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

[Cyphus]

i think some of these vs.-rankings need to be reconsidered...
was this done by a ness player?...cuz those ness scores are rediculous...
7 on link...8 on roy? etc, etc, lol.

outside that..i guess i just find it very wierd apparently Samus does better against fox than sheik

a few other minor questionable stuff...but i guess overall its mostly reasonable.

 

[Zankoku]

yoshi with jump out of shield is high tier afterall

Yeah, Yoshi's jump out of shield is savage tech.

 

[Mogwai]

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

Um, what the hell. how do you figure that ratio is relevant? I mean, I understand how you constructed 'M', it's the ratio of the matchup vs. average matchup against that character, but that doesn't make any sense, it always weights the M to be higher for characters with a better sum of all matchups on the chart, right?

. . . and then N and L/G (I'm assuming they're supposed to be the same thing) where are they coming from? isn't the Matchup supposed to be handling how they should be winning and losing? I honestly have no idea where those numbers could possibly come from.

Seriously, you need to explain some of these decisions better, they don't make sense to me.

 

[Shai Hulud]

Um, what the hell. how do you figure that ratio is relevant? I mean, I understand how you constructed 'M', it's the ratio of the matchup vs. average matchup against that character, but that doesn't make any sense, it always weights the M to be higher for characters with a better sum of all matchups on the chart, right?

. . . and then N and L/G (I'm assuming they're supposed to be the same thing) where are they coming from? isn't the Matchup supposed to be handling how they should be winning and losing? I honestly have no idea where those numbers could possibly come from.

Seriously, you need to explain some of these decisions better, they don't make sense to me.

There's nothing wrong with the power formula. The problem is with the formula for the number of players using each character. Even after 1000 iterations there's only 7.19% using Sheik and 1.4% using Bowser.

In reality I'm not sure there's an accurate way to predict how players should switch their characters based on their power. I mean if everyone wanted to maximize his chances of winning, he would just go to the character with the highest power ranking on the first iteration (Sheik).

I'm going to try an arbitrary player redistribution like this:
1) 17%
2) 15%
3) 12%
4) 8%
5) 6%
6) 5%
7) 4%
8) 3.5%
9) 3%
10) 2.5%
11) 2.5%
12) 2.5%
13) 2%
14) 2%
15) 2%
16) 2%
17) 1.5%
18) 1.5%
19) 1.5%
20) 1.5%
21) 1%
22) 1%
23) 1%
24) 1%
25) .5%
26) .5%

These values are totally arbitrary. I just picked some that seemed sensible and that added to 100%.

 

[Virgilijus]

Using these new percents, my list has changed:

Character
Falco 0.94____1.463054187
Sheik 0.795____1.378121284
Fox 0.675____1.312138728
Marth 0.665____1.306805075
IC 0.335____1.143622722
Peach 0.285____1.120890774
Samus 0.085____1.034587996
J Puff -0.305____0.885014138
C.Falcon -0.42_____0.84501845
Ganon -0.445____0.836547291
Doc -0.575____0.793721973
Mario -0.94_____0.683501684
Luigi -1.04_____0.655629139
Y. Link -1.4_____0.5625
Link -1.545____0.527883881
DK -1.58_____0.519756839
Ness -1.635____0.507159005
Roy -1.754____0.480604086
Pikachu -1.845____0.46092038
Yoshi -1.91_____0.447178003
Zelda -2.02_____0.424501425
Kirby -2.125____0.403508772
Mr. G&W -2.275____0.374570447
Mewtwo -2.615____0.313197636
Pichu -2.725____0.294498382
Bowser -3.325_____0.201201201

The second column is simply a point on a scale from -5 to 5 telling, on average, the odds chance (in a completely skill and mindgame equal tournament) the character will move forward with the higher the number the greater the probability.

The third column is simply a ratio of the probability they will have an advantageous matchup (their number minus negative five) over the probability of a non advantageous mathcup (5 minus their number). 2 is the maximum while 0 is the minimum; it's a nice scale.

All results formulas were the same as my other post, only with a change in the new percents.

 

[Shai Hulud]

I made some improvements to my program, but I haven't tampered with the matchup chart itself yet. Using my arbitrary percentages from above, I got what seemed to be some pretty good results, but upon checking with different iterations, the list never stabilizes. The difference in % use is so large that the character population greatly shifts each iteration. In other words, the tier list depended heavily on the previous character population.

I think the only way to get good results is to find the actual % values of each character. After all, real Smashers don't change their character decesions 10,000 times a second.

