quote:
How is it decided who is playing from a set of players? Example: at some point there are 3 of the top 5 players wanting to play, the system described by you seems to give an advantage (league points) to the 2 players that will actually play, even if the 3rd player was also available. |
This is all a system that uses the current matchmaker, so it would decide who plays who. Players in the matchmaker have their search band widen as they wait, so if two of three players play a game, then the third player will play one of them if they attempt a rematch. quote:
With values given, the income from position 1 and 2 playing each other repeatedly would basically allow them to reach a position that no-one can catch up with (net 25 league points per game, 500% income compared to net 5 league points per game for position 4+5). |
Sure, but for this to happen you would need to have the top two players isolated in their own timezone from the other top players. If anyone they can match against is around while they try to play each other, then the third party will end up matched with them. We would possibly need a few extra measures against dodging, but as long as the dodged player goes back in the queue at the maximum search range (and at the "head" of the queue) then there won't be a problem. Perhaps the ladder should have some sort of artificial cap that ensures the 10th player can always match with the top player, if that is not already the case. I was fairly sure this was the case when I designed the matching band numbers, but since then the win/loss streak matching rating bonus/penalty was introduced and I've lost track of how the bands behave. The relationships between the points are designed to strike a balance between activity and skill. With the proposed numbers a player stuck in second place only has to 80% more games than the player in first place to win the league. This seems like a good balance to me. The ratio of subsequent rewards reflects how much you think skill should count compared to activity.
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quote:
Every time a top five player finishes a full game (ie, one that was scored for rating purposes) they receive the following league points: |
Wonder if it is good to encourage activity only for the top X players. Is there any reason not to have the system extended to everybody, like 1 point for below position 100, 2 points for positions between 100 to 50, etc. To prevent farming there should be some limit of points gained per day to avoid people just start a game and resign immediately.
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quote:
Wonder if it is good to encourage activity only for the top X players. Is there any reason not to have the system extended to everybody |
Keep in mind it takes 2 people to make a game so any time a top5 player decides to play, somebody else also gets to play (which may be another top5 but hopefully not). Top 6+ people already have an incentive in the form of getting to reach higher ranks (while top5 risk a lot by playing and have little to gain since they are already top).
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quote:
Top 6+ people already have an incentive in the form of getting to reach higher ranks. |
If I would join and play 2-3 games in a row with a top 5 player (and, probably get beaten), I will switch to another game type. If by playing a top 5 player I would get "ahead" of someone with similar rating but that played less, then maybe I will continue to try to beat the top 5 player. This is also good for the someone with similar rating with me, because if I am matchmaking for the league, he has a chance to be matched with me (not true if I got bored of getting beaten and left). It depends indeed on who will be online (if enough are online it's not a problem), but if it happens that the top X players (most passionate probably) are always online, other people might not overlap as easily, meet mostly top X and get bored to play and loose, while the top X players get points...
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I'm much less opposed to league rating if we keep WHR next to it AND keep it visible. If league rating is already reset every 4 month, it is NOT needed to also reset WHR. Just leave WHR as is, then no spare month is needed. Whether the points are taken from before or after the game does not necessarily matter: For an elo system, the points after the previous game are the same as the points before the next game. For WHR, the points before and after the game are the same according to WHR-internal time after everything has been calculated. But there is a second type of time: real time. After a game happens in real time, the whole WHR-internal timeline changes. It makes sense to calculate everything according to the last real time status of the WHR-internal timeline, but not according to the real timeline of the last WHR-internal time. The former causes unintuitive changes while not playing, though. The latest numbers that     GoogleFrog suggested remind me a lot of Fibonacci numbers. So why not directly use those for consistency? According to the Moivre-Binet formula, the x-th Fibonacci number converges to an exponential function a*b^x with a = 1/sqrt(5), b = (1+sqrt(5))/2 = 1.618. GoogleFrog's number for player at ladder rank x is approximately a*b^(10-x). As the constant scaling factor a*b^10 doesn't matter, we may as well say b^-x. A continous exponential function compared to discrete Fibonacci numbers has the advantage that lower ranked players are not excluded. I think GoogleFrog chose those numbers because he intuitively wanted the exponential behavior. But what is a good value for b? Points proportional to exp(natural WHR) make a lot of sense from the math of WHR, so I think it'd be nice to make it so. natural WHR = (WHR - 1500)/(400/ln(10)) But if we want to use ladder positions instead of WHR, we need a way to estimate WHR from ladder positions. By assuming that WHR is distributed equidistantly over ladder positions and looking at the current top1 and top50 values, we get b = 10^((3434-2250)/(50-1)/400) = 1.15 which is already more sane than the above 1.618. However, WHR distances are not equal. Better ladder positions have higher WHR distances between each other. Therefore, the above assumed equidistant distribution does still exclude all but the top players. By assuming a Gaussian normal distribution, I come to the conclusion that the ideal number of points for a game proportional to exp(natural WHR) is exp(sigma*erfinv(1-(2*x-1)/N)) where sigma is the natural WHR standard deviation of all players, erfinv the inversion of the error function erf, x the ladder position and N the number of all players. Every league start, sigma can be set as the WHR standard deviation of all players of the previous league divided by 400/ln(10). Usually, sigma is 1, but for us I guess rather sigma is 4. Similar to b, sigma determines how much better players get more income. I think, GoogleFrog had mostly the top players in mind because he is a top player himself. For sigma >= 2, the above formula is similarly extreme as his suggestion for top5 players, then gets more to the b=1.15 solution for top50 players and so on for average players.
