Alliance Quest Tiers Restructured by Percentage

Comments

• DNA3000 Member, Guardian Guardian › Posts: 19,827 Guardian

  December 2017

  The current trend does not appear to be exponential. Part of the problem with the AQ data we currently have is that we don't have data for a seven week stretch and that is making the jump seem larger than it actually is.
  
  This is what the data looks like, with a linear trend line:
  
  
  
  This is the same data with an exponential trend line:
  
  
  
  The data looks more consistent with linear than exponential increase, which is what you'd expect if most of the rise is due to prestige increases which cannot increase exponentially. The linear trend line extrapolates about 1.6 million point increase per AQ week on average. That's actually consistent with an increase in prestige of about 75 points per AQ week for an alliance running Map 5x5, given the data posted here: https://forums.playcontestofchampions.com/en/discussion/comment/226043/#Comment_226043 .
  
  Given that, I don't think the expert tier cut off increase is due primarily to a shift to Map 6. I think it is more likely the result of the increased availability of 5* champions slowly increasing prestige across the board for the alliances in the expert tier.

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• DTMelodicMetal Member Posts: 2,785 ★★★★★

  December 2017

  Interesting points. I'm not sure the linear trend line has more validity than the exponential trend line, mostly because there may not be enough data to answer that question. What criteria are you going be to establish the linear trend line looks more consistent than the exponential trend line? The final data point (last week's AQ cycle results) is above the maximum of the linear trend line, but below the maximum of the exponential trend line.
  
  It's been a while since my last statistics class, but the equation to calculate the slope of a line may shed some light on this. If you take the earliest data that shows what score was enough to stay in expert tier (week 3, 37,424,120 points) and the most recent week that shows what score was enough to stay in expert tier (week 27, 80,055,921 points), it's possible to calculate how many points the cutoff to stay in expert tier should be increasing each week. The slope of a line (y2 - y1)/(x2 - x1), which in this case is (80,055,921 - 37,424,120)/(27-3), which simplifies to 42631801/24, which equals 1,776,325.042 points). Thus, a liner increase in points required to stay in expert tier for AQ would show an increae by approximately 1,776,325 points per week/cycle.
  
  It seems like the increase in points required to stay in expert tier fluctuates between trends of linear and exponential increases, with some instances of exponential increase occurring between weeks four and five (8+ million increase), weeks six and seven (5+ million increase), and weeks thirteen and fourteen (7+ million increase). Perhaps free map costs are a catalyst for alliances increasing how often they do Maps 5 and 6?
  
  I think one of Primmer79's comments in the link you posted is valid, that both alliances increasing their prestige and increasing how often they do Maps 5 and 6 are responsible for the rate of points increase to stay in expert tier. Lastly, do you think restructuring alliance quest tiers by percentage (i.e., arena tiers, alliance war tiers) is something to be considered?

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• DNA3000 Member, Guardian Guardian › Posts: 19,827 Guardian

  December 2017

  DTMelodicMetal wrote: »

  Interesting points. I'm not sure the linear trend line has more validity than the exponential trend line, mostly because there may not be enough data to answer that question. What criteria are you going be to establish the linear trend line looks more consistent than the exponential trend line? The final data point (last week's AQ cycle results) is above the maximum of the linear trend line, but below the maximum of the exponential trend line.

  
  The R^2 for linear is 0.88 and the R^2 for exponential is 0.84.
  
  The best linear fit line uses least squares fitting, which you can google search if you want to see the math, but the idea is basically to create a line that minimizes the distance from the line to all the points in your graph. The linear lsf line is 1,605,756.7x + 35,285,179.32 (I displayed the equation in the chart above so you can see it). I didn't turn on R^2 for the charts above but the short form explanation of R^2 is that the closer it is to 1.0 the closer the fit the curve is. It isn't 100% kosher to compare R^2 between linear and exponential fits, but I think its good enough for our purposes here.
  

  It's been a while since my last statistics class, but the equation to calculate the slope of a line may shed some light on this. If you take the earliest data that shows what score was enough to stay in expert tier (week 3, 37,424,120 points) and the most recent week that shows what score was enough to stay in expert tier (week 27, 80,055,921 points), it's possible to calculate how many points the cutoff to stay in expert tier should be increasing each week. The slope of a line (y2 - y1)/(x2 - x1), which in this case is (80,055,921 - 37,424,120)/(27-3), which simplifies to 42631801/24, which equals 1,776,325.042 points). Thus, a liner increase in points required to stay in expert tier for AQ would show an increae by approximately 1,776,325 points per week/cycle.

  
  This line assumes none of the data points between them exists. Its close, but not the best linear fit for the data.
  

  It seems like the increase in points required to stay in expert tier fluctuates between trends of linear and exponential increases, with some instances of exponential increase occurring between weeks four and five (8+ million increase), weeks six and seven (5+ million increase), and weeks thirteen and fourteen (7+ million increase). Perhaps free map costs are a catalyst for alliances increasing how often they do Maps 5 and 6?