We need to open a new poll, asking tournament-going smashers who they main. I think we also need a better matchup chart. We could open a thread in each section asking the members there to make matchup values for their character, then attempt to eleminate discrepancies.

Virgiligus--

Which percents did you use? If you used the ones I just suggested then you should check your results for different iterations. I got several lists that looked very different at the top and bottom. The bottom five tended to move around a lot, as well as the top five. Sometimes Fox on top, sometimes Marth, sometimes Sheik, sometimes Falco.

This makes sense actually. I'll show two consecutive iterations to show why:

This one was for 10,000 iterations.

1) Fox : 6.306000000000001
17.0
2) Sheik : 6.0044
15.0
3) Falco : 5.919399999999999
12.0
4) Marth : 5.817000000000001
8.0
5) Peach : 5.425600000000001
6.0
6) J. Puff : 5.362400000000001
5.0
7) ICs : 5.092200000000001
4.0
8) Samus : 4.5360000000000005
3.5000000000000004
9) Ganon : 4.3924
3.0
10) C. Falcon : 4.3706000000000005
2.5
11) Doc : 4.1526000000000005
2.5
12) Mario : 3.6543999999999994
2.5
13) Pikachu : 3.526200000000002
2.0
14) Ness : 3.105000000000001
2.0
15) Link : 2.883800000000001
2.0
16) Luigi : 2.8706
2.0
17) Y. Link : 2.782800000000001
1.5
18) Zelda : 2.6754000000000007
1.5
19) Yoshi : 2.618
1.5
20) DK : 2.458800000000001
1.5
21) Mr. G&W : 2.3823999999999996
1.0
22) Roy : 2.1304
1.0
23) Kirby : 2.1142
1.0
24) Mewtwo : 1.6938000000000002
1.0
25) Pichu : 1.4986000000000002
0.5
26) Bowser : 0.9964000000000002
0.5

And this one was for 10001.

1) Sheik : 6.306000000000001
17.0
2) Falco : 6.0044
15.0
3) Marth : 5.919399999999999
12.0
4) Fox : 5.817000000000001
8.0
5) ICs : 5.425600000000001
6.0
6) Peach : 5.362400000000001
5.0
7) Samus : 5.092200000000001
4.0
8) C. Falcon : 4.5360000000000005
3.5000000000000004
9) Mario : 4.3924
3.0
10) J. Puff : 4.3706000000000005
2.5
11) Ganon : 4.1526000000000005
2.5
12) Doc : 3.6543999999999994
2.5
13) Ness : 3.526200000000002
2.0
14) Y. Link : 3.105000000000001
2.0
15) Pikachu : 2.883800000000001
2.0
16) Roy : 2.8706
2.0
17) Link : 2.782800000000001
1.5
18) Luigi : 2.6754000000000007
1.5
19) Zelda : 2.618
1.5
20) Yoshi : 2.458800000000001
1.5
21) DK : 2.3823999999999996
1.0
22) Mewtwo : 2.1304
1.0
23) Mr. G&W : 2.1142
1.0
24) Bowser : 1.6938000000000002
1.0
25) Pichu : 1.4986000000000002
0.5
26) Kirby : 0.9964000000000002
0.5

Let's just look at the top five. In the first one we have
1) Fox
2) Sheik
3) Falco
4) Marth
5) Peach

In the second we have

1) Sheik
2) Falco
3) Marth
4) Fox
5) ICs

So from the first list, characters that do well against Fox, Sheik, and Falco in particular should move up. I'm not sure why Sheik moved up--probably because the current matchup chart gives her 4 - 6 against spacies which I don't think is that accurate. Falco moved up because he beats Fox and Sheik. Marth moved up because he beats Fox. ICs moved up because they have even matchups against Fox, Falco, and Marth, and positive vs. Sheik. The Peach counter is not that significant since only 6% are playing Peach in that model.

I think what this tells us is that the tier list is pretty fluid and dependent on the current tournament character population rather than on the matchups. So the only way to get meaningful results would be to use the actual current tournament character population.

Actually, I suppose I could average the results over a certain number of iterations. I'll look into that...

 

[phanna]

In my thread I made it clear that it was a living document and since it's based on the opinions of many, it's guaranteed to have people disagree with it, but overall it's approaching a better state. What I'm most excited about for this project is that it might help people verbalize to me what changes need to be made in my chart; for instance I'm seeing a lot of comments about Ness, I wish people would post some solid changes they want to see in my thread. This is especially important because right now ChozenOne and I are going through the last 18 pages of posts over 4 months and will be performing an update (which can be re-factored into these calculations). So if you want to get your 2 cents in before the next update, go post:

smashboards.com/showthread.php?t=92025

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.