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   Brackman the short answer is that a mathematically perfect system is useless if it is too opaque for players to meaningfully interact with. The fundamental goal of all our ladder systems is to generate fun for players, not to be some sort of beautiful confluence of stats and relations! quote:
Whether the points are taken from before or after the game does not necessarily matter: |
It matters because it is nice to receive the increased point income for the win that makes you move up a ladder position, and it would be unnecessarily saddening to receive fewer points after a game where you rank down. You can even rank down on a won game if the ladder shifts while you are playing. I am fully aware that this edge case will barely affect the ladder and is mathematically meaningless. Of course the rating system doesn't draw a distinction between the end of the last game and the start of the next. However, players do. quote:
The latest numbers that GoogleFrog suggested remind me a lot of Fibonacci numbers. So why not directly use those for consistency? |
I quickly realised that the property I was going for, that the rank N player only had to be about half as active as the rank N+1 ladder to beat them in league points, results in a sequence of numbers that differ by an approximately constant factor. I didn't pick the Fibonacci numbers because they are not round and, if applied across the whole set of players that receive points, make the points gained by the top players too large. quote:
But if we want to use ladder positions instead of WHR, we need a way to estimate WHR from ladder positions. By assuming that WHR is distributed equidistantly over ladder positions and looking at the current top1 and top50 values, we get |
This quote is out of context, but, in general, we don't need a way to estimate WHR from ladder positions to use ladder position instead of WHR. We can just use ladder position. Brackman I've got to go hotfix the lobby as it was broken by a sudden infra release, so I have not plugged some values in to your league points equation to get a feel for your proposal. Nevertheless, I highly doubt that equation yields a set of nice integers. Aside from this you haven't provided any justification for your system. What are the criteria for a good system and which criteria does your system satisfy? You haven't spelled any of these out, only hinting that you value mathematical consistency and including all players. quote:
I think, GoogleFrog had mostly the top players in mind because he is a top player himself. For sigma >= 2, the above formula is similarly extreme as his suggestion for top5 players, then gets more to the b=1.15 solution for top50 players and so on for average players. |
Rather than guessing, look at the thought processes I laid out in previous posts:
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"This position is recorded as your final league position, in essence your personal best, for the league. The aim here is to make players feel like they can keep playing games without risking their current position."
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"Every player will, at the end of a league, receive some sort of trophy or indicator of the best position they reached during the league. This metric is intended to be a more of a personal incomparable achievement, something that they can strive to improve upon for the next league."
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"The aim of the league points system is to encourage activity at the top of the ladder, and to give the league a definite winner that isn't just dependent on the ranks at the end."
