This is just too perfect.
I didn't see your analysis. I joined this thread very late.Oh boy. This is going to take a while.
First of all, I'd like to ask you something... Did you actually read my earlier post, in which I crunched all the numbers to show what would actually happen if both teams had equal proportions of skilled and unskilled players? I went to a lot of trouble to do that. If you're going to challenge my conclusion, the least you could do is actually look at my method and point out where it has a relevant flaw.
Second, in your own example, you have chosen a very poor way to illustrate the two teams. If you are going to represent Pirates as a slice of the pie, with the outside (the "crust," if you will) being the good players, then in your full pie that represents Ninjas, you should also let the "crust" of that full pie represent the good players. That would make it far easier to see what happens when you spin the Pirate slice around the pie. (Spoiler alert: It would be perfectly even matchups all around, dooming your theory.) But instead, you chose to represent the skilled Ninja players as another slice of the pie, needlessly complicating matters. And from that mistake springs another flaw...
You have not shown that the slice of good Ninja players is the same proportion of the whole pie as the "crust" of good Pirate players is of the entire slice that represents Pirate players. For all I know just looking at your drawing, you could have underestimated the size of the slice that you needed to properly represent Team Ninja, making it so that Team Pirate actually has a greater proportion of skilled players.
But actually, it's even worse than that, because, without going to the trouble of employing Calculus techniques to precisely calculate everything, I can't even be certain that you didn't overestimate the size of the slice for skilled Ninja players. The problem is that you have grossly oversimplified your analysis, with this summary of "Pirates win" and "Ninjas can win." What actually happens is that, as you spin the full Pirate slice into the slice of skilled Ninja Players, the win rate varies according to how much overlap there is. Depending on the overlap, the win rate for Ninjas could be 40%, 80%, 50.5%, 50.00003%... There are an infinite number of distinct possibilities. You would need to rely on Calculus to accurately assess the results, not this simplistic and vague "Pirates win" and "Ninjas can win."
But, of course, you wouldn't have needed to use Calculus in the first place if you had just chosen a better drawing--one that was easier to analyze correctly... Really, I think that if you had actually read and understood my analysis, you wouldn't have reached such an erroneous conclusion in the first place.
Bottom line: Pirates won more because they had a greater proportion of skilled players, not because of some quirk of the matchmaking process.
Yeah, if there was an uneven proportion of skill between the two teams, that'd be a concern. However, it'd be possible for an unskilled player to drop out and be replaced by a skilled player. When they drop out, chances are likely they'll re-emerge elsewhere.There is also the danger that a skilled Ninja team trying to stick together would suffer from dilution as members drop out and are replaced by lesser players, and given the sheer size of the teampool, the risk of getting unskilled replacements is dramatically higher.
Then please go back and read it. Or, for that matter, check out Zombie Aladdin's dice example here:I didn't see your analysis. I joined this thread very late.
Why would they not overlap properly if you put the skilled Ninjas in a crust instead of a slice? The total population of Ninjas is represented by the entire pie; no matter where you put the Pirates slice, it will fully overlap the Ninja population in some way. I just want you to use the same distribution method for Ninjas as you do for Pirates so that the skill distribution in that overlap will be the same for each team. Just try it and see what happens.The reason the Pirate's had a crust for good players, and the ninjas a slice, is so that when you spin it like a roulette wheel, they overlap properly, i.e. in the two directions. If for example, I didn't make it a crust, but a slice of the slice (like to the left or right), then all of the slice all the time wouldn't represent the whole Pirate team.
The reason Ninja's don't get a crust, is so that the Pirates and Ninjas can overlap in a cross-section. That's the only way using the pie method to allow for everything to be equal. So having the Ninja be a pie slice doesn't complicate things. I think you're over-complicating the simplicity of it.