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

No you actually haven't. I'm very conscious of the shortcomings of my chart, but a lot of the people in this thread are really just beating on all my hard work and I'm a little bitter for it. For instance, you've made zero useful contributions to my thread, here is every post you've made in it:

this is a horrible chart for us colorblind people LOL

but i do see a lot of dark red on that bowser section xD

awesome, us colorblind people are happy now!

i liked it so much i actually gave rep, i never give rep lol

lol roy is the worst character in the game, heres my "roy is the worst" chart to prove it

NOT worst characters: All characters but roy
Worst character: Roy
Cutest Character: Bowser

your bowser matchups are the matchups that are for a bowser that isn't good, thus making them useless xD

i still love the chart, just the idea of the chart, and it looks pretty too.

lol... roy. XD

the problem with what OneWingSephiroth is saying is that he is taking the small differences in matchups way to far.

if shiek can **** a low tier character 5-0 and fox only ***** that character 5-1, who freaking cares, you are still ****** their faces off. a few points here and there dont matter, the important matchups are the matchups you'll be seeing (for example shiek, fox, falco, marth, peach (not so much peach anymore though)) you are making the bottom tier vs top tier matchups where the character just gets ***** seem like its a big deal when zomg bowser can win a couple vs falco, but still get his face torn off, but vs shiek he wont win any matches.

subtleties ftw.

haha apparently bowser is way way worse than i thought, o wellz

maybe i'll post my thoughts on bowser's matchups at some point. but probably not, its not really important, hes a horrible character that nobody cares about except for me lol

ness is horrible lol

i'll give some bowser matchups sometime too

who cares, ness is horrible lol @ earthbound

false

both characters are terrible wastes of time though, if you wanted to ACTUALLY be good that is

haha somebody forgot float cancel XD

and ithink you forgot the actual jumping animation frames... those numbers aren't right XD

ness isn't fast, and isn't good.

why is there so much ness discussion going on? lol

what makes you think i said anything positively about bowser here? hes a terrible character, ness is also terrible

XD

JFox just owned mood4food hard

step 1: pick up bowser *note it doesn't matter if its an amazing bowser player or a horrible one*
step 2: play a shiek *note: the shiek has to be good, not "great" but definitely good
step 3: continue playing said shiek for roughly 4 hours
step 4: after losing to said shiek for 4 or so hours, weep uncontrollably
step 5: punch shiek player in the face, just because.

there is no hope, there is no prayer, no matter what, you will ALWAYS lose 100% to a good shiek that is trying to win at all.


edit: when people say "pro" they aren't refering to them being signed (generally speaking) and doing such is ridiculous in this kind of context. the best X LOW TIER player in the world would never ever ever get signed unless he had some serious amazing top tier backup goin on.

pro is just refering to those who are best with their character
saying taj isn't pro yet as m2 is absolutely ludicrous and makes me want to punch things. in fact, i might just sit the person next to me in the study hall i'm in right now because thats so dumb. and i dont even know him.

excuse you? wtf who do you think you are, I dont think you've ever made a useful post on any thread, all you do is start crap with people you dont even know. dont even give me that "bowser is a john" BS. i'm so glad i don't live anywhere near you, and that I dont know anyone like you.

you have no reason to post things like that

maybe you're just a dic.k so when you act like a dic.k to people you can john and say "I act that way because I actually AM male reproductive organs".

ok so i'm afew pages back just reading and i wanted to say a few things



you continually show his movelist as being something impressive and his recovery not being the most vulnerable thing i've ever seen, that is simply RIDICULOUS, ness is a horrible horrible character, he is NOT one of the fastest characters, he is NOT competitive, and no amazing ness player will be taking out any ACTUAL good fox in a tourney, so quit pretending that matchup is reasonable. the ability to juggle fox does NOT make you counter fox, if it did than OMG BOWSER counters fox (some people actually believe this)

@ shine/rest comparison
*dies*
wtf ridiculous, tahts the dumbest thing i've ever read, you act like its difficult to land shine lol

@using "virtually" all of his air moves
Bowser (when used properly - yeah, its rare) defintely uses every single move he has available to him in every single matchup, using every move you have doesn't mean you have a good moveset, or mean the character is good, or have any weight on matchups, and wtf is the word virtually doing in there, every character can do "virtually" all of their air moves lol

@removing moves nonsense
wtf are we removing moves for? that has no place in this argument wtf lol
durh remove bowsers up b and he is utterly useless in every matchup
remove peaches dsmash and she is significantly less threatening
remove fox's shine and maybe hes not an uber god
remove ness... from the game, and we dont get ness fanboys ruining potentially useful threads

@back throw strength on mario FD
wtf thats ridiculous, maybe with horrible di in the wrong direction

nobody can beat fox lol

nope, nobody can beat fox.