For most players, the goal of the league can be to climb as high as they can. This goal doesn't work for players who have reached the top of the league. Indeed, when a player reaches the top they have "won" and don't have any reason to participate further. If the top player doesn't play then it will be hard for those just below them to dethrone them, frustrating their goal of climbing as high as possible. Furthermore, the gap between the 2nd and 3rd player may be so great that most of the top 10 gives up once they reach spot three. Basically, the ladder could ossify from the top. This has already happened at times in the history of Zero-K and it is well known that players can stick around in the top 10 with very little activity. I expect the effect to be more pronounced when players feel like they have "won" a finite league before it ends. Notably, this issue doesn't exist lower down the ladder. The gaps between players are relatively small so there is always a bit of room to strive for the next ladder spot. If a player loses in the middle of the ladder happens to lose motivation (we can't force them to play) then they won't block the goal of the league for everyone else, they can just be routed around. The feeling that players outside the top 5 are "missing out" on league points is real, but if you want to talk about this aspect then start here rather than ending here. There are a few factors to take into account. If we give league points to everyone then we emphasise activity over skill at the lower levels. I think it is probably healthier for players to focus more on their personal position rather than comparing their own points and activity to others. Here is a proposal for league points for everyone. | Rank | Threshold | Drop Threshold | League Points | | Top 1 | - | - | 180 | | Top 2 | - | - | 110 | | Top 3 | - | - | 70 | | Top 4 | - | - | 50 | | Top 5 | - | - | 35 | | Top 6 | - | - | 28 | | Top 7 | - | - | 25 | | Top 8 | - | - | 22 | | Top 9 | - | - | 20 | | Top 10 | - | - | 18 | | Dark Blue | 20 | 24 | 15 | | Light Blue | 50 | 60 | 12 | | Yellow | 100 | 120 | 9 | | Orange | 150 | 180 | 7 | | Sub-Orange | 225 | 270 | 5 | | Red | 300 | 360 | 4 | | Grey | everyone | - | 3 |
The point gains outside the top 10 directly correspond to rank colour. This gives players a boost when they reach a rank threshold, and gives them that boost for as long as they remain at or above the 20% ladder threshold. Maintaining integers at the lower level pushes the numbers at the top of the range outside the human friendly range. This system puts more focus on activity for everyone across the ladder, possibly to an unhealthy extent.
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To answer your question, my goal was to make league points proportional to number of games times exp(WHR) to rate the product of activity and skill. This simple goal makes the resulting numbers consistent and includes all players. Of course, this goal can be seen as arbitrary. I think your numbers go in the same direction, just that making them constant integers makes them more arbitrary. quote:
Nevertheless, I highly doubt that equation yields a set of nice integers. |
Of course, I don't care about integers :D. With a prefactor of a=2.5, sigma=2 and N=400, I get similar numbers as you do in your last post, just more continous and consistent. I think the main remaining questions are how we want to weigh weaker players, which means choosing b or sigma, and whether we want such a system at all. Also, as    malric already implied, resign becomes OP if game number is used. Should we take game time instead? I would still like to emphasize that I prefer WHR not to be reset when league rating is reset. Also, I'm wondering if it wouldn't make more sense to have one rating for skill and one for activity instead of mixing it up.
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If you don't care about integers then you don't care about players feeling like they are in control and interacting with the league, rather than feeling like the league is an arbitrary black box. Your arbitrary numbers and my arbitrary numbers are not on the same standing because my numbers are grounded by the goal of having players use and enjoy the league. I say how I intend my numbers to fulfill this goal, and you can critic them on this basis. Your numbers don't appear to have any such foundation. This is a game design problem, not a theoretical exercise in stats! quote:
I get similar numbers as you do in your last post, just more continous and consistent. |
Continuity is monotonous and your form of consistency is limiting. Having your league points per game go from 9.842 to 9.849 because you went from position 86 to 85 on the ladder is deeply unexciting. Having your points per game leap from 7 to 9 when you hit top 100 is a milestone. My scaling factor intentionally climbs from around 1.3 at the low end to 1.6 at the top. quote:
Also, as malric already implied, resign becomes OP if game number is used. Should we take game time instead? |
Pure game time motivates people to sit idle in long games, as that reduces downtime. Perhaps some sort of equation could be developed to balance time and quantity. Perhaps such a thing is already implemented. I dimly recall there being an equation for XP that rises to 100% over 10 minutes or so. Resign being OP could be taken as an argument against having league points for the whole ladder. It is relatively easy to police the top few slots as keeping a top spot is lucrative, and I'm sure players will complain if they notice the top players farming games. quote:
I would still like to emphasize that I prefer WHR not to be reset when league rating is reset. Also, I'm wondering if it wouldn't make more sense to have one rating for skill and one for activity instead of mixing it up. |
Why don't you want WHR reset, and in what way does adding a simple activity rating make sense?
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quote:
Pure game time motivates people to sit idle in long games, as that reduces downtime. |
Not sure if already clear or not, will list what I would like as a non top player:
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have other people my level active (in matchmaker queue)
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have some bonus if I am active over a similarly skilled player less active
Qualitatively I think a league points would look like:
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for every X league points you get a bonus on the league ladder (X could depende on the skill value, such that if the difference between you and the one above you is large you need more league points to be in front of him)
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you get a maximum Y league points for activity per day (this should be a formula with both time spent playing and number of games)
Some observations:
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a matchmaker with diverse ranks is quite important - it would eliminate a lot of cases, for example if you get matched with someone close to your skill and resign or try to stall you will loose more because skill is much more valuable than play time/games. But if you get matched with a top 10 you can immediately resign...
