Most of the MCoC community is so entitled its sickening. Monopolize a game mode? Rofl the sense of entitlement is worse. People should look at this horrible Cap Commissary event. They see a reward unreachable and start dozens of threads about it. Yes it is a bad event, yes it has a reward, IT DOESNT MEAN YOU SHOULD GET IT. Sometimes you just gotta be ok with what you get, and as a UC/CAV/Smaller Roster/Casual Player, you should be happy with the rewards you get. There will always be a richer, bigger or someone who tried harder getting more accept it
You mean entitled as in wanting reign of the GC every Season, and wanting control over the VT as well?
If they are good enough to get to GC please let them in, not ask to be accomodated to get into it, because that's exactly what entitlement is. I don't want to reign GC every season, I WANT TO get into GC every season, and managed to do it regardless of how the changed the mode for 11 seasons. See the difference? I don't put excuses to get what I want.
Most of the MCoC community is so entitled its sickening. Monopolize a game mode? Rofl the sense of entitlement is worse. People should look at this horrible Cap Commissary event. They see a reward unreachable and start dozens of threads about it. Yes it is a bad event, yes it has a reward, IT DOESNT MEAN YOU SHOULD GET IT. Sometimes you just gotta be ok with what you get, and as a UC/CAV/Smaller Roster/Casual Player, you should be happy with the rewards you get. There will always be a richer, bigger or someone who tried harder getting more accept it
You mean entitled as in wanting reign of the GC every Season, and wanting control over the VT as well?
If they are good enough to get to GC please let them in, not ask to be accomodated to get into it, because that's exactly what entitlement is. I don't want to reign GC every season, I WANT TO get into GC every season, and managed to do it regardless of how the changed the mode for 11 seasons. See the difference? I don't put excuses to get what I want.
No one is asking for anyone to be let into the GC. That point has been made multiple times. That's great. Good for you. That doesn't mean you speak for what's best for everyone else in BGs.
Most of the MCoC community is so entitled its sickening. Monopolize a game mode? Rofl the sense of entitlement is worse. People should look at this horrible Cap Commissary event. They see a reward unreachable and start dozens of threads about it. Yes it is a bad event, yes it has a reward, IT DOESNT MEAN YOU SHOULD GET IT. Sometimes you just gotta be ok with what you get, and as a UC/CAV/Smaller Roster/Casual Player, you should be happy with the rewards you get. There will always be a richer, bigger or someone who tried harder getting more accept it
You mean entitled as in wanting reign of the GC every Season, and wanting control over the VT as well?
If they are good enough to get to GC please let them in, not ask to be accomodated to get into it, because that's exactly what entitlement is. I don't want to reign GC every season, I WANT TO get into GC every season, and managed to do it regardless of how the changed the mode for 11 seasons. See the difference? I don't put excuses to get what I want.
No one is asking for anyone to be let into the GC. That point has been made multiple times. That's great. Good for you. That doesn't mean you speak for what's best for everyone else in BGs.
I never mentioned GC, you did and I answered. Who is running in circles now? And how is it that I don't talk for the best of everyone and you do? Cause you claimed numerous times that you are not talking for yourself?
You continue to focus on how people aren't good enough to get into the GC. One of us is talking about what's best overall. The other is concerned with keeping people from getting anywhere. That's not hard to see. Nice try, though. You scared someone might listen?
You continue to focus on how people aren't good enough to get into the GC. One of us is talking about what's best overall. The other is concerned with keeping people from getting anywhere. That's not hard to see. Nice try, though. You scared someone might listen?
Where does it say GC in there Captain Nitpick? Scared? Are you keyboard taunting me? Rofl You are pathetic Get into GC, or give me your IGN lets see if I'm scared 🤣
You continue to focus on how people aren't good enough to get into the GC. One of us is talking about what's best overall. The other is concerned with keeping people from getting anywhere. That's not hard to see. Nice try, though. You scared someone might listen?
Where does it say GC in there Captain Nitpick? Scared? Are you keyboard taunting me? Rofl You are pathetic Get into GC, or give me your IGN lets see if I'm scared 🤣
Most of the MCoC community is so entitled its sickening. Monopolize a game mode? Rofl the sense of entitlement is worse. People should look at this horrible Cap Commissary event. They see a reward unreachable and start dozens of threads about it. Yes it is a bad event, yes it has a reward, IT DOESNT MEAN YOU SHOULD GET IT. Sometimes you just gotta be ok with what you get, and as a UC/CAV/Smaller Roster/Casual Player, you should be happy with the rewards you get. There will always be a richer, bigger or someone who tried harder getting more accept it
You mean entitled as in wanting reign of the GC every Season, and wanting control over the VT as well?