I only point this out because you all blame me for the shortcomings, saying that you yourself have tried to correct them, when that couldn't be further from the truth - you never posted what any of bowsers specific match-ups should be, or how I should change them.

Summary: We're doing an update of the chart. Stop whining about your opinions, and go post what you want to see happen and why before the next update comes out. Telling someone in this thread or my thread that errors exist doesn't help anyone; try suggesting at least ONE, ANY specific correction that could be made.

 

[Gimpyfish62]

lol?

wtf was that about XD

multiple quotes were me saying "I like this" and clear joke posts like "nobody can beat fox"

you just randomly quoted every single post of mine, settle down lol

i didn't correct anything because i dont care that much, the only person who could make a fairly accurate bowser matchups list other than myself is arash, and the only people that would care would be people who'd already message me anywas, so i dont particularly care about that list, or this list, because they aren't accurate. i dont care enough to correct them, so ggz i guess


EDIT: when was the last time i posted in that thread anyways? lol long ago

quoting every post a person has ftw i guess

 

[phanna]

In case anyone missed the main purpose of my last post: We're updating the chart, go post changes you think should be made.

i didn't correct anything because [...] i dont care enough to correct them

So don't talk down to the efforts of this thread or my efforts then, it's kind of hurtful when I spent so much time trying to make a nice chart :-\

 

[Gimpyfish62]

if i wanted to correct them i would have just made my own chart, i'm not trying to be insulting, nobody could possibly know EVERY matchup in the game accurately enough to make a chart, even with compilation efforts it'd be difficult, i said multiple times i like the concept, but delivery is near impossible, most everything is biased its just to hard

 

[ArticulacyFTW]

I really, really dislike all this bashing of you Gimpyfish, but you don't seem to understand something: if you don't care, we would prefer if you stopped posting.

It seems to me that if you really didn't care you probably wouldn't have posted so many times in both of these threads. So if you do care, and if you're going to complain about how they suck, please, at least do what apparently only you (and one other person) can do to improve it: give "accurate" Bowser match-ups to Phanna.

 

[Gimpyfish62]

i'm only posting in response wtf do peopel not understand that LOL

getting posted at and not responding looks horible

EDIT: if you notice i posted once that this is a good concept, but its flawed, the just responded to people

i haven't been randomly coming in saying THIS IS THE SUCK AND THAT IS THE SUCK GRAAAGGHH I HATE YOU ALL

lighten up everyone geeze lol

 

[LunInSpectra]

LMAO He quoted every single post. That was actually pretty rude. I see phanna differently now.

 

[Banks]

I see phanna the same: not at all because he just super wavedashes away.


BA DUM PSSSSSH </cymbal>

 

[3GOD]

I created my own program as well!

After 31 iterations it stabilizes with the following results (reordering the list based on the results):

My model was similar to the original, but I made the number of players using a character (N) depend VERY heavily on the power of the character in comparison to the others...something like:

N = T ^ (Alpha*P/S)

where T is the total number of people playing (260000 for my experiment - initially 10000 per character), P is the power for the individual character, and S is the sum of all character powers. Alpha is a parameter that I used to control how largely the value of N depends upon P...for my experiment I used 10 for Alpha. I had to scale the results each time to maintain a steady number of 260000 players (you can check and the numbers add up), but it's just a matter of multiplication to achieve this.

One thing that sets apart my code from others I've seen is that mine has a test for a stable solution. I have the program terminate when TOL < 0.0001. What is TOL?

Take a character's current power and subtract his previous power. Take the absolute value of this quantity. Sum these absolute values for all characters and this is the value of TOL. In other words, the program ends when the sum of the changes in power (from one iteration to the next) varies no more than 0.0001.

One great thing about my code is that I can easily change the values of Alpha and the tolerance TOL to see what happens. For instance, if people think that it's unrealistic to have 43000 Falcos to 200 Bowsers - the parameter Alpha can change this ratio.

 

[Shai Hulud]

I created my own program as well!