What you're forgetting is that said matchups will not necessarily favor one team to the same degree. (Again, this problem is caused by your choice to represent skilled Ninjas as a slice instead of just using a "crust" for both Pirates and Ninjas.) If you place your Pirate slice completely on the unskilled Ninja area, the win rate for Pirates might be 55% (because there's only the small "crust" of skilled players giving them an advantage). However, if you instead place the Pirate slice so that it completely overlaps the skilled Ninja slice, Ninjas could enjoy a win rate of as much as 95%. (These numbers are based on an assumption of 10% skilled players.) Thus, even though it's more likely that the slice will end up somewhere that gives Pirates an advantage, the much higher degree to which Ninjas can be favored balances it out.You are right when you say,
"What actually happens is that, as you spin the full Pirate slice into the slice of skilled Ninja Players, the win rate varies according to how much overlap there is. Depending on the overlap, the win rate for Ninjas could be 40%, 80%, 50.5%, 50.00003%... There are an infinite number of distinct possibilities."
And that is exactly what the diagram shows. When the game makes a matchup, it's like spinning the wheel, and where it lands determines what match occurs. It's simply showing that it's more likely for the pirate slice to land on the unskilled Ninja sector, than the skilled ninja sector.
You don't need calculus because we're not using exact figures. The diagram is innacurate because it's crudely drawn, but it perfectly portrays what happens, imo.
I.e. there is a chance that the matchup will be completely in favor of pirates, and there's another chance that the patchup will be completely in favour of ninjas. What's confusing about it?
That's not actually true as long as the proportions of skilled and unskilled players are the same as they are on the opposing team. Yes, a larger pool of players means that there are more unskilled players that you could get paired up with, but it also means that there are more skilled players that could become your teammates. Thus, it all balances out in the end.There is also the danger that a skilled Ninja team trying to stick together would suffer from dilution as members drop out and are replaced by lesser players, and given the sheer size of the teampool, the risk of getting unskilled replacements is dramatically higher.
Then please go back and read it. Or, for that matter, check out Zombie Aladdin's dice example here:
http://squidboards.com/threads/next-us-splatfest-pirates-vs-ninjas.10254/page-7#post-114216
If each team has equal proportions of skilled and unskilled players, then their win rates will be equal as well, regardless of popularity differences. That's all there is to it.
Why would they not overlap properly if you put the skilled Ninjas in a crust instead of a slice? The total population of Ninjas is represented by the entire pie; no matter where you put the Pirates slice, it will fully overlap the Ninja population in some way. I just want you to use the same distribution method for Ninjas as you do for Pirates so that the skill distribution in that overlap will be the same for each team. Just try it and see what happens.
What you're forgetting is that said matchups will not necessarily favor one team to the same degree. (Again, this problem is caused by your choice to represent skilled Ninjas as a slice instead of just using a "crust" for both Pirates and Ninjas.) If you place your Pirate slice completely on the unskilled Ninja area, the win rate for Pirates might be 55% (because there's only the small "crust" of skilled players giving them an advantage). However, if you instead place the Pirate slice so that it completely overlaps the skilled Ninja slice, Ninjas could enjoy a win rate of as much as 95%. (These numbers are based on an assumption of 10% skilled players.) Thus, even though it's more likely that the slice will end up somewhere that gives Pirates an advantage, the much higher degree to which Ninjas can be favored balances it out.
Proving the end result of all this mathematically would indeed involve Calculus because it's based on a thing called "continuous probability." Feel free to look that up in your own time; I'm not going to attempt to teach it.
No, you're using the crust for Pirates and a slice for Ninjas because your point wouldn't work in any other type of diagram.Look, the reason why the Pirates get a crust and the Ninjas get a slice is because it's necessary for the pie diagram. Believe me when I say that if you do it any other way, using the pie-sector method doesn't accurately represent ALL the possible matchups.
Notice that I never once said "skilled players" or "unskilled players" when describing the numbers on the dice. Where an unskilled player ends and a skilled player begins is completely subjective; it's a continuum, not a set of categories. You can set whatever number you like as the minimum to represent good players, but even then, an unskilled team will still likely beat an even less skilled team, and a great team will still likely lose to an even greater team.Okay so I read Zombie Alladin's post, and you're right with your diagram (or analogy). But the reason why I think it's not right is because un-skilled players far outnumber skilled players.