If they are good enough to get to GC please let them in, not ask to be accomodated to get into it, because that's exactly what entitlement is. I don't want to reign GC every season, I WANT TO get into GC every season, and managed to do it regardless of how the changed the mode for 11 seasons. See the difference? I don't put excuses to get what I want.
You really are thick enough to not realize I am answering to you? You brought up the GC subject.
I pointed out that it's not a sound argument to call people entitled when that can be said for many arguments. People want repeat access to the GC, all the Rewards of the VT, AND they want to squash the concerns of people who are sequestered to the VT. Sounds pretty entitled to me.
It is the simplicity of the examples that is the problem. Instead I decided to tackle the more appropriate question: when you add a tanking player who on average wins 50% of the time and loses 50% of the time, how does that affect the average number of matches it takes for players to promote, which is a measure of how much resources on average the players will have to burn due to the presence of the tanking player.
A while back I actually did the long form calculations to figure this out, because sometimes that's just how I roll (also, I was worried I had forgotten how to do it). However, I'm too lazy to do that again, so instead I just did what everyone does: Monte Carlo it with stochastic simulation.
Given players of different average win percentage, this is how many matches it takes, on average, to promote out of a Vibranium tier which requires five trophies:
It is important to note here that the number of matches it takes is not linear relative to win percentage, it is almost exponential. And the reason is because fundamentally speaking, players above 50% win percentage are promoting due to different dynamics. All players can get lucky and string together a bunch of wins, no matter what their win percentage is. But the probability of doing so decays rapidly with win percentage. But players above 50% win percentage have an extra factor in play: their trophy win/loss ratio is biased toward promotion. On average they are gaining trophies with every match. Eventually that upward pressure will cause them to promote, no matter how unlucky they are. But conversely, players below 50% win percentage are biased downward. Without luck, they *never* promote. Which is intentional, by the way.
When we introduce a tanking player that starts winning and losing at a 50% rate (to keep them within the tier indefinitely, at least until they decide to stop tanking) they start skewing the win/loss percentages. You might think that half the time they are giving out wins and half the time they are giving out losses, so there can't be any advantage to that overall. But that would be wrong. Here's the average number of matches to promote when 5% of all players are tankers in a tier, and when 20% of all players in a tier are tankers:
Tanking has a relatively low impact on the high win percentage players. And that makes sense. When a tanker randomly gives them a win, it is a win they would have likely gotten anyway. When they give those players a loss their win percentage allows them to recover from that loss relatively quickly. When 5% of the players are tankers, meaning that on average you run into them about one in twenty matches, the overall impact on the high percentage players is almost nothing. It is increasing their average number of matches by less than one - because even though it looks like it is adding two more matches required, that wasn't guaranteed (the player could have lost regardless) and those losses are distributed across a lot of players. But the converse impact is very noticeable. When you start randomly handing out wins and losses to low percentage players, those players equilibrium position is actually zero trophies. Most of the time they are losing, so their tendency is to always drift towards zero. This is something simplified models do not account for. Low percentage players do not progress out by building up wins - if they could, they would have a higher than 50% win percentage. They do so by getting lucky - by stringing together enough lucky wins to overcome the natural tendency to fall back to zero.
Hitting a low percentage player with a loss is hitting them with a loss they were likely to get anyway. Giving them a win is giving them something they usually don't get, and because the odds of stringing together a long string of wins drops exponentially with how long the string needs to be, every win you give a low percentage player disproportionately benefits them. For 35% win percentage players, it can reduce their average number of matches from about 136 to 123, a reduction of 13 matches.
Given that the average match increase for high percentage players is less than one - even for players just barely over the 50% mark - the only way for this to average out in such a way that the cost being shifted to high percentage player was higher than the cost being saved by low percentage players would be if the high percentage players outnumbered the low percentage players by something like a ten to one ratio. But that's impossible, since they are matching against each other in that tier.
Tanking shifts trophies from high percentage players to low ones, and that's unambiguously a benefit for the low percentage players. That isn't really something that can be disputed in anything but corner case examples that don't match reality. But beyond that, the amount of benefit being shifted around is disproportionate to the amount of trophies being moved around. The high percentage players are being hurt a little, while the low percentage players are being benefitted a lot, because their promotion mechanics are *dramatically* improved by running into tankers. Enough to where the presence of tankers can literally be the difference between promotion and non-promotion.
