Mathematically Calculated Tier List. SECOND RESULTS IN! First post updated.

[Zankoku]

We can't do that unless someone has data on how well each character does on each stage.

 

[Gimpyfish62]

now perhaps you see why i dont like this idea, its horendously inacurate

 

[Overswarm]

If you thinik of this as an "iron man" tier list, it works out.

How well a certain character would do, on average, if he had to play a random character.

Or, how well a certain character would do if they had to play EVERY character.


Other than that, it's mostly waste. If it accounted for the # of characters out there (so that Falco was weighted more than Kirby) it would be alright.

 

[Mogwai]

I'm tired of these posts.

This would be good if it took into acount weighting higher tier characters more than lower tier characters

Please read the process and understand that this process DOES weigh higher tiered characters more heavily. Higher tiered characters increase in popularity as their power increases and as their popularity increases, the power formula weights them more, it works out.

 

[Pat/Pro]

How could shiek be #1 if he has 3 counters while say falco only has 1.

 

[pockyD]

How could shiek be #1 if he has 3 counters while say falco only has 1.

why even make a post like this if you're not going to make an attempt to understand the math?

I really think the people that don't want to think about the details of the procedure can just ignore this and don't worry about the results either

 

[Gimpyfish62]

the problem with this isn't just that its kind of a silly idea, but also that phanna's list is also innacurate, so innacurate silly math concepts plus innacurate variables makes for innacurate lists

 

[Mogwai]

the problem with this isn't just that its kind of a silly idea, but also that phanna's list is also innacurate, so innacurate silly math concepts plus innacurate variables makes for innacurate lists

Gee, thanks, and there's absolutely no one upset with the current tier list. . .

Some people want the tier list to reflect matchups and viability and be based on something tangible, rather than people coming out of the br saying, we looked at tournies and this is what the tier list is. So whatever, I'm giving them something. I'm not saying it's more accurate or better. And I am saying that the only way in which this is correct is if Phanna chart is correct. So if you don't like the Phanna chart, then you can obviously assume the results from this project are completely worthless and I encourage you to stick with that opinion and stop posting on my thread about how this is wrong. If you legitimately see something wrong with the math, let me know, but stop telling me that the math is silly and inaccurate when you don't understand what I'm doing.

 

[Gimpyfish62]

the tier list thats in place right now isn't quite correct either, but we are discussing it and making it accurate right now

EDIT: i havne't looked at the math because on a conceptual level i dont agree with it, i bet your equations are sound but they are based on false inaccurate variables such as "how many of X char exist" and phanna's matchup chart.

look at where ness is on your list, i cried becaues of that. lol
i bet the ness players like this system

 

[Overswarm]

I'm tired of these posts.



Please read the process and understand that this process DOES weigh higher tiered characters more heavily. Higher tiered characters increase in popularity as their power increases and as their popularity increases, the power formula weights them more, it works out.

I'm unsure as to whether or not you were addressing me, but...

I was referring to the number of Falco players compared to the number of Kirby players.

There are more of them, so if Sheik does amazing against Kirby but sucks hardcore against Falco, she wouldn't get as much of a bonus as someone who did amazing against Falco but sucked against Kirby.

 

[moogle]

Gimpyfish, in response to your posts, I'll quote something I posted earlier:

The only problem in all this is that the match up chart (in which you based all of this off of) is completely inaccurate. Therefore, many (if not all) of your results will be inaccurate.

Yeah, this is true. >_< (Though the chart isn't as bad as you make it seem.)

I guess what we're doing is boiling down Phanna's chart into a tier list... with as much mathematical soundness as possible. Any discrepancies between our list and the tier list would be caused by one of three things: inaccuracies in our math, inaccuracies in Phanna's list, and inaccuracies in the official list.

Once we're satisfied with our math, then we can directly compare our results with the official tier list. Then some nice healthy arguments could ensue, like why is Phanna's list so mean to Bowser.. or so nice to Ness? Could it be a problem with the official tier list?

Overswarm and others: Wesley is well aware of the problem of the proportions of high tiers vs low tiers. I proposed a better way to model these proportions, and Wesley has shown his approval. Hopefully it will be used in his next update.

 

[Mogwai]

I'm unsure as to whether or not you were addressing me, but...

I was referring to the number of Falco players compared to the number of Kirby players.

There are more of them, so if Sheik does amazing against Kirby but sucks hardcore against Falco, she wouldn't get as much of a bonus as someone who did amazing against Falco but sucked against Kirby.

Seriously, all you needed to do was read my post to know that the matchups get weighted. Is that too much to ask?