My point, if I can say it in a way that makes is that, all of Pirate's skilled players always have a game. Every throw of the green dice, whether you get a 1 or a 6, will match a purple ninja dice from 1-6. But sometimes the Purple 6's get mirror matches.
So you don't even have to roll the green dice, just have all the dice numbers represented, and roll the purple ones. The pirates don't have the chance, per se. because all the pirates are always in play. A number of high purple rolls will be in mirror matches. All high green rolls are in play.[/spoiler]
This diagram does not accurately analogize to the Splatfest for the reason as the pie chart: You're lumping all of the "skilled" players together like it's some monolithic entity that travel together and play together. In order for that diagram to work, both Team Pirates and Team Ninjas should have even stripes of "skilled" and "unskilled" at equal intervals down the bars.
Okay, this diagram best represents my thoughts, on why the least popular team wins (I was on team Pirate btw). The dice analogy doesn't work because it's infinite, and in that analogy, you can have everyone as skill 6 at the same time, which doesn't represent reality.
The bright green and purple represent the skilled pirates and ninjas respectively. I also scaled the picture so that the proportions are the same.
If you have any problems with my theory, please refer to this gif. I don't like to make people read walls of text.
Nope, I was on Team Ninja. Just because you're too salty to admit the truth doesn't mean that I am. The math proves that the popularity difference is not what put Team Ninja at a disadvantage; Pirates won because they had a greater proportion of skilled players. It's as simple as that.Wow, a bunch of dummies on Team Pirate can't do math and keep saying "Oh, it's because our team was full of awesome players, such as myself"
I seriously fought my own team 90% of the matches and I made it to King. The other Team Ninja teams were amazing and completely going to waste.
What a bunch of goobers, if I had been on the winning team and the other side was complaining about endless mirror matches I wouldn't be posting "My Team just had better players."
I assume all the Pirates saying this were also on Team Car and just think they are teh uberness.
You bet I have a problem with your diagram, and it's still the same problem I've been trying to explain to you this whole time. You've oversimplified the results into "Pirates win," "Tie," and "Ninjas win," as if they all have equal weight, but they don't. Whenever your diagram says "Pirates win," Pirates are only winning slightly more matches than they are losing, whereas when your diagram says "Ninjas win," at certain points, Ninjas are winning slightly more than they're losing, but at other times, they're winning an overwhelming majority of their matches. That's why the wins balance out; in your diagram, Pirates can have a smaller advantage for a longer period of time, but Ninjas can have a much bigger advantage for a shorter period of time.If you have any problems with my theory, please refer to this gif. I don't like to make people read walls of text.
The odds do not represent just one match; they represent many thousands of matches. And over the course of those thousands of matches, Pirates are not going to win every one of those matches in which they have a 55-45 advantage; in fact, they're going to lose almost half of them. In contrast, over the course of thousands of matches, Ninjas are going to lose very few of those matches in which they have a 95-5 advantage. Thus, the total wins will indeed balance out over the course of thousands of matches.BUT, (and you're right about the degrees), it actually doesn't matter. Again think, about the wheel being spun once for every match. the Ninjas win that match with 95% or 55%, it's still just one win, and the pirates have much more games with >50% to win, than with <50%.
Hey, if I'm wrong I'm wrong. Doesn't mean I can't develop the wrong side until it's proven wrong.Nope, I was on Team Ninja. Just because you're too salty to admit the truth doesn't mean that I am. The math proves that the popularity difference is not what put Team Ninja at a disadvantage; Pirates won because they had a greater proportion of skilled players. It's as simple as that.
Just to clarify, that remark about saltiness was directed at Geprodis, not you. I know you said you were on Team Pirate.Hey, if I'm wrong I'm wrong. Doesn't mean I can't develop the wrong side until it's proven wrong.
It's alright, just try to avoid it next time.(Sorry for the double post; I only just noticed this comment, and I didn't want to bury my reply to it in my longer post.)
Okay, but whatever.Just to clarify, that remark about saltiness was directed at Geprodis, not you. I know you said you were on Team Pirate.