  
  Maybe, but once you start looking at the data that way, statistical analysis goes out the window. By definition, statistical analysis assumes that the data points you have are "scattered" around the true trend by random fluctuations, which in the real world would cause alliances to score more or less points due to unpredictable changes you can't account for. But once you start assuming those data points don't represent an average trend but actually represent very specific events happening on each individual week, you can't extrapolate a trend anymore. At least, not with these very simplistic analyses.
  

  Lastly, do you think restructuring alliance quest tiers by percentage (i.e., arena tiers, alliance war tiers) is something to be considered?

  
  Its unclear to me if that would have any significant impact. For one thing, we don't know how the number of alliances are growing. Its also clear to me looking at the detailed data that a similar thing is happening in AQ that happens in basic and featured arena scoring. There is a general "consensus" guess as to what score is necessary to achieve something. Scores tend to cluster around that general consensus and more rapidly rise and fall above and below it. That means changing the cutoff alliance count might not change cutoff scores by much, because it would just encourage alliances close to the cutoff to try harder, up to a certain point.

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• SiriusBreak Member, Guardian Guardian › Posts: 2,156 Guardian

  December 2017

  Perhaps just add a new reward tier? Considering the coming of 6* champs, and the addition (finally) of T5 catalysts, maybe it's time to add a new reward tier. That way Expert tier will be more likely to have a cutoff closer to 55 million instead of 80.

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• DTMelodicMetal Member Posts: 2,785 ★★★★★

  December 2017

  The best linear fit line uses least squares fitting, which you can google search if you want to see the math, but the idea is basically to create a line that minimizes the distance from the line to all the points in your graph. The linear lsf line is 1,605,756.7x + 35,285,179.32 (I displayed the equation in the chart above so you can see it). I didn't turn on R^2 for the charts above but the short form explanation of R^2 is that the closer it is to 1.0 the closer the fit the curve is. It isn't 100% kosher to compare R^2 between linear and exponential fits, but I think its good enough for our purposes here.

  
  You clearly understand statistics to a far greater extent than I do. I trust your judgement on this.
  

  Maybe, but once you start looking at the data that way, statistical analysis goes out the window. By definition, statistical analysis assumes that the data points you have are "scattered" around the true trend by random fluctuations, which in the real world would cause alliances to score more or less points due to unpredictable changes you can't account for. But once you start assuming those data points don't represent an average trend but actually represent very specific events happening on each individual week, you can't extrapolate a trend anymore. At least, not with these very simplistic analyses.

  
  I'm assuming you're alluding to analyses such as hierarchical models/bayesian statistics?
  

  Its unclear to me if that would have any significant impact. For one thing, we don't know how the number of alliances are growing. Its also clear to me looking at the detailed data that a similar thing is happening in AQ that happens in basic and featured arena scoring. There is a general "consensus" guess as to what score is necessary to achieve something. Scores tend to cluster around that general consensus and more rapidly rise and fall above and below it. That means changing the cutoff alliance count might not change cutoff scores by much, because it would just encourage alliances close to the cutoff to try harder, up to a certain point.

  
  I get where you're coming from with not knowing if restructuring alliance quest tiers by percentage is worth considering without knowing the game's rate of alliance growth. Considering that both arena rewards/tiers and alliance war rewards/tiers are and have been structured by percentage for close to a year (except for top 800 in featured arena), I think that structuring alliance quest rewards/tiers on the same model is something that could work.
  

  Perhaps just add a new reward tier? Considering the coming of 6* champs, and the addition (finally) of T5 catalysts, maybe it's time to add a new reward tier. That way Expert tier will be more likely to have a cutoff closer to 55 million instead of 80.

  
  I really like this idea. Donating 133,335 gold, 29,170 battle chips, and 12,500 loyalty in return for 1,375 glory/six Map 3 Crystals/four Map 4 crystals/25,000 T4BC Shards (Advanced Tier Milestones/Top 700 Rank Rewards) compared to 2,420 glory/nine Map 5 crystals/one Map 6 crystal/one T4BC/one greater glory crystal (First 10 Expert Tier Milestones/2,101-2,800 Rank Rewards) is a deters alliances from striving to maximize their AQ potential (see pictures below). Kabam removed points for defender kills in AW because they said points for defender kills discouraged players from finishing their paths. Adding a new tier to AQ milestone/rank rewards could accomplish something similar for AQ. I've spoken to a large amount of players in global and in line recruiting chats that have said the AQ maps they run are dependent on rewards instead of their members' level of skill and/or potential. Adding a new AQ tier could be something that prevents both the inclusion of 6* champs and the large increase in number of 5* champs from taking the fun and excitement out of AQ.
  
  
  
  
  
  

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• Wordy12 Member Posts: 208 ★

  January 2018

  My brain hurts.....
  But I agree with you nonetheless

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• Wordy12 Member Posts: 208 ★

  January 2018

  And I'm actually in a class for this.....

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