After 31 iterations it stabilizes with the following results (with the current Tier order):

Character - Power - Number of Players Using Character:
Fox - 5.33094759505265 - 31593
Falco - 5.58011746960059 - 43724
Shiek - 5.52658742525571 - 40775
Marth - 5.32398215418824 - 31307
Peach - 5.08459247924727 - 22912
C. Falcon - 4.25876326551998 - 7804
ICs - 4.79041208209364 - 15611
Samus - 4.80890422803092 - 15992
Doc - 4.13853176241343 - 6671
Jiggs - 4.61253805983503 - 12379
Mario - 3.67667799782824 - 3653
Ganon - 4.28986081179068 - 8127
Link - 3.29072504957195 - 2208
Luigi - 3.75119839884973 - 4026
DK - 3.15799795109290 - 1857
Roy - 2.88979014256341 - 1309
Y. Link - 3.43628166051163 - 2670
Pikachu - 2.81130689035888 - 1182
Yoshi - 2.66228037252594 - 973
Zelda - 2.84844490053860 - 1240
Mr. G&W - 2.34159731859519 - 640
Ness - 2.88932170715420 - 1308
Bowser - 1.39734771824317 - 187
Kirby - 2.70530375142222 - 1029
Pichu - 2.06456241224604 - 446
Mewtwo - 1.93624929010882 - 377

That seems very suspect. What did you use for initial character distribution and how did you determine character choices each iteration? Also, did you use Phanna's values where a 7 means 70% victory or scale them for best 2/3?

Here are my results using the poll of the week percentages--

1) Sheik : 6.663359999999999
5.33
2) Falco : 6.379979999999999
12.120000000000001
3) Marth : 6.250164
14.46
4) Fox : 5.909224000000001
11.469999999999999
5) ICs : 5.4071880000000005
2.75
6) Peach : 5.378652000000001
5.489999999999999
7) Samus : 5.309464
5.489999999999999
8) Ganon : 4.977727999999999
3.39
9) C. Falcon : 4.935956000000001
4.36
10) J. Puff : 4.854316000000001
2.91
11) Doc : 4.344492000000002
4.04
12) Mario : 3.9430959999999997
2.91
13) Luigi : 3.703540000000001
2.58
14) Y. Link : 3.553208
0.97
15) Ness : 3.3752440000000012
2.02
16) Link : 3.310556000000001
6.0600000000000005
17) DK : 3.165064
0.65
18) Roy : 2.912268000000001
2.75
19) Pikachu : 2.901460000000001
1.4500000000000002
20) Zelda : 2.8653440000000012
0.8099999999999999
21) Yoshi : 2.841056000000001
2.5
22) Mr. G&W : 2.253032
0.97
23) Kirby : 2.0393720000000006
1.37
24) Mewtwo : 1.8335800000000002
0.8099999999999999
25) Pichu : 1.5108400000000002
0.8099999999999999
26) Bowser : 1.267292
1.53

This list seems pretty suspect as well. I don't think the percentages are very accurate. I do think the Ice Climbers are about where they should be, though. The matchup chart needs to be updated to include wobbling--probably add 1 for every matchup.

Lol-- I just did that and it made ICs # 1.

 

[Banks]

if fox isn't number one, it's wrong

 

[3GOD]

That seems very suspect. What did you use for initial character distribution and how did you determine character choices each iteration? Also, did you use Phanna's values where a 7 means 70% victory or scale them for best 2/3?

Looks like you caught me before my editing was done . I hope I explained my code enough. As for the Phanna numbers - I just used 0 - 10 in my matrix - I don't think scaling them should make a huge difference, but I can try that later.

One thing I really don't like is seeing Fox as far below Sheik as he is since he pretty much beasts against all high tiers except falco...I'm sure some adjustments can be made and also the new Phanna chart will provide new results.

 

[Shai Hulud]

Looks like you caught me before my editing was done . I hope I explained my code enough. As for the Phanna numbers - I just used 0 - 10 in my matrix - I don't think scaling them should make a huge difference, but I can try that later.

One thing I really don't like is seeing Fox as far below Sheik as he is since he pretty much beasts against all high tiers except falco...I'm sure some adjustments can be made and also the new Phanna chart will provide new results.

I really don't see how you can predict what characters people would use. There are way too many factors besides the matchup, like ease of use, novelty, familiarity, ignorance of the matchups, likelihood to be counterpicked, etc.

We'll get the best results using actual current use percentages. Even if a new tier chart changed what characters people used, it wouldn't happen overnight.

Well I made my own arbitrary formula: F = pow(A, B * P / S) where F is the Fraction using a certain character etc.

I also made a few minor changes on the matchup values...for the best results yet.