In fact, it would be worth actually looking at how many players promote, rather than the average number of matches it takes to promote. After all, if the average drops from 136 to 93, who's going to put that much effort in anyway? Maybe the effort required drops, but not enough so that anyone actually benefits form it. So let's look at the statistical average number of players that actually promote, given a certain win percentage and a certain maximum number of matches before the player just gives up. We'll look at the 35% win percentage case, and look at how many players would promote, as a percentage of the total, if the players were willing to play for 25 matches, 50 matches, and 100 matches. And we''ll compare that to how many players promote if 5% of their matches run into tankers, and 20%.
The presence of tankers doesn't just decrease the average number of matches required on paper, it causes more players to promote out of the tier. At the 50 match limit, running into tankers just one time in twenty on average (this is statistically random: I'm not calculating on the assumption that they run into tankers literally once every twenty matches) causes about 2.5% more players to promote. That's a measurable number, and since promotion is one way that doesn't just mean 2.5% more players promote, that means 2.5% more players are promoting continuously throughout the season. And in the case where tankers are 20% of all players in the tier, a whopping 8.4% more players as a percentage of the total are promoting out of the tier.
These numbers are not counterbalanced by high percentage players not promoting, because at these numbers they are all still statistically likely to promote. For example, at 65% by 50 matches 99% of all players are promoting with or without tankers present.
That low percentage players are benefiting is, as I said, simply a statement of fact. But the statistical calculations show that not only are they benefiting, they are benefiting by several times more than the high percentage players are being hurt, because when it comes to how many matches it takes to promote, which is ultimately the statistic most players care about, and how many players of various strengths actually promote, which is ultimately what many players observe as problematic, tankers a) decrease the effort it takes to promote by a noticeable amount and b) cause noticeably more lower strength players to promote by lowering the amount of luck they need to do so.
Full disclosure: anyone who wants to bother, here's the quick and dirty script I used to calculate various BG trophy situations. I used it in the past to explore different scoring formulas, different track lengths, and I modified it to look at promotion histograms and the effects of tanking players on the statistics. Sorry, quoting python sucks on the forums, so its an image of the source. The code is also a bit ugly, because you have to pay me to make pretty code.
It is the simplicity of the examples that is the problem. Instead I decided to tackle the more appropriate question: when you add a tanking player who on average wins 50% of the time and loses 50% of the time, how does that affect the average number of matches it takes for players to promote, which is a measure of how much resources on average the players will have to burn due to the presence of the tanking player
I'm not quoting the whole thing. Few points on the whole thing:
1. 50% win percentage is not the same as tanking. Tanking is 50% wins without promoting. It takes out several permutations that results in the 50% win rate leading to promoting. In your own model, someone winning 50% of the time will promote on an average between 22 and 45 matches (I don't know if that's right, in the linked post you seem to suggest that a person winning 50% of the time would only need 20 matches to get 5 trophies.). I'm not sure your model differentiates between a player with 50% win rate and someone who is tanking.
2. Wins and losses do not happen in isolation - for every win, there is someone at the other end losing and vice versa. Average win rate across the group is always 50%. Your model doesn't factor this in. For e.g. in your table above a player winning at 25% needs 715+ matches to promote - at 25% they win 179 matches and lose 536 matches. Is that a net positive of 357 trophies? Did 71 other players promote due to this? Or going by your table which suggests 9 wins to promote at 75% win rate, did 79 players promote before the 1 player with 25% promoted? The best case seems to be that 72-80 people promote over those 715 matches and not just one player (one every 9-10 matches). When you bring this down to 65-35, that implies 10+1 players promoting every 136 matches or ~58 players promoting every 715 matches (one every ~12 matches). Closer you get to 50-50, the average number of matches played across the whole group only increases. Which is what tanking does.
3. When a high percentage win player promotes out of a group, they transfer their win percentage to the lower percentage players. Because, as explained earlier, win rates at a group level are constant - every match has a winner and a loser. I would guess that your model doesn't account for this either. If there are 3 players in a tier one with 25% win rate and one with 50% win rate, then the 3rd person has to have a 75% win rate. Once the person with 75% win rate promotes in 9 matches, they remaining 2 don't stay at 25% and 50%, it can be 25%-75% or 50%-50% or anything in between. Whatever it is, the 25% player doesn't need 700+ matches to promote anymore (just after 9 matches).
If I were to hazard a guess, the outputs in your second table is same as the output for changing the win percentage from (x% to x*80% + 20%*50%). For example under the 45% column, 41.26 is simply the average number of matches needed to promote for someone with 46% win rate (45%*80% + 20%*50%). You can take the tanking % up to 90% or 95% and everyone will concentrate around the 50% win rate mark.
I used simple models as simple models allow you to articulate all possible outcomes. If your theory doesn't hold up in a simple model, you should at least consider that there may be a flaw. You have posted multiple times that you base your progression on waves of competitive intensity. And you conveniently ignore all of that in the model above.