As to whether I'm addressing you, yes, among other people who have said the exact same thing. So I decided to simplify it and put it into as plain words as I felt did the process justice. But, since that still didn't make it clear enough:

HIGHER TIER MATCHUPS GET WEIGHTED MORE THAN LOWER TIER ONES

The fact that this doesn't happen in the first iteration doesn't mean that it doesn't happen. Once one calculation gets done, more people start playing high tiered characters. Once that happens, high tiered matchups get weighted heavier. It's not that complicated.

the tier list thats in place right now isn't quite correct either, but we are discussing it and making it accurate right now

EDIT: i havne't looked at the math because on a conceptual level i dont agree with it, i bet your equations are sound but they are based on false inaccurate variables such as "how many of X char exist" and phanna's matchup chart.

look at where ness is on your list, i cried becaues of that. lol
i bet the ness players like this system

Dude, I would've cried because of it too if I thought Ness's matchups were anywhere near what they are on the Phanna chart. There are some inaccuracies on the Phanna chart and no character is more blatantly overrated on it than Ness, so naturally, with these numbers, he gets way overrated by the current system. However, this is not a flaw in the math, rather, it is a flaw in the Phanna chart. I'm willing to live with these flaws until I feel like the math is correct and then I will direct my attention to how the chart should be altered to best reflect accurate matchups.

Since you haven't looked at the math, I don't understand how you disagree with it. Also, how many of X char exist, is not a variable that we estimate. It's something that developes over further iterations of the system, but I don't know why I'm trying to explain it to you since you obviously don't care about the process. So, whatever, if you hate everything about this, just stop posting on the thread so that it won't get bumped and hopefully everyone will stop paying attention so that your dream of this project dying can finally come true.

EDIT:

Overswarm and others: Wesley is well aware of the problem of the proportions of high tiers vs low tiers. I proposed a better way to model these proportions, and Wesley has shown his approval. Hopefully it will be used in his next update.

It will most certainly be used in the next iteration. As you have put it, it's a fix addressing the proportions, not the way matchups are weighted. Matchups are and will continue to be weighted by my power formula in the first post, which addresses weighing matchups in the most logical way possible: directly proportional to the ratio of players playing each character.

 

[ArticulacyFTW]

Since you haven't looked at the math, I don't understand how you disagree with it. Also, how many of X char exist, is not a variable that we estimate. It's something that developes over further iterations of the system, but I don't know why I'm trying to explain it to you since you obviously don't care about the process. So, whatever, if you hate everything about this, just stop posting on the thread so that it won't get bumped and hopefully everyone will stop paying attention so that your dream of this project dying can finally come true.

Quoted for truth. Gimpyfish, this project is entirely accurate, once we work out a kink or two, with the exception of the Phanna chart, which Wesley has acknowledged on SEVERAL occasions. Wesley has also asked for input on how to improve the chart.

What is your beef with this beyond the innaccurate Phanna chart? If you have none, please, contribute something positive--like tell us how to fix the chart. If you do have a problem, but you have no idea how to articulate it besides calling this silly and/or bad, then please, stop posting in the thread.

If, however, you have legitimate criticism, let us know so that we can improve what we (mostly Wesley) are doing.

 

[Gimpyfish62]

step one should be making sure matchups make sense, and since that list doesn't exist and never will the entire concept is flawed, thats why i haven't looked at the math, conceptually i disagree so why would i agree with the forumula?

the formula probably makes sense, if we have accurate numbers, which we never ever will.

EDIT: ps, if you are using the current tire list to decide how many of certain chars there are (which is sort of relevant i suppose it has to be for a mathmatical equation) thats just plain silly. XD

 

[Overswarm]

He's probably looking at the first poll of the week, although that is severely dated as well.



I still haven't found exactly what you're referencing. I'm not talking about high tier vs. low tier, I'm talking about NUMBERS of players.

A mathematically calculated tier list can only be useful if it uses accurate numbers of players per character. As there are more Fox players out there than most others, characters that do well against Fox should be weighted differently so that they appear higher on the tier list.

Currently Sheik, who dominates low tier but gets destroyed by top tier, is on the top of the list, which shows you haven't done weight by numbers.

 

[Virgilijus]

the formula probably makes sense, if we have accurate numbers, which we never ever will.

EDIT: ps, if you are using the current tire list to decide how many of certain chars there are (which is sort of relevant i suppose it has to be for a mathematical equation) thats just plain silly. XD

Yeah, the numbers will never be completely accurate, but they aren't going to vary too much.

