group means -99 and -30. Difference : 69.
The group shift from the gold example is 123 and 118.
Link to chart
Final example: -14 point loss or +10 point gain:
-82 3 -138 -58 -2 -72 -58 -73 -61 -58 -53 -68 -8 -16 -80 -88 -9 -65 -77 -76 -79
Removing -13 gives group means -66 and -4. Difference: 62.
Link to chart
The difference between the two groups in most cases are close to the previously established division modifier 63 in diamond. Assuming it is the same here we can correct the data we have and collaps the two groups to a single one. The first example
-59 -70 20 -60 -57 23 -67 -70 26 26
then becomes:
-59 -70 -43 -60 -57 -40 -67 -70 -37 -37
and the average is -54.
Here are tables of the results corrected for division offsets
Gold opponents
-10/+14 : -54
-11/+13 : -25
-12/+12 : ?
-13/+11 : +26
Silver opponents
-11/+13 : -151
-12/+12 : ?
-13/+11 : -99
-14/+10 : -66
To summarize: I'm aware that I'm not posting anything groundbreaking here. The data points I have are to few to draw any conclusions. They can only serve as indications. I have removed a lot of matches in my analysis. Maybe more information can be gotten from those, I don't know. However, my guess is:
1: For every extra point you win/lose in a match your opponent becomes about 27 points better/worse.
2: The division modifiers for silver and gold are about the same as for diamond. Actually the group differences in the gold examples were a little bit too large, so I'm not sure about this one.
3: The point difference between silver and gold is about 125.
Again, it's difficult to draw conclusions, but for a long time I have had the feeling that the league offset between silver and gold is quite small, less than 150 points, and this data supports that. Anyway, I like fiddling with numbers, so I post this even if the results are vague. Take it for what it's worth.
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That's really quite interesting. I've been doing a similar thing, except only in my head, to see where I stand. Perhaps I will start recording it like you
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I also forgot to mention that when I subtract my opponents points from my own I use the points before the match, because that is what the matchmaking system used when it decided to match us together.
Also, using this type of data one can start guessing the division modifiers for the lower leagues. For example, one of my last matches against Zhuren was a +14 point win for me. Subtracting his points from mine (before the match and with bonus pool removed) gives the difference 26.
Since it was a +14 point win we look at this graph, which contains all my gold -10/+14 matches:
+26 clearly belongs to the upper group. This was a match where my opponent was very slightly favored (due to my +14 point gain), so the lower group should be players in divisions with the same division modifier as me, and the upper group is not. If we assume that my division is S-rank (looks like it from the charts) Zhurens division (Tal'darim Pi) is A-rank.
There are a few problems:
1: I didn't write down my opponents divisions in my match history. They may have changed since the matches.
2: Only one data point per division is not enough. Working through my complete match history may give more, but problem 1 above makes it difficult. Maybe sc2ranks can be of use.
3: The charts in my previous post only seem to contain two groups, ie two different division modifiers. I assume S and A rank are most common, and others, if they exist, are rare. If they exist, a lot more data would be needed to find them.
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United States12235 Posts
That is interesting information indeed, Mendelfist. I don't know if we can go back in time with SC2Ranks like we would need to, and my match history tracking hasn't been as robust as yours. It does seem a good idea to mainly factor matches where 10-14 points are won or lost for both players. One issue that SC2Ranks has is that it can't identify your opponent, that can only be done in-game. If only we had a bot that could track that in-game =)
Another edge case would be players who you face and record their data, but who have been promoted or demoted after that very game. I guess that would be fairly easy to identify due to the 73+bonus point reset, but improper handling of that could result in bad data, so we'll need to be aware.
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On February 15 2011 03:28 Excalibur_Z wrote:
That is interesting information indeed, Mendelfist. I don't know if we can go back in time with SC2Ranks like we would need to, and my match history tracking hasn't been as robust as yours
My idea about using sc2ranks would only be to make sure that the players haven't changed division since the match, nothing else. It would still be a lot of manual work though.