I'm happy to continue this discussion, if you are actually interested in exploring what is an engaging problem. If you are only interested twisting things around to fit into what you've already decided to be the right answer, let's agree to disagree. I only took this up because you asked someone to take the other side of the debate, I don't mind being proven wrong but not on that back of biased analysis.
Other than all matchmaking not being tier based, the battlegrounds a couple seasons back where the AW rewards also tied in, will go down as the best BG season ever.
It's just a drag now of facing much bigger accounts without also facing small ones. Here come the 7r3's in a couple months while many still don't have one 7r2.
As I've said before, I am fine facing the latgest accounts as long as I get to face the smaller ones too. But here we are. I only want to autoplay 3 matches every 2 days, because the MM is BS.
I only took this up because you asked someone to take the other side of the debate, I don't mind being proven wrong but not on that back of biased analysis.
You're correct, I really should have been much more specific. If you think this is a biased analysis, then I have been mostly wasting my time, because this is far too much sophisticated effort for what is ultimately, whatever this is. At least I now know that this isn't as obvious as I thought, which is something, and also why.
These kinds of stochastic analyses aren't super difficult to follow in general, with proper explanation. But with a hostile audience, it would take way too much time to explain the foundations of precisely why these sorts of representative analysis is done, and what the point of it is. To know precisely how valid model reduction is done is one of those things I routinely take for granted, but having thought through the steps required, is almost certainly beyond the scope of even my forum posts.
When someone promotes out of a tier, that does change the dynamics of the tier, however, in the specific case of a player capable of tanking in the tier, if they choose to start winning and promote the time they spend doing so is tiny compared to all the time before they entered the tier and the time spent tanking. It is a statistically insignificant period between the two, which is why for purposes of estimation it is reasonable to look at the statistics with them not there compared to with them there. However at this point proving that is left as an exercise for the reader, because the proof would be long, require significant foundation, and almost certainly not change a thing. This sort of thing is a fun time at the office, but it should probably be reserved for academic discussion, not advocacy.
You really are thick enough to not realize I am answering to you? You brought up the GC subject.
I pointed out that it's not a sound argument to call people entitled when that can be said for many arguments. People want repeat access to the GC, all the Rewards of the VT, AND they want to squash the concerns of people who are sequestered to the VT. Sounds pretty entitled to me.
lol, so it's cool for you to call endgame players entitled but not low players who are begging for more rewards that they aren't good enough to earn on their own? Got it chief!
You really are thick enough to not realize I am answering to you? You brought up the GC subject.
I pointed out that it's not a sound argument to call people entitled when that can be said for many arguments. People want repeat access to the GC, all the Rewards of the VT, AND they want to squash the concerns of people who are sequestered to the VT. Sounds pretty entitled to me.
lol, so it's cool for you to call endgame players entitled but not low players who are begging for more rewards that they aren't good enough to earn on their own? Got it chief!
I said it's probably not a good argument for anyone to call anyone entitled because when one finger is pointing at someone else, 3 more are pointing at themselves. Chief.
You really are thick enough to not realize I am answering to you? You brought up the GC subject.
I pointed out that it's not a sound argument to call people entitled when that can be said for many arguments. People want repeat access to the GC, all the Rewards of the VT, AND they want to squash the concerns of people who are sequestered to the VT. Sounds pretty entitled to me.
lol, so it's cool for you to call endgame players entitled but not low players who are begging for more rewards that they aren't good enough to earn on their own? Got it chief!
I said it's probably not a good argument for anyone to call anyone entitled because when one finger is pointing at someone else, 3 more are pointing at themselves. Chief.
It's so noble of you to decide that no one should call anyone entitled after you've been shown to be the one who feels that they deserve rewards that you can't earn. What a hero.
Pretty sure I can earn them. I'm not even at the stage I'm talking about changing anymore. The question of whether or not I can climb has never been an issue. Sounds like you're trying hard to keep an argument going. Sorry for that experience.
I only took this up because you asked someone to take the other side of the debate, I don't mind being proven wrong but not on that back of biased analysis.
You're correct, I really should have been much more specific. If you think this is a biased analysis, then I have been mostly wasting my time, because this is far too much sophisticated effort for what is ultimately, whatever this is. At least I now know that this isn't as obvious as I thought, which is something, and also why.
These kinds of stochastic analyses aren't super difficult to follow in general, with proper explanation. But with a hostile audience, it would take way too much time to explain the foundations of precisely why these sorts of representative analysis is done, and what the point of it is. To know precisely how valid model reduction is done is one of those things I routinely take for granted, but having thought through the steps required, is almost certainly beyond the scope of even my forum posts.