I was about to quote a famous Richard Feynman quote, but it may be considered inappropriate so I'll paraphrase: math equations may not always serve a purpose, but they're fun and that's why we do them

 

[pockyD]

Currently Sheik, who dominates low tier but gets destroyed by top tier, is on the top of the list, which shows you haven't done weight by numbers.

stop being ignorant

it means he hasn't weighted enough, but if you stopped arguing stupidly and making 10 posts without realizing the simple truth that was stated in the original post (which is that the proportion of players IS weighted over time) and that has been acknowledged multiple times (that the number of players needs to scale more sharply to power level for each iteration), you could save us all some time and yourself some embarrassmnet

 

[Overswarm]

stop being ignorant

it means he hasn't weighted enough, but if you stopped arguing stupidly and making 10 posts without realizing the simple truth that was stated in the original post (which is that the proportion of players IS weighted over time) and that has been acknowledged multiple times (that the number of players needs to scale more sharply to power level for each iteration), you could save us all some time and yourself some embarrassmnet

He hasn't really posted where he's getting the numbers.... If this is supposed to be mathematical, you'd have to have numbers of players but I haven't really see those.

I like this idea, but I'd like to see where this stuff is coming from. It seems like he's just saying "there are an even number of players" and then just repeating the same calculations over and over again and slightly altering the number of players based on those initial calculations.

If that's the case..... I can save you some time. Falco wins.

 

[pockyD]

I like this idea, but I'd like to see where this stuff is coming from. It seems like he's just saying "there are an even number of players" and then just repeating the same calculations over and over again and slightly altering the number of players based on those initial calculations.

That's exactly what he's doing, and the reason the first results seem "inaccurate" is because (as has been stated COUNTLESS TIMES) the populations aren't changing by enough for each iteration to ultimately produced a properly segregated result

also, this isn't really about determining only the "best" character by this standard; doesn't matter that much who "wins"

 

[Overswarm]

That's exactly what he's doing, and the reason the first results seem "inaccurate" is because (as has been stated COUNTLESS TIMES) the populations aren't changing by enough for each iteration to ultimately produced a properly segregated result

also, this isn't really about determining only the "best" character by this standard; doesn't matter that much who "wins"

Isn't there a way to get legitimate results by using actual (estimated) population of characters?

I'm pretty sure you could get a mod to do a poll that asks "who is your main character" for this, it's a neat idea.

 

[pockyD]

What's more objective than starting at equal numbers though? all that it results in is requiring more iterations, but with the help of a computer, that couldn't take more than a few seconds right?

besides, gimpyfish already explained how this entire thing is worthless so who cares am i rite

 

[Overswarm]

What's more objective than starting at equal numbers though? all that it results in is requiring more iterations, but with the help of a computer, that couldn't take more than a few seconds right?

besides, gimpyfish already explained how this entire thing is worthless so who cares am i rite

It's not entirely worthless. Phanna's chart isn't entirely worthless either. While his chart isn't perfect, the numbers aren't going to be off by more than 3 at the most, which means mostly good results.

It would certainly be more objective to start off at equal numbers and SIMULATE how the smash community would change, but using actual estimated numbers from a large population would be crazy neat.

Can you imagine looking at the current smash population, then looking at a matchup chart, waiting a few seconds, and BAM

If you want to do well in today's smash scene, the characters that are systematically doing the best are...

That would be amazing. It would also be a semi-scientific way of seeing if Phanna's chart is wrong anywhere. We can expect Fox and Falco to be towards the top, but if Ness is say, 6th, we could say "that obviously is not right, Ness is not doing that well".

It'd be pretty cool.

 

[Gimpyfish62]

actually phanna's bowser matchup list is horendous and multiple matchups are off by more than 3 XD

3 to be off is MONSTROUS btw

 

[Mogwai]

It's not entirely worthless. Phanna's chart isn't entirely worthless either. While his chart isn't perfect, the numbers aren't going to be off by more than 3 at the most, which means mostly good results.

It would certainly be more objective to start off at equal numbers and SIMULATE how the smash community would change, but using actual estimated numbers from a large population would be crazy neat.

Can you imagine looking at the current smash population, then looking at a matchup chart, waiting a few seconds, and BAM

If you want to do well in today's smash scene, the characters that are systematically doing the best are...

That would be amazing. It would also be a semi-scientific way of seeing if Phanna's chart is wrong anywhere. We can expect Fox and Falco to be towards the top, but if Ness is say, 6th, we could say "that obviously is not right, Ness is not doing that well".

It'd be pretty cool.