1) Falco : 6.20206238701241
14.661475069359991
2) Fox : 6.038579905961688
13.043401552587
3) ICs : 5.495654273564149
8.845610239237073
4) Peach : 5.444383373342781
8.527077109744372
5) Sheik : 5.382927727739016
8.160347061136347
6) Marth : 5.379331457416073
8.13938191909366
7) Samus : 5.075579262005153
6.549814606776291
8) J. Puff : 4.680645090476803
4.937878123317099
9) Ganon : 4.483247029777007
4.28763185690668
10) C. Falcon : 4.27637617099386
3.697871630170653
11) Doc : 3.981728428587147
2.9951443876620822
12) Luigi : 3.565766464260057
2.2243171684768313
13) Mario : 3.423436499654071
2.009005228267471
14) Y. Link : 3.068156976746233
1.5581575831933954
15) Link : 2.8547212307906116
1.3375385201279049
16) Ness : 2.688618514869357
1.187696577879478
17) Pikachu : 2.59033366074129
1.10706401098007
18) DK : 2.586862490334235
1.1043186153319533
19) Roy : 2.454247880415929
1.0043772767077275
20) Zelda : 2.450321120291828
1.001560082481517
21) Yoshi : 2.2077370579318103
0.8420091881553633
22) Mr. G&W : 2.085638792718709
0.7715894501008794
23) Kirby : 1.9495943106710647
0.7000406450643532
24) Mewtwo : 1.491530164285472
0.5044555616964682
25) Pichu : 1.4081203854787219
0.4752380141459441
26) Bowser : 0.8854669617743739
0.32699852139937685

ICs are top-tier

 

[Mogwai]

All, right, I've finally gotten around to tuning my program to using e^P to weigh the powers for redistributing the population. Here are the results:

Falco Players: 17.96% Power Level: 5.80
Sheik Players: 15.68% Power Level: 5.66
Marth Players: 12.63% Power Level: 5.44
Fox Players: 12.16% Power Level: 5.41
Peach Players: 8.87% Power Level: 5.09
Ice Climbers Players: 5.98% Power Level: 4.70
Samus Players: 5.88% Power Level: 4.68
Jigglypuff Players: 4.49% Power Level: 4.41
Ganon Players: 2.97% Power Level: 4.00
C. Falcon Players: 2.60% Power Level: 3.86
Doc Players: 2.25% Power Level: 3.72
Luigi Players: 1.57% Power Level: 3.36
Mario Players: 1.20% Power Level: 3.09
Y. Link Players: 0.95% Power Level: 2.86
Link Players: 0.76% Power Level: 2.64
DK Players: 0.61% Power Level: 2.41
Roy Players: 0.50% Power Level: 2.22
Ness Players: 0.49% Power Level: 2.20
Zelda Players: 0.48% Power Level: 2.17
Pikachu Players: 0.45% Power Level: 2.11
Kirby Players: 0.38% Power Level: 1.93
Yoshi Players: 0.37% Power Level: 1.90
Mr.G&W Players: 0.28% Power Level: 1.62
Pichu Players: 0.20% Power Level: 1.29
Mewtwo Players: 0.18% Power Level: 1.20
Bowser Players: 0.11% Power Level: 0.70

While I still don't think these results are great, they're very clearly a step in the right direction. The %s of people playing each character are much more realistic, with top characters getting around 15%ish and low tier characters getting less than 1%. The progression from 10000 each to a stable set is actually pretty cool to look at, so I hope I can post a graphic of it soon.

I'm going to update the first post now and I think I'll be making a graph to show how the populations change throughout until becoming stable. I'm liking some of the new ideas coming in and others are confusing me, so I'll try to address them all soon. Thanks for all the intrest guys, I'm happy this idea has come so far already.

 

[Zenjamin]

quite nice, thanks for undertakeing this.


however that matchup isnt verry accurate for ganon imo.
i wish it was, i play ganon. but no pro ganon player has ranked him so well aganst him so high in individual matchups

 

[Shai Hulud]

All, right, I've finally gotten around to tuning my program to using e^P to weigh the powers for redistributing the population. Here are the results:

I'm going to update the first post now and I think I'll be making a graph to show how the populations change throughout until becoming stable. I'm liking some of the new ideas coming in and others are confusing me, so I'll try to address them all soon. Thanks for all the intrest guys, I'm happy this idea has come so far already.

There aren't enough people playing low tiers in your model. I tried using e as well but I get better distribution for arbitrary alpha and beta in F = pow(A, B * P / S), then after each iteration scale by dividing over the sum of the fractions.

 

[3GOD]

All, right, I've finally gotten around to tuning my program to using e^P to weigh the powers for redistributing the population. Here are the results:

BIG LIST

While I still don't think these results are great, they're very clearly a step in the right direction. The %s of people playing each character are much more realistic, with top characters getting around 15%ish and low tier characters getting less than 1%. The progression from 10000 each to a stable set is actually pretty cool to look at, so I hope I can post a graphic of it soon.