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a perfect ranking can probably be given only in very restricted settings (all with all players, on same maps), which I feel tournaments are for. The league system in my opinion will be great to encourage more activity across the ladder, so perfect ranking should not be a primary objective.
These are just my thoughts, I agree problem is complex, but think is good to reflect also qualitatively from time to time.
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quote:
But if you get matched with a top 10 you can immediately resign... |
I really hope the culture of paradoxical anti-competitive personal drama gets a solution. To be specific; players who have done well enough to get into the top 20 complaining when they get matched with myself or other top 10 players. To those people: If you climbed the ranked ladder, what did you expect to happen as you got better, that you would just be matched with a larger, growing pool of less skilled players than yourself? You occasionally see dodging, or (now unpunished) game abandoning before plop. At the minimum, bitch talk. It's a little repetitive to see complaints about the matchmaker, excuses or disclaimers from that demographic when you do get a game. I don't really see it as the ongoing responsibility of competitive players to take up the added guilt/burden of interacting with these players when they decide that they've reached their absolute plateau. Consequently, I think whatever does change should emphasize the "Competitive" message. If a player doesn't have competitive spirit, then other gamemode options should still cater for them and be more encouraged. The addition of the casual 1v1 room seems to have been somewhat succesful in that regard and the culture of unpressurized improvement is growing, thankfully. But ultimately, repeat game abandonment should have some sort of discouraging mechanism. Mutual !exit votes are fine, and common where life's surprises cause a game to need to be delayed. But repeat abandon absolutely needs to be seen as a forfeit and have some (maybe gradually ramping) WHR implications, if not barring the player from ranked play for a certain duration. Since internet disconnections and powerouts exist, infrequently, said system should probably regen back upto 0 punishment within X timeframe as not to punish honest unavoidable issues.
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quote:
To those people: If you climbed the ranked ladder, what did you expect to happen as you got better, that you would just be matched with a larger, growing pool of less skilled players than yourself? |
I expect they were hoping for games against a reasonable selection of players around their own skill level... the rate of which does seem to decrease sharply around 2400-2600 ladder ranking.
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quote:
I expect they were hoping for games against a reasonable selection of players around their own skill level... the rate of which does seem to decrease sharply around 2400-2600 ladder ranking. |
A fair expectation, however, I think being concerned with machine output like ratings and !predict is part of the problem here. It's not uncommon for me to see the pattern of the opponent connecting, running !predict, seeing the numbers and giving up on the spot. But here's the thing, we drive the machine - not the other way around. Natural fluctuations in player's willpower and skill can absolutely be the basis for defiance. Another flaw with treating !predict as gospel is that if I had a 10% chance to beat Godde, succeeded, and re-predict and it says 20% now, according to the machine I have effectively doubled in skill. And I'm meant to believe that? The point I'm trying to make is that all of our mechanisms of DEFINING skill gaps are mathematically extreme and don't translate into human friendly, or encouraging, data. There's a saying along the lines that the #1 swordsman fears the unknown swordsman far more than the #2. Absolutely appicable to ZK with all the cheese and mad strats people pull.
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quote:
players who have done well enough to get into the top 20 complaining when they get matched with myself or other top 10 players. |
I think highest I got was around 40 on matchmaking (did not play in 6 months though) - so that's what I meant by "not top player". And what I would hope a league would encourage is people playing, such that you get a chance to play with people close to your rank and system determines how good you "really" are. To the extreme to explain the point: if top 5 players are always online (only ones incentivized by league points) and other players come each day at random time and play one game, the top 5 positions will be completely real (that's good) because they played a lot, while positions after top 5 can be quite inexact because people play mostly with top 5 (that's bad). I know in reality it will not be as this extreme case, but if the system works for top 5, why wouldn't it work for everybody?
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quote:
A fair expectation, however, I think being concerned with machine output like ratings and !predict is part of the problem here. It's not uncommon for me to see the pattern of the opponent connecting, running !predict, seeing the numbers and giving up on the spot. But here's the thing, we drive the machine - not the other way around. Natural fluctuations in player's willpower and skill can absolutely be the basis for defiance. |
This is all very easy to say. I do not think that the output of !predict is the most important reason why most people walking into a game against the highly-ranked MM players think that game is going to be onesided and unfun.
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I get you. I'm just saying it's a re-inforcing crutch that further compounds the attitude. I get that the reputation of the player is also involved - though often blown out of proportion. There's no system we can implement that solves ZK Mythology. At least seasonal leagues remove the near-decade of rating accrual that currently serves to discourage up-and-comers. One less reason not to participate.