I agree that that rating would be useful, but seriously, instead of writing your next post, read the thread, we've already been over this. . .

actually phanna's bowser matchup list is horendous and multiple matchups are off by more than 3 XD

3 to be off is MONSTROUS btw

Then for the love of god, stop b!tching about how wrong it is and inform us how it is wrong and why it is wrong.

 

[Gimpyfish62]

i already did, i'm not whining i dont really care at all

i've said that its not accurate, and it never will be, mainly because of the inaccuracies of phanna's list

 

[pockyD]

then take it up with phanna's list =\

there's a separate thread for the inaccuracies in the phanna chart so if that's where your issues lie, resolve them there

 

[Zankoku]

Gimpyfish clearly cares enough to tell us exactly why we should stop bothering at all.

Overswarm, I'll put this out as clearly as I can for you.

P = S(M * N)/T
P: Power
S: Sum of all characters
M: Matchup vs. a given character (Taken from Phanna chart)
N: Number of players playing a given character
T: Total number of Players

Notice that in the Power formula, we are indeed taking into account the number of players playing a given character, denoted by the variable N. But how do we get N, you ask? Well,

N = T * (P / S)
N: Number of players playing the character
T: Total number of players
P: Relative power of the character
S: Sum of all character's powers

Since we are, thus far, only interested in the end result of the tier list, and not much in the beginning, N for each character starts at an equal number, say 100000. As a character's Power increases or decreases, so too does the Number of players for that character change, based on the character's power compared to the world.

Number of players for each character is truly important, and if they weren't, Sheik would be top tier, which is why Wesley has been looking into making the weight of power on a character's popularity greater. My own experiments brought me to this result:
http://smashboards.com/showpost.php?p=2256043&postcount=53
where Falco is #1. Bowser is dead last because, as Gimpyfish noted, the phanna chart has its greater share of inaccuracies in many matchups for certain characters.

 

[Gimpyfish62]

i'm not like bashing anyone here and i havne't really been posting anything new, when somebody posts directly at me i feel like i should at least respond lol

 

[DippnDots]

Um, Ganon has a power level of over... NINE THOUSAND!!!!!!!!!!!!!!!


@TJK
Liked it about five years ago, I just saw power level and couldn't resist

 

[TJK1997]

Ahh Dots DBZ you like.

 

[shogun]

Number of players wouldn't pose any accuracy to how "powerful" a character is.

 

[Zankoku]

Number of players wouldn't pose any accuracy to how "powerful" a character is.

They determine how relevant a character matchup is in the environment.

 

[Shai Hulud]

I assume by "sum of all characters" you mean [ Sigma from i = 1 to 26 (Mi x N) ] / T

It would be simpler to use a fractional value for character populations F = N / T just to have fewer variables.

N = T * (P / S)
N: Number of players playing the character
T: Total number of players
P: Relative power of the character
S: Sum of all character's powers

This formula is flawed, as it will only stratify the power levels without changing their rankings, if I'm not mistaken. The number of players using Sheik, for instance, will increase with each iteration until all players use Sheik.

It's possible I'm missing something. I haven't examined this too closely at this point.

Edit: I've written a program for calculating the list but it's taking ages to download the JDK on this computer...

Also, I'm not sure the matchup values from Phanna's chart are really that relevant. What I mean is that working under the assumption of equal skill and the accuracy of the chart, an 8 - 2 advantage doesn't mean 80% victory. It's more like 100% victory since matches are played best 2/3 or 3/5 requiring a 67% advantage or 60% advantage for 100% victory, at least for the purposes of this calculation. So we should probably change all 7s and higher to 10s and all 3s and lower to 0s. This should remove Sheik from the #1 position because she's currently there because of the overwhelming advantage over low tiers, whereas other top tiers merely have a great advantage. But whether the advantage is great or overwhelming, the top tiers will win. making the difference irrelevant.

Actually it shouldn't be difficult to convert the Phanna values into actual win %s for best 2/3. And...browsing the rest of the thread I see this has already been done. Articulacy's numbers look incorrect but here are Wesley's:

0 - 0%
1 - 2.8%
2 - 10.4%
3 - 21.6%
4 - 35.2%
5 - 50%
6 - 64.8%
7 - 78.4%
8 - 89.6%
9 - 97.2%
10 - 100%

These should be much more meaningful than the Phanna matchup values.

Now we just need accurate Phanna values and we should be able to get an accurate matchup-based tier list.

Of course, there's also the issue of counterpicking...not just characters but stages. It would be possible to write a program to consider all this, but first we'd need accurate charts for every matchup on every stage, as well as estimates of counterpick likelihood. Like CF is much more likely to be counterpicked by Sheik than Peach to be counterpicked by YL, though the matchups are the same.