I'm going to update the first post now and I think I'll be making a graph to show how the populations change throughout until becoming stable. I'm liking some of the new ideas coming in and others are confusing me, so I'll try to address them all soon. Thanks for all the intrest guys, I'm happy this idea has come so far already.

Interesting results and almost identical to mine:

1) I see your current results have Fox below Marth, while mine has Fox in third and Marth in fourth - in both of our results they are very close to each other.

2) I noticed the reversal of Samus/ICs in our lists, but again they are ranked very closely to each other.

3) Everything else (order wise) is identical in our results. Even the "closeness" of rankings like Roy and Ness.

I think these are pretty good results, but again they are dependent on the Phanna chart.
I have a strongly held belief that Fox should be higher than Sheik (only slightly), but unless the chart is changed, I don't see this happening mathematically.

 

[Shai Hulud]

Using the actual matchup values I get

1) Falco
2) Sheik
3) Marth
4) Fox
5) Peach
6) ICs
7) Samus
8) J. Puff
9) Ganon
10) C. Falcon
11) Doc
12) Mario
13) Luigi
14) Y. Link
15) Link
16) Ness
17) DK
18) Pikachu
19) Zelda
20) Roy
21) Yoshi
22) Kirby
23) Mr. G&W
24) Mewtwo
25) Pichu
26) Bowser

which is identical to Wesley's list through 11) and pretty close after that. I suspect we won't be able to get a definitive order for the lower tiers because it depends so much on their use statistics and how low the model represents them.

Ice Climbers for top tier.

Oh, and 3God, if you make the changes I did to the chart and scale the values to actual win percentages you get a much more sensible tier list, which I listed above.

These are some changes I made to get this list:
Fox vs. Sheik - 6.5
Fox vs. Marth - 5
Fox vs. CF - 6.5
Falco vs. Sheik - 6.5
Sheik vs. Marth - 6
Marth vs. CF - 6

1) Falco
2) Fox
3) Marth
4) Sheik
5) Peach
6) Samus
7) ICs
8) J. Puff
9) Ganon
10) C. Falcon
11) Doc
12) Luigi
13) Mario
14) Y. Link
15) Link
16) Ness
17) DK
18) Pikachu
19) Zelda
20) Roy
21) Yoshi
22) Mr. G&W
23) Kirby
24) Mewtwo
25) Pichu
26) Bowser

That's without the change to the Ice Climbers matchups, whose current position doesn't reflect use of the infinite. They should be up around 3 - 4 once that is accounted for, and Peach may consequently increase in rank as an IC counter.

 

[Zankoku]

No way, Roy definitely has the top tier in the bag. After all, he has teh phire.

My list is unchanged from my previous test, but since everyone is posting theirs...
Falco - 18.04% - 5.79
Sheik - 15.65% - 5.65
Marth - 12.66% - 5.44
Fox - 12.18% - 5.4
Peach - 8.84% - 5.08
ICs - 6.01% - 4.7
Samus - 5.90% - 4.68
J.Puff - 4.52% - 4.41
Ganon - 2.98% - 3.99
C. Falcon - 2.60% - 3.86
Doc - 2.25% - 3.71
Luigi - 1.38% - 3.23
Mario - 1.20% - 3.08
Y. Link - 0.95% - 2.86
Link - 0.77% - 2.63
DK - 0.61% - 2.41
Roy - 0.50% - 2.22
Ness - 0.49% - 2.19
Zelda - 0.48% - 2.17
Pikachu - 0.45% - 2.11
Kirby - 0.38% - 1.92
Yoshi - 0.37% - 1.9
Mr. G&W - 0.28% - 1.62
Pichu - 0.20% - 1.29
Mewtwo - 0.18% - 1.19
Bowser - 0.11% - 0.7

 

[Banks]

how many times can people say "roy has fire" sarcastically. I think it never ends, really. always ALWAYS someone says it. ITS FRIGGEN HILARIOUS

 

[Zankoku]

He's either going to win with fire, or he's going to win by virtue of having his own ranking project forums.

 

[Mogwai]

There aren't enough people playing low tiers in your model. I tried using e as well but I get better distribution for arbitrary alpha and beta in F = pow(A, B * P / S), then after each iteration scale by dividing over the sum of the fractions.

I kinda disagree, I think that's a pretty accurate representation of low tiers in a tournament setting. On my last list, 67.3% of the players were playing Fox, Falco, Sheik, Marth, and Peach, and only 7.33% were playing characters currently specified as low tier, which I think is pretty darn accurate.