It does seem a good idea to mainly factor matches where 10-14 points are won or lost for both players.
Yes, but note that grouping together all matches in the interval 10-14 points won't work, because that is a large skill difference. You have to put -10/+14 matches in one group, -11/+13 in another and so on. I still don't know if any useful information can be gained from matches where my gain (or loss) is not equal to my opponents loss (or gain). Using those too would give us a lot more data, but I'm not sure how.
To be more clear: Grouping opponents together like I did makes the skill difference between me and them very precise, but what is the skill difference between me and my opponent if I won 12 points and he lost only 10? It's ambiguous.
One issue that SC2Ranks has is that it can't identify your opponent, that can only be done in-game.
Replays work too, because there is an URL to the battle.net page there. Sc2gears can extract it. Actually, an application that would take a replay, follow the link and extract relevant data from battle.net and save it would be very useful. Doing it by hand is prone to errors.
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United States12235 Posts
On February 15 2011 03:51 Mendelfist wrote:
Replays work too, because there is an URL to the battle.net page there. Sc2gears can extract it. Actually, an application that would take a replay, follow the link and extract relevant data from battle.net and save it would be very useful. Doing it by hand is prone to errors.
Funny that you mention that, Vanick has been working on just such a program. It was put on hold once we discovered the point reset at 73+bonus, but I'll poke him to resume progress today.
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On February 15 2011 03:28 Excalibur_Z wrote:
Another edge case would be players who you face and record their data, but who have been promoted or demoted after that very game. I guess that would be fairly easy to identify due to the 73+bonus point reset, but improper handling of that could result in bad data, so we'll need to be aware.
I found two people with score 73+bonus points, and one of them is indeed one that doesn't fit the data. Its number 4 in this chart, so you are right. That is something to look out for. I didn't think of that.
EDIT: When I think more about it, the problem will persist several matches after promotion. Those people need to be removed from the analysis somehow.
![[image loading]](http://www.lysator.liu.se/~john/chart2.png)
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I think there is a lot of danger in picking and choosing which data to use, unless you (and I'm talking about "you" in a general sense, not to any specific person) want to make just a broad generalization, or be specific about providing a caveat about your data.
One thing that struck me was you (back to the personal you now) only report on matches where you win/lose 10-14 points. Did you toss out the other games, or did you not have any?
I've noticed that a lot of people can be put into a bucket -- they are pretty consistent and not super good (ie. they aren't hitting masters in 25-30 games). Those people generally win or lose between 10 and 14 points per game. But not everyone fits in that category. This is more likely true if you play in a small region, play while drunk/on tilt etc, play random, experiment a lot with wacky builds or off-races, etc, and/or play non 1v1. It can also happen in lower leagues if you have a huge hole in your abilities (can't respond to cheese, never make detection, etc) which doesn't come up often, but when it does you end up losing to someone a lot worse than you.
When you analyze the data for people in the first category, a lot of things make "sense." For example, I think if you take the formula of the guy who took his ball home, I think it does work for this subset of people. But it doesn't work for everyone. Call them outliers, anomalies, or whatever, but they exist and can't be hand-waved away.
For example, let's take 2 cases which are in some ways very similar but also very different.
In case 1, you have a player who generally goes +14, -12, +14, -12 etc. In every set of 2 he gains about 2 points, and probably will get promoted at some time if he can keep that up.
In case 2, you have a player who generally goes +8, +8, -14, +8, +8, -14. In every set of 3 he gains about 2 points, but I doubt this person will ever get promoted. He's actually a candidate for demotion, despite his 67% win record.
Normally you don't hit case 2. But it can happen; it happened to my 2s partner and I. We both play random, and so when we both hit our best races, we would often crush, and when we both got our worst races, we would often get crushed.