When someone promotes out of a tier, that does change the dynamics of the tier, however, in the specific case of a player capable of tanking in the tier, if they choose to start winning and promote the time they spend doing so is tiny compared to all the time before they entered the tier and the time spent tanking. It is a statistically insignificant period between the two, which is why for purposes of estimation it is reasonable to look at the statistics with them not there compared to with them there. However at this point proving that is left as an exercise for the reader, because the proof would be long, require significant foundation, and almost certainly not change a thing. This sort of thing is a fun time at the office, but it should probably be reserved for academic discussion, not advocacy.
It is biased because this is where we get, if we logically extend your argument: 1. The most beneficial set-up is everyone at a 50% win rate (ideally almost everyone tanking, but you don't seem to differentiate between the two). The gains for people with win-rates below 50% is more than the losses for the people with win-rates above 50%. 2. We also know that everyone at 50% win rate is the most stable a tier can be, this is the point where progression out of that tier is at its slowest.
1 & 2 are exact opposite conclusions, it seems difficult that they can co-exist.
I'll point out a single oddity in your previous analysis. Let me know if I'm reading it wrong.
The presence of tankers doesn't just decrease the average number of matches required on paper, it causes more players to promote out of the tier. At the 50 match limit, running into tankers just one time in twenty on average (this is statistically random: I'm not calculating on the assumption that they run into tankers literally once every twenty matches) causes about 2.5% more players to promote. That's a measurable number, and since promotion is one way that doesn't just mean 2.5% more players promote, that means 2.5% more players are promoting continuously throughout the season. And in the case where tankers are 20% of all players in the tier, a whopping 8.4% more players as a percentage of the total are promoting out of the tier.
These numbers are not counterbalanced by high percentage players not promoting, because at these numbers they are all still statistically likely to promote. For example, at 65% by 50 matches 99% of all players are promoting with or without tankers present.
With no tanking. 99% of all players with 65% win-rates will promote out by 50 matches. 28.5% of players with 35% win-rate promoted out of the tier in those same matches (all those matches were played against someone right?).
But in the period between 50 to 100 matches, only 23% of those players (51.5% - 28.5%) promote? Once the almost all the players with 65% win rates have promoted, the win rates for the players with 35% win-rates has to go up. Despite this over an equivalent period, fewer of those players will promote? Even if we consider the proportion of remaining players (23% of 71.5% remaining players = 32% of players), there is only a 3.5% improvement in the proportion of those players promoting. This does not match up with your first table that changing win-rate from 35% to 45% will reduce the number of matches required to promote by over 60%.
More importantly, your model suggests that more players will promote out of a tier when they are losing 2 games while winning one on an average as compared to when they are losing 1 and winning 1 on an average.
Your base assumption is that a win rate for a player is constant. Which is why you believe tanking is beneficial because it gives lower strength players more wins that they could otherwise get. But in reality, lower strength players benefit a lot more when higher strength players completely exit the tier vs. farming wins there.
A while back I actually did the long form calculations to figure this out, because sometimes that's just how I roll (also, I was worried I had forgotten how to do it). However, I'm too lazy to do that again, so instead I just did what everyone does: Monte Carlo it with stochastic simulation.
Given players of different average win percentage, this is how many matches it takes, on average, to promote out of a Vibranium tier which requires five trophies:
This model is extremely helpful if one is trying to calculate their resource costs while trying to progress through BG. If I wanted to estimate what would be my energy cost to get to GC, this is perfect. Because my win-rate is just an average of all the matches I play.
However, it doesn't represent the group outcomes of a PVP game mode. Because if I'm winning at 65%, someone else is losing at the same rate - it could be one person or a group of 100 people, for the set of matches I played in, they cannot win at any other rate.
If you have 3 players with 75%, 65% and 55% win rates, then the fourth player automatically has a 5% win rate, if there are only 4 players in the tier. If there are 6 you could have 45%, 35% and 25%. I will happily take the bet that in this group of 6 players, the player with 35% win-rate will promote much sooner than 139 matches on average.
Once the 75% winning player goes out, the odds become 70%/60%/50%/40%/30. A few games later this turns into 65%/55%/45%/35%, then 60%/50%/40% and then 55%/45%. From there it's 20-25 matches to promotion. Even if everyone resets to zero when someone promotes (you cannot go below zero), which they don't, that's somewhere around 70 matches for the person with 35% win rate to promote out of the tier. That's a 50% lesser than the 139 you are forecasting.
Your model doesn't work at n=2, n=4 or at n=6. It really only works at n=infinity. We have ~200K players in BGs across 18 tiers and GC.