I've considered using arbitrary values for weighing the powers for purposes of calculating the new distribution of players. They sure would make scaling the distributions easier, but adding this sort of input makes this process slightly more subjective, which is precisely what we don't want. I'm not trying to say that e isn't necessarily an arbitrary decision, but at least no one can say that we designed it solely to make our equations model the established tier list.

 

[3GOD]

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%

How are you computing these numbers? For instance, Bowser has a 1 vs. Fox meaning that in a "Best of 9" series, Bowser will win 1 match to 5 wins for Fox. I guess you are then saying that Bowser has a 1/6 chance (or 16.67%) of winning any given match. So for a "Best of 3" series, the odds that Bowser will win 2 matches are (1/6)*(1/6) = 1/36 = 2.8% approximately. Is this what you are using to come up with these numbers?

Also, remember that finals matches are usually "Best of 5" or sometimes even more. Perhaps (for the hypothetical Bowser/Fox match), instead of doing (1/6)^2 for the odds of winning a set, it should be (1/6)^2.2 or something to reach some kind of middle ground between "Best of 3" and "Best of 5" while still weighting it more toward the "Best of 3" since most series will be of that type.

I think I might try to incorporate this into my code when I get home this afternoon.

ps - Is anyone else using some kind of stopping criterion like I mentioned? I am thinking that I should improve this stopping condition somehow to ensure that stability is reached - any ideas? Maybe I'll just make the changes be small over 10 iterations or something.

 

[Wave⁂]

How did you calculate the number of people playing a certain character?

 

[Shai Hulud]

How are you computing these numbers? For instance, Bowser has a 1 vs. Fox meaning that in a "Best of 9" series, Bowser will win 1 match to 5 wins for Fox. I guess you are then saying that Bowser has a 1/6 chance (or 16.67%) of winning any given match. So for a "Best of 3" series, the odds that Bowser will win 2 matches are (1/6)*(1/6) = 1/36 = 2.8% approximately. Is this what you are using to come up with these numbers?

I take a 1 to mean out of 10 games played, Bowser will win one of them. There's a 10% chance he'll win any one of those games. So if you take a random three games, the win conditions are

WWL
WLW
LWW

If the Phanna value is P then let M = P / 10 and

Win Percentage = M * M + M * M * (1 - M) * 2 = M^2(3 - 2M)

You can do this for best 3 / 5 as well.

WWW = M^3
WWLW = M^3(1 - M)
WWLLW = M^3(1 - M)^2
WLWW = M^3(1 - M)
WLLWW = M^3(1 - M)^2
WLWLW = M^3(1 - M)^2
LLWWW = M^3(1 - M)^2
LWLWW = M^3(1 - M)^2
LWWLW = M^3(1 - M)^2
LWWW = M^3(1 - M)

Summing these yields

Win Percentage = M^3(6M^2 - 15M + 10)

which gives the following win percentages:

P--3/5---------2/3
0 - 0%-------- 0%
1 - 0.856%----2.8%
2 - 5.792%----10.4%
3 - 16.308%---21.6%
4 - 31.75%----35.2%
5 - 50.0%------50%
6 - 68.256%---64.8%
7 - 83.692%---78.4%
8 - 94.208%---89.6%
9 - 99.144%---97.2%
10 - 100.0%---100%

Assuming I made no algebraic mistakes. I put the best 2/3 percentages there also for comparison.

 

[Mogwai]

How did you calculate the number of people playing a certain character?

It's good to know your name is not misleading. Just read, if you don't get it after reading, then ask what particularly is confusing you.

 

[ArticulacyFTW]

How are you computing these numbers? For instance, Bowser has a 1 vs. Fox meaning that in a "Best of 9" series, Bowser will win 1 match to 5 wins for Fox. I guess you are then saying that Bowser has a 1/6 chance (or 16.67%) of winning any given match. So for a "Best of 3" series, the odds that Bowser will win 2 matches are (1/6)*(1/6) = 1/36 = 2.8% approximately. Is this what you are using to come up with these numbers?

As Shai Hulud has already pointed out his methods (which, I think, are not accurate to the intents of Phanna's chart, but may be more accurate in reality) I won't correct you on that point. If you wanted to get the correct values for the method that you started (1 is a 1/6, 2 is 2/7 and so on) then the numbers I posted actually do turn out to be correct. Shai Hulud ( I believe) said mine were incorrect because I used a similar method to yours to actually calculating the individual game percentages, rather than each number out of 10.

For ease, I repost my numbers here:


Match-up 0