What happened to us is we would sometimes lose games we should win a couple times in a row. Our sigma grew (rightfully so) and it would start pairing us lower. We'd end up beating a team and only get 5-7 points for them. We would get paired against another team, slightly better, and sometimes lose. So the system would pair us even lower. As a result for a while we had a record that looked like: -14, -15, +6, -14, +5, +5, -17, +7, -14, +5, +8, etc
At one point we were doing bad enough I thought we might get demoted soon, despite our 58% win record. Luckily we patched up most of our holes, and did eventually manage to get to diamond.
Now, most people don't get into that spiral. But the loose correlation between MMR and rank points is broken for people who do get into that spiral. And there are probably other conditions too which can do the same thing which I just don't know about because they didn't happen personally to me.
And that's why you get those people who are a couple hundred rank points ahead of other people who don't get promoted going, wtf is going on... because all the people people on the "normal" track get promoted at about the normal time and don't raise a cry.
Now, to circle back to my reply, I think it's possible that keeping close track of who you play, what their rank points were and comparing it to how much you gained or lost to try and come up with division offsets might work, but I think it's important to consider that perhaps you shouldn't be looking for a 100% fit. You seem to be doing this already by discarding a subset of your population, and I guess what I'm saying is that you may still have some outliers occasionally even in the data you are keeping.
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On February 15 2011 07:20 random user wrote:
One thing that struck me was you (back to the personal you now) only report on matches where you win/lose 10-14 points. Did you toss out the other games, or did you not have any?
I did provide my complete match history. As you can see for yourself, wins/losses outside this range exist, but are too few to be useful.
Now, to circle back to my reply, I think it's possible that keeping close track of who you play, what their rank points were and comparing it to how much you gained or lost to try and come up with division offsets might work, but I think it's important to consider that perhaps you shouldn't be looking for a 100% fit. You seem to be doing this already by discarding a subset of your population, and I guess what I'm saying is that you may still have some outliers occasionally even in the data you are keeping.
Yes, I agree with what you say. This type of analysis works for me, because my MMR is reasonably stable. It probably won't work for everyone. But I haven't cherry-picked the data. I have discarded all matches where my point loss isn't equal to my opponents point gain and vice versa for reasons already stated. Of the remaining matches there were only 5 that seemed like anomalies. These are to be expected. One reason is that newly promoted opponents don't have points and MMR that match. These 5 are the only matches I removed because they "didn't fit". The rest were removed prior to that and should not skew the results. The results are uncertain, but that is because the data points are too few, not because of any picking and choosing.
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Mendelfist, that's really cool. Getting closer to the Grand Unified ladder. 
We could get more people using this method to discover division/league offsets, and construct something like this:
Offset
-150 - Masters
0 - S Diamond
63 - A Diamond
126 - B Diamond
150 - S Platinum
189 - C Diamond
213 - A Platinum
252 - D Diamond
.... etc .... All the way down to Bronze if we get enough data
So then people can use this method to discover their division type, and then estimate their MMR:
Points - Used Bonus - Offset = MMR
With caveats that it's only an estimate and only works if your ladder points have stabilized blah blah.
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On February 15 2011 08:48 KillerDucky wrote:Mendelfist, that's really cool. Getting closer to the Grand Unified ladder. We could get more people using this method to discover division/league offsets, and construct something like this:
Offset
-150 - Masters
0 - S Diamond
63 - A Diamond
126 - B Diamond
150 - S Platinum
189 - C Diamond
213 - A Platinum
252 - D Diamond
.... etc .... All the way down to Bronze if we get enough data
So then people can use this method to discover their division type, and then estimate their MMR: Points - Used Bonus - Offset = MMR With caveats that it's only an estimate and only works if your ladder points have stabilized blah blah.
That would be another metric, another way to gauge points between divisions and tiers, but please don't call it MMR, becasue that isn't MMR.
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United States12235 Posts
Yeah, we've been calling that "adjusted rating" or "adjusted points".
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We could call them "Universal Points" or "Pure Points". UnP as abreviation for example.