Your model would be the right model to use, if BG was players playing against randomly generated decks of varying strength. In this case difficulty of a tier is constant, for a period of a season you can assume that the strength of the player is also constant. So their win rates are constant. In that case, players with 65% win rates are all out of the tier having player less than 50 matches while only 51% players with 35% win-rate have promoted while playing 100 matches on average as they can keep playing against the AI generated decks instead of the weaker active player base in their tier. The infinite supply of decks available to keep the competition level in a tier constant.
Comments
I don't want to reign GC every season, I WANT TO get into GC every season, and managed to do it regardless of how the changed the mode for 11 seasons.
See the difference? I don't put excuses to get what I want.
That's great. Good for you. That doesn't mean you speak for what's best for everyone else in BGs.
Who is running in circles now?
And how is it that I don't talk for the best of everyone and you do? Cause you claimed numerous times that you are not talking for yourself?
You scared someone might listen?
Where does it say GC in there Captain Nitpick?
Scared? Are you keyboard taunting me? Rofl
You are pathetic
Get into GC, or give me your IGN lets see if I'm scared 🤣
You really are thick enough to not realize I am answering to you?
You brought up the GC subject.
A while back I actually did the long form calculations to figure this out, because sometimes that's just how I roll (also, I was worried I had forgotten how to do it). However, I'm too lazy to do that again, so instead I just did what everyone does: Monte Carlo it with stochastic simulation.
Given players of different average win percentage, this is how many matches it takes, on average, to promote out of a Vibranium tier which requires five trophies:
It is important to note here that the number of matches it takes is not linear relative to win percentage, it is almost exponential. And the reason is because fundamentally speaking, players above 50% win percentage are promoting due to different dynamics. All players can get lucky and string together a bunch of wins, no matter what their win percentage is. But the probability of doing so decays rapidly with win percentage. But players above 50% win percentage have an extra factor in play: their trophy win/loss ratio is biased toward promotion. On average they are gaining trophies with every match. Eventually that upward pressure will cause them to promote, no matter how unlucky they are. But conversely, players below 50% win percentage are biased downward. Without luck, they *never* promote. Which is intentional, by the way.
When we introduce a tanking player that starts winning and losing at a 50% rate (to keep them within the tier indefinitely, at least until they decide to stop tanking) they start skewing the win/loss percentages. You might think that half the time they are giving out wins and half the time they are giving out losses, so there can't be any advantage to that overall. But that would be wrong. Here's the average number of matches to promote when 5% of all players are tankers in a tier, and when 20% of all players in a tier are tankers:
Tanking has a relatively low impact on the high win percentage players. And that makes sense. When a tanker randomly gives them a win, it is a win they would have likely gotten anyway. When they give those players a loss their win percentage allows them to recover from that loss relatively quickly. When 5% of the players are tankers, meaning that on average you run into them about one in twenty matches, the overall impact on the high percentage players is almost nothing. It is increasing their average number of matches by less than one - because even though it looks like it is adding two more matches required, that wasn't guaranteed (the player could have lost regardless) and those losses are distributed across a lot of players. But the converse impact is very noticeable. When you start randomly handing out wins and losses to low percentage players, those players equilibrium position is actually zero trophies. Most of the time they are losing, so their tendency is to always drift towards zero. This is something simplified models do not account for. Low percentage players do not progress out by building up wins - if they could, they would have a higher than 50% win percentage. They do so by getting lucky - by stringing together enough lucky wins to overcome the natural tendency to fall back to zero.
Hitting a low percentage player with a loss is hitting them with a loss they were likely to get anyway. Giving them a win is giving them something they usually don't get, and because the odds of stringing together a long string of wins drops exponentially with how long the string needs to be, every win you give a low percentage player disproportionately benefits them. For 35% win percentage players, it can reduce their average number of matches from about 136 to 123, a reduction of 13 matches.
Given that the average match increase for high percentage players is less than one - even for players just barely over the 50% mark - the only way for this to average out in such a way that the cost being shifted to high percentage player was higher than the cost being saved by low percentage players would be if the high percentage players outnumbered the low percentage players by something like a ten to one ratio. But that's impossible, since they are matching against each other in that tier.
Tanking shifts trophies from high percentage players to low ones, and that's unambiguously a benefit for the low percentage players. That isn't really something that can be disputed in anything but corner case examples that don't match reality. But beyond that, the amount of benefit being shifted around is disproportionate to the amount of trophies being moved around. The high percentage players are being hurt a little, while the low percentage players are being benefitted a lot, because their promotion mechanics are *dramatically* improved by running into tankers. Enough to where the presence of tankers can literally be the difference between promotion and non-promotion.