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I don't think it's the reputation either. I think it is largely an accurate assessment of how competitive and fun those games are, in fact, going to be. Furthermore I do not expect the primary consequence of adding penalties for dodging games to be fewer people dodging games rather than sticking around and playing them. I expect it to be fewer people queueing MM in the first place.
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malric I'm not sure what you mean by "for every X league points you get a bonus on the league ladder". Are you saying that receiving league points should boost you on the skill ladder? This is far from what I have in mind, so if you have a suggestion for a system you should spells yours out explicitly rather than as a modification of what I've laid out. In my proposal league points and the ladder are separate:
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League points don't affect any part of the MM ladder. They don't change people's rankings or change who they can play.
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League points just keep accruing as you play MM games. They aren't modified any other way.
quote:
To the extreme to explain the point: if top 5 players are always online (only ones incentivized by league points) and other players come each day at random time and play one game, the top 5 positions will be completely real (that's good) because they played a lot, while positions after top 5 can be quite inexact because people play mostly with top 5 (that's bad). I know in reality it will not be as this extreme case, but if the system works for top 5, why wouldn't it work for everybody? |
Here is why I think league points may work for the top 5 but not for everyone:
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If you're in the top 5 you have a decent shot at winning the league, both through the relative rate at which you gain league points and due to the possibility of advancement.
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The top N player has less opportunity to feel unfairness at the top N+1 player is beating them in league points, purely through activity, because the unfairness is mitigated by the top N+1 player gaining league points at a significantly lower rate.
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The incentive for resigning quickly to gain points is significantly reduced when the rate of point gain changes dramatically if you gain or lose a rank.
Basically, for someone at position 80, their league point standing is almost entirely based on how active they are compared to players of ranks 20 to 200. Is rewarding pure activity in this way useful and helpful? I'm coming around to the idea that points for everyone may have enough advantages to outweigh the issues, but it does introduce issues. We would probably need to do a bit more to combat resigning for rapid point gain, and possibly introduce rate limits.
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quote:
Yes yes yes. League refreshment promotes more play, more innovation and ultimately more fun. Newer up-and-comers can finally feel like they have a stab at the big league player's positions without having to first conquer almost a decade of rating acquisition. |
I don't think the ladder adjusts so slowly that "decades of rating acquisition" is a real effect that prevents players from climbing the ladder. I don't know whether you meant to imply that you think it is, or whether you're just saying that this effect is perceived to exist. I agree that it is a psychological effect. I don't think the league should only be aimed at highly competitive thing. Initially I thought it would be about gaining personal bests, with the league points only being there to keep the top active when they run out of personal improvement.
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quote:
Are you saying that receiving league points should boost you on the skill ladder? This is far from what I have in mind, so if you have a suggestion for a system you should spells yours out explicitly rather than as a modification of what I've laid out. |
I think the effect of your system with league points is that it requires (top X) people in the league to (also) play to keep their position. I think it is good, I was just suggesting it is probably good for more than top X. quote:
the top 5 but not for everyone: |
Comments on the points:
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if league is only about winning (and not about general position), I will probably not play. I seldom play nowadays 1v1 because it feels (for me) unbalanced, because (probably) not enough people play. I tried Saturday evening (prime time), I got 2 unbalanced games and 2 more balanced ones and there were only 3 games going overall. It is not bad, but if people around my position play rarely I might not be able to advance. Ex (for current ranking): Above me -
  PresidentNyan played one game 2 weeks ago, next batch of games 7 weeks ago. Below me is  StStephenHawking whom played a batch of games 7 games 1 week ago, and next batch of games 3 weeks ago. I played 4 games in 6 months.
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yes, the league points should not enable you to jump too much, but in my opinion there could be trade-off between being present to play games (which must be rewarded) and winning games
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then maybe league points should be given for the winner (inverse proportional to skill difference) and for waiting in the queue. In the end you want to have some reward for waiting, so why not just give it directly (subject to rate limits, ofc!)
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to combat resigning for rapid point gain, and possibly introduce rate limits. |
I am sure you can find a good formula, I am not sure it will be easy to understand - both in my opinion are objective for any system. quote:
with the league points only being there to keep the top active when they run out of personal improvement. |
I think bottom can also run out of personal improvement as much as top. Just worth mentioning: I am not active in 1v1 (or passionate about it) and I do not feel strongly about the ideas above, I see it more as an abstract problem and enjoy thinking of solutions...
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