But if you think about it, MMR would be something very close to that, since it would be a pure system which calculates how good are you, and compares you to your oponent. Heck we could even predict how many point players will gain/lose in a game if we discover enough data.
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On February 10 2011 11:22 SDream wrote:Show nested quote +On February 10 2011 10:38 michaelhasanalias wrote:On February 10 2011 07:24 Excalibur_Z wrote:On February 10 2011 07:22 SDream wrote:On February 10 2011 07:04 Excalibur_Z wrote:On February 10 2011 06:36 SDream wrote:
michaelhasanalias, another thing that I want to share with you that I just remembered.
There has been proved that we have 7 tiers on Diamond (S->F).
But it was also proved that most platinum players get promoted to E Diamond divisions, not F ones.
Why would that be so? My theory is that the moving average of most players only stabilizes enough to become diamond once they are "E rank" worth with their MMR. What's your? Another thing I noticed yesterday was that there appear to be more 3v3/4v4 tiers per league in NA, but more 1v1 tiers in KR and EU. Maybe the more popular a game type is, the more tiers need to be created? Are you trying to say F Rank diamond could be a "dead" tier?Now that we know that 100% of the divisions most be filled in order to another one to be made, we can more easily prove silver-platinum tiers looking at the time of creation of new divisions, is there still a 95 player division when that happened? That means 2 different tiers. So I think we can work from there to finally confirm these tiers. Mm, no, not necessarily. I mean we have confirmed seven tiers on KR and EU and SEA and LA but never NA for Diamond 1v1. However, I was looking at some other leagues and Silver 3v3 and 4v4 for example have 3 distinct tiers on NA, but only 2 on KR and EU. I mean maybe it differs per region by design. I think this is exactly the case. The division that the 3700 point Bronze player is in offers strong, albeit somewhat anecdotal, supporting evidence That division was started 3 months ago, and still only has 67 players in it. This means that they can't find enough players that bad (presumably many 0-5 players do get placed there) that actually stay in that division. I've forget to correct you before, but the division of this bronze guy is full (100 players). Edit: The link isn't working anymore, what happened? Did he changed his name?? Anyway, I saw it full on the official site (eu.battle.net) o.O Edit2: I jsut noticed that more than 20 players in that division are tied with 0 points, but it does have 100 players on it. Edit3: I found him again: http://eu.battle.net/sc2/en/profile/1652040/1/wApToofck/ladder/19971#current-rankand he has 3705 points now. I am starting to think it is a huge bug, maybe a result of negative mmr bug??? o.o I found it fun how he changed his nick just when we were discussing him haha
This bronze player has 3800 points already. Very high offset or very high moving average? Make your bets 
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United States12235 Posts
Okay, so that throws out the 40% idea. Hm...
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I doubt activity has anything to do with bonus pool since I could play all day every day for a week and still not be considered active since the number is over 2700 now. Heck if I was a 0 point bronze player I could play forever and not be considered active. More than likely it is based off of some threshold of a certain number of games over a certain recent time period. Is there some reason you don't suspect this?
As for the talk of division tiers below diamond I have some questions about it.
Diamond is a huge league compared to plat/gold/silver and it originally was the only league you could not place into. To be in diamond you had to be promoted into a division while having your points adjusted down to 73. When you place into a league below diamond you start with 0 points, and when you calculated the division offsets originally you discovered that they were ALWAYS a multiple of the same number.
So the question then is where are these points actually earned? Are we to assume that players in low divisions are getting 1,2,3 or more points per game than they should? Once they reach the division offset they get the normal amount of points, but if this were the case then players would not all have offsets that were consistently multiples of same number. If the division modifiers are applied to players upon promotion (for example if the 3100 pt bronze player was promoted to diamond, in this theory he would be S class) then this would imply that division modifiers only existed in diamond. Of course now that you can place into diamond and division tiers still exist it seems unlikely.
So if you are always given 73 points at promotion and you will always earn the correct number of points per game how then are division modifiers implemented and what function do they serve?