In fact, it would be worth actually looking at how many players promote, rather than the average number of matches it takes to promote. After all, if the average drops from 136 to 93, who's going to put that much effort in anyway? Maybe the effort required drops, but not enough so that anyone actually benefits form it. So let's look at the statistical average number of players that actually promote, given a certain win percentage and a certain maximum number of matches before the player just gives up. We'll look at the 35% win percentage case, and look at how many players would promote, as a percentage of the total, if the players were willing to play for 25 matches, 50 matches, and 100 matches. And we''ll compare that to how many players promote if 5% of their matches run into tankers, and 20%.
The presence of tankers doesn't just decrease the average number of matches required on paper, it causes more players to promote out of the tier. At the 50 match limit, running into tankers just one time in twenty on average (this is statistically random: I'm not calculating on the assumption that they run into tankers literally once every twenty matches) causes about 2.5% more players to promote. That's a measurable number, and since promotion is one way that doesn't just mean 2.5% more players promote, that means 2.5% more players are promoting continuously throughout the season. And in the case where tankers are 20% of all players in the tier, a whopping 8.4% more players as a percentage of the total are promoting out of the tier.
These numbers are not counterbalanced by high percentage players not promoting, because at these numbers they are all still statistically likely to promote. For example, at 65% by 50 matches 99% of all players are promoting with or without tankers present.
That low percentage players are benefiting is, as I said, simply a statement of fact. But the statistical calculations show that not only are they benefiting, they are benefiting by several times more than the high percentage players are being hurt, because when it comes to how many matches it takes to promote, which is ultimately the statistic most players care about, and how many players of various strengths actually promote, which is ultimately what many players observe as problematic, tankers a) decrease the effort it takes to promote by a noticeable amount and b) cause noticeably more lower strength players to promote by lowering the amount of luck they need to do so.
Full disclosure: anyone who wants to bother, here's the quick and dirty script I used to calculate various BG trophy situations. I used it in the past to explore different scoring formulas, different track lengths, and I modified it to look at promotion histograms and the effects of tanking players on the statistics. Sorry, quoting python sucks on the forums, so its an image of the source. The code is also a bit ugly, because you have to pay me to make pretty code.
1. 50% win percentage is not the same as tanking. Tanking is 50% wins without promoting. It takes out several permutations that results in the 50% win rate leading to promoting. In your own model, someone winning 50% of the time will promote on an average between 22 and 45 matches (I don't know if that's right, in the linked post you seem to suggest that a person winning 50% of the time would only need 20 matches to get 5 trophies.). I'm not sure your model differentiates between a player with 50% win rate and someone who is tanking.
2. Wins and losses do not happen in isolation - for every win, there is someone at the other end losing and vice versa. Average win rate across the group is always 50%. Your model doesn't factor this in. For e.g. in your table above a player winning at 25% needs 715+ matches to promote - at 25% they win 179 matches and lose 536 matches. Is that a net positive of 357 trophies? Did 71 other players promote due to this? Or going by your table which suggests 9 wins to promote at 75% win rate, did 79 players promote before the 1 player with 25% promoted? The best case seems to be that 72-80 people promote over those 715 matches and not just one player (one every 9-10 matches). When you bring this down to 65-35, that implies 10+1 players promoting every 136 matches or ~58 players promoting every 715 matches (one every ~12 matches). Closer you get to 50-50, the average number of matches played across the whole group only increases. Which is what tanking does.
3. When a high percentage win player promotes out of a group, they transfer their win percentage to the lower percentage players. Because, as explained earlier, win rates at a group level are constant - every match has a winner and a loser. I would guess that your model doesn't account for this either. If there are 3 players in a tier one with 25% win rate and one with 50% win rate, then the 3rd person has to have a 75% win rate. Once the person with 75% win rate promotes in 9 matches, they remaining 2 don't stay at 25% and 50%, it can be 25%-75% or 50%-50% or anything in between. Whatever it is, the 25% player doesn't need 700+ matches to promote anymore (just after 9 matches).
If I were to hazard a guess, the outputs in your second table is same as the output for changing the win percentage from (x% to x*80% + 20%*50%). For example under the 45% column, 41.26 is simply the average number of matches needed to promote for someone with 46% win rate (45%*80% + 20%*50%). You can take the tanking % up to 90% or 95% and everyone will concentrate around the 50% win rate mark.
I used simple models as simple models allow you to articulate all possible outcomes. If your theory doesn't hold up in a simple model, you should at least consider that there may be a flaw. You have posted multiple times that you base your progression on waves of competitive intensity. And you conveniently ignore all of that in the model above.