 

[Shai Hulud]

Okay I wrote my program using the above scaled Phanna values and here are the results after 25 iterations:

1) Sheik 203.58773555502478
2) Falco 194.0665940545958
3) Marth 190.37297628719756
4) Fox 188.97153215039734
5) Peach 173.49775308489373
6) ICs 173.35112265483647
7) Samus 168.97996702277462
8) C. Falcon 162.41799640639266
9) Ganon 160.08832115380915
10) J. Puff 153.17667919212747
11) Doc 145.36184148794504
12) Mario 137.80435442272594
13) Ness 122.78752737721302
14) Luigi 118.38606519675307
15) Y. Link 117.29993317101878
16) Pikachu 115.89268137569779
17) Link 112.69209888139062
18) Zelda 100.6001673920934
19) DK 98.83073899540551
20) Yoshi 98.53631611776235
21) Mr. G&W 95.97314481981954
22) Roy 94.81646330752403
23) Kirby 72.46756650344965
24) Mewtwo 69.10740399253369
25) Pichu 59.39899397892415
26) Bowser 54.0023392402158

Obviously there are some problems with the matchup chart. For one, I think it underestimates the extent to which spacies beat low tiers, and it underestimates their advantage over Sheik. And I don't know what the heck is going on with Ness. I don't know much about the low tier matchups but I would probably change some of the space animal values, like

Fox vs. Marth - 5
Falco vs. Marth - 6
Fox vs. Sheik - 7
Falco vs. Sheik - 7

I'll tweak the chart a little and see if I get some more sensible results.

These results are almost the same as Wesley's--I think the difference stems from my use of the adjusted Phanna values.

Also I think I could tweak the formulae a bit to give more weight to positive matchups against high-power characters. My current program already does that, just maybe not enough.

 

[Problem2]

Top Tier
1) Sheik 203.58773555502478
2) Falco 194.0665940545958
3) Marth 190.37297628719756
4) Fox 188.97153215039734
5) Peach 173.49775308489373
6) ICs 173.35112265483647

High Tier
7) Samus 168.97996702277462
8) C. Falcon 162.41799640639266
9) Ganon 160.08832115380915
10) J. Puff 153.17667919212747
11) Doc 145.36184148794504

Mid Tier
12) Mario 137.80435442272594
13) Ness 122.78752737721302
14) Luigi 118.38606519675307
15) Y. Link 117.29993317101878
16) Pikachu 115.89268137569779

Low Tier
17) Link 112.69209888139062
18) Zelda 100.6001673920934
19) DK 98.83073899540551
20) Yoshi 98.53631611776235
21) Mr. G&W 95.97314481981954
22) Roy 94.81646330752403

Bottom Tier
23) Kirby 72.46756650344965
24) Mewtwo 69.10740399253369
25) Pichu 59.39899397892415
26) Bowser 54.0023392402158

There. I made it easier to read and separated it into tiers based on 30 point increments. This tier list looks more accurate in the Top and high tiers, but in the lower tiers, it seems off. Roy is nearly Bottom Tier, and Ness is in mid tier. That can't be right.

 

[Omega Ownage]

ur totally wrong like bowser is not a bad character whats so ever...so what if hes not popular he sure is hell strong. HE DEFINITLY BEAT YOSHI AND G&W. You cant seriously make this own your own.....its very very cheap make sure and ask ppl b4 u post this garbage >: o

 

[Gimpyfish62]

ur totally wrong like bowser is not a bad character whats so ever...so what if hes not popular he sure is hell strong. HE DEFINITLY BEAT YOSHI AND G&W. You cant seriously make this own your own.....its very very cheap make sure and ask ppl b4 u post this garbage >: o

bowser is DEFINITELY a "bad character" but hes not even close to the worst XD

he should be above ness, game and watch, and just below yoshi

yoshi with jump out of shield is high tier afterall

 

[Sensai]

^^^

It's math and the man still argues.

JUST KIDDING! <3<3

And I like this idea. I'll be keeping my eye on this....

 

[Gimpyfish62]

i'm just posting regarding the person that said bowser ISNT bad LOL

 

[tshahi10]

IMAO
it should be

P = S(M * (N/G))/T

P: Power
S: Sum of all characters
M: Ratio of a character's Matchup vs. all the characters combined (Taken from Phanna chart)
N: Number of players winning with a given character
L: Number of players losing with a given character
T: Total number of ssbm Players who are included of playing that character

feel free to say something, dont be harsh