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Actually I was just thinking about it and I think it makes sense to me now.
League modifiers serve to allow newer players a chance to attempt to catch up in points to older players who have been accumulating points longer. This works outside of bonus pool and is only a real issue in diamond (pre masters league) but the effects exist in the other leagues and could have prompted blizzard to include them in all leagues. This is because non-bonus pool points inflate at the very elite levels of the ladder, where as other leagues players will tend to stabilize or get promoted. Of course not everyone gets promoted in a timely fashion and points can accumulate in lower leagues as well.
The first set of elite players got promoted to diamond and their non-bonus points were calculated at 73 + a diamond league modifier. These are the original s-class divisions. As time went on that '73' grew, prompting the need to include an offset in newly created divisions to try and even them out. For these players their non-bonus points would be calculated as 73 + diamond league modifier - new divisional modifier. Upon completing a game these players point totals would be arbitrarily low prompting the system to award them additional points for their wins while costing them less points for their losses.
This system could work for placing players as well, to serve to accelerate their points. This also implies that eventually new masters divisions will include offsets.
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United States12235 Posts
On February 16 2011 02:40 DiDigital wrote:
I doubt activity has anything to do with bonus pool since I could play all day every day for a week and still not be considered active since the number is over 2700 now. Heck if I was a 0 point bronze player I could play forever and not be considered active. More than likely it is based off of some threshold of a certain number of games over a certain recent time period. Is there some reason you don't suspect this?
As for the talk of division tiers below diamond I have some questions about it.
Diamond is a huge league compared to plat/gold/silver and it originally was the only league you could not place into. To be in diamond you had to be promoted into a division while having your points adjusted down to 73. When you place into a league below diamond you start with 0 points, and when you calculated the division offsets originally you discovered that they were ALWAYS a multiple of the same number.
So the question then is where are these points actually earned? Are we to assume that players in low divisions are getting 1,2,3 or more points per game than they should? Once they reach the division offset they get the normal amount of points, but if this were the case then players would not all have offsets that were consistently multiples of same number. If the division modifiers are applied to players upon promotion (for example if the 3100 pt bronze player was promoted to diamond, in this theory he would be S class) then this would imply that division modifiers only existed in diamond. Of course now that you can place into diamond and division tiers still exist it seems unlikely.
So if you are always given 73 points at promotion and you will always earn the correct number of points per game how then are division modifiers implemented and what function do they serve?
The only information we have is that bonus pool is the activity metric, that it accumulates 90 points per week, and by filtering a particular number of "bonus weeks behind" we can get a closer representation of the 2/18/20/20/20/20 league distribution. I think that those Bronze players who are anchored to zero points are suffering from this exact problem: they're unable to spend enough bonus pool to be considered active (whether that's 90 per week or enough to get above the inactivity threshold is still unclear) and therefore are considered inactive. This means they're not counted among the active Bronze population which makes Bronze larger than it should be, and this may explain the 44% number that SC2Ranks is reporting compared to the expected 20%. Furthermore, to actually get promoted into Silver from Bronze you need to get pretty deep into Silver, and this effect cascades into the higher leagues which may not have an insignificant impact.
The division tiers themselves are multiples of 63, and the point reset after a league change is spent bonus + 73. So we're dealing with two constants here, but the reason those constants exist is still a mystery. Maybe they really are just arbitrary numbers? Maybe they're certain predefined values based on how granular they want the separation between tiers to be (which at 63 points would be roughly 5 wins over losses against equal opponents)?