I'm happy to continue this discussion, if you are actually interested in exploring what is an engaging problem. If you are only interested twisting things around to fit into what you've already decided to be the right answer, let's agree to disagree. I only took this up because you asked someone to take the other side of the debate, I don't mind being proven wrong but not on that back of biased analysis.
It's just a drag now of facing much bigger accounts without also facing small ones. Here come the 7r3's in a couple months while many still don't have one 7r2.
As I've said before, I am fine facing the latgest accounts as long as I get to face the smaller ones too. But here we are. I only want to autoplay 3 matches every 2 days, because the MM is BS.
These kinds of stochastic analyses aren't super difficult to follow in general, with proper explanation. But with a hostile audience, it would take way too much time to explain the foundations of precisely why these sorts of representative analysis is done, and what the point of it is. To know precisely how valid model reduction is done is one of those things I routinely take for granted, but having thought through the steps required, is almost certainly beyond the scope of even my forum posts.
When someone promotes out of a tier, that does change the dynamics of the tier, however, in the specific case of a player capable of tanking in the tier, if they choose to start winning and promote the time they spend doing so is tiny compared to all the time before they entered the tier and the time spent tanking. It is a statistically insignificant period between the two, which is why for purposes of estimation it is reasonable to look at the statistics with them not there compared to with them there. However at this point proving that is left as an exercise for the reader, because the proof would be long, require significant foundation, and almost certainly not change a thing. This sort of thing is a fun time at the office, but it should probably be reserved for academic discussion, not advocacy.
1. The most beneficial set-up is everyone at a 50% win rate (ideally almost everyone tanking, but you don't seem to differentiate between the two). The gains for people with win-rates below 50% is more than the losses for the people with win-rates above 50%.
2. We also know that everyone at 50% win rate is the most stable a tier can be, this is the point where progression out of that tier is at its slowest.
1 & 2 are exact opposite conclusions, it seems difficult that they can co-exist.
I'll point out a single oddity in your previous analysis. Let me know if I'm reading it wrong. With no tanking. 99% of all players with 65% win-rates will promote out by 50 matches. 28.5% of players with 35% win-rate promoted out of the tier in those same matches (all those matches were played against someone right?).
But in the period between 50 to 100 matches, only 23% of those players (51.5% - 28.5%) promote? Once the almost all the players with 65% win rates have promoted, the win rates for the players with 35% win-rates has to go up. Despite this over an equivalent period, fewer of those players will promote? Even if we consider the proportion of remaining players (23% of 71.5% remaining players = 32% of players), there is only a 3.5% improvement in the proportion of those players promoting. This does not match up with your first table that changing win-rate from 35% to 45% will reduce the number of matches required to promote by over 60%.
More importantly, your model suggests that more players will promote out of a tier when they are losing 2 games while winning one on an average as compared to when they are losing 1 and winning 1 on an average.
Your base assumption is that a win rate for a player is constant. Which is why you believe tanking is beneficial because it gives lower strength players more wins that they could otherwise get. But in reality, lower strength players benefit a lot more when higher strength players completely exit the tier vs. farming wins there.
However, it doesn't represent the group outcomes of a PVP game mode. Because if I'm winning at 65%, someone else is losing at the same rate - it could be one person or a group of 100 people, for the set of matches I played in, they cannot win at any other rate.
If you have 3 players with 75%, 65% and 55% win rates, then the fourth player automatically has a 5% win rate, if there are only 4 players in the tier. If there are 6 you could have 45%, 35% and 25%. I will happily take the bet that in this group of 6 players, the player with 35% win-rate will promote much sooner than 139 matches on average.
Once the 75% winning player goes out, the odds become 70%/60%/50%/40%/30. A few games later this turns into 65%/55%/45%/35%, then 60%/50%/40% and then 55%/45%. From there it's 20-25 matches to promotion. Even if everyone resets to zero when someone promotes (you cannot go below zero), which they don't, that's somewhere around 70 matches for the person with 35% win rate to promote out of the tier. That's a 50% lesser than the 139 you are forecasting.
Your model doesn't work at n=2, n=4 or at n=6. It really only works at n=infinity. We have ~200K players in BGs across 18 tiers and GC.
Your model would be the right model to use, if BG was players playing against randomly generated decks of varying strength. In this case difficulty of a tier is constant, for a period of a season you can assume that the strength of the player is also constant. So their win rates are constant. In that case, players with 65% win rates are all out of the tier having player less than 50 matches while only 51% players with 35% win-rate have promoted while playing 100 matches on average as they can keep playing against the AI generated decks instead of the weaker active player base in their tier. The infinite supply of decks available to keep the competition level in a tier constant.