Those are some good questions. We know that the division tiers exist to normalize ratings across a league, and maybe even across all leagues. We'll use Minigun as an example. He has two accounts, one in Diamond and one in Master. On InflowMini, which is in Diamond and in an E-Rank division (+315), his adjusted rating is 1065 (3740 [points] - 315 [E-rank offset] - 150 [comparing to Master, so Master offset] - 2703 [current max bonus pool] + 493 [his unspent pool]). On ROOTMinigun, he's in Master with an adjusted rating of 992 (3640 [points] - 2703 [current max] + 55 [unspent]). (I realize that's a huge coincidence that the difference between his first profile and his second is 73). Regardless, 1065 is pretty close to 992, and this makes sense because his skill level probably hasn't changed from one account to another. Now, if you had another player who was less skilled, which means he would be placed in a lower division tier, he may have an adjusted rating that is around 700, but the division offset would boost that up to around 800 or 900, and suddenly he becomes a lot more competitive with players of higher skill in points only. An even weaker player might have an adjusted rating of 500, but with league/division offsets might be closer to 700 or 800. The division tiers themselves are not enough to disturb the ladder rankings because the gap in skill from one tier to another is generally enough to overcome the offset. However, they do a good job in hiding it, which motivates players to keep playing. If it were all one contiguous ladder and there were no league/division offsets, you would have players like Mini hundreds and hundreds of points above lower-level players, which I suppose could be seen as discouraging.
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On February 16 2011 03:17 Excalibur_Z wrote:
We know that the division tiers exist to normalize ratings across a league, and maybe even across all leagues.
Is this the opposite reason they exist?
See where I am going below:
On February 16 2011 02:40 DiDigital wrote:
So the question then is where are these points actually earned?
You saw the answer to this once Master League started. Everyone was getting +20 per win and -6 per loss because their displayed rating was below their MMR. So basically each player was favored in the same match up so the system could accelerate the displayed rating to come in line with MMR more quickly.
Remember points loss is your MMR vs your opponents displayed rating.
On February 16 2011 02:40 DiDigital wrote:
Are we to assume that players in low divisions are getting 1,2,3 or more points per game than they should? Once they reach the division offset they get the normal amount of points,
Again displayed vs MMR is the thing that affects point gain or loss.
On February 16 2011 02:40 DiDigital wrote:
but if this were the case then players would not all have offsets that were consistently multiples of same number. If the division modifiers are applied to players upon promotion (for example if the 3100 pt bronze player was promoted to diamond, in this theory he would be S class) then this would imply that division modifiers only existed in diamond. Of course now that you can place into diamond and division tiers still exist it seems unlikely.
The amount of points does not indicate what class player he would be promoted to, his hidden MMR does.
In fact once his is promoted and placed in the MMR appropriate division with his points at spent bonus pool +73 his gains and losses should be relatively stable, this is due to the fact that the division offsets exist. (Unlike initial creation of Master League, where points gain and losses were unstable for a period due to the upper level of MMR being higher than the threshold that would get you to masters)
On February 16 2011 02:40 DiDigital wrote:
So if you are always given 73 points at promotion and you will always earn the correct number of points per game how then are division modifiers implemented and what function do they serve?
I think this question is very interesting. The division modifiers allow for promotion based on where MMR stabilizes. Because post promotion points are spent bonus pool +73, the modifier serves to immediately adjust your displayed rating so that points gains and losses are relatively stable immediately after promotion regardless of how much bonus pool you have spent.
Speculation:
The system waits for your MMR to stabilize for promotion. Perhaps the tiers are necessary only to account for spent bonus pool at the time of promotion, so that the creation of masters league phenomenon is not seen constantly on the ladder.
The fewer number of games you play to raise your MMR would get you promoted to a higher ranked division, so that when people play against you their points gain loss is less affected by the fact that you have a high MMR and a low displayed rating.
Conversely, someone that spends their entire bonus pool before making it to diamond would need a larger modifier, since their displayed rating could be much higher than their MMR. Then the -315 would again bring things in line more quickly for matchmaking purposes.
So I propose tiers are a function of unspent bonus pool at the time of promotion to help to stabilize the matchmaking point gain and loss.
Perhaps if looking at it as tiers are a function of ladder stability rather than normalization may help in better understanding. Or is this just saying the same thing you already understand?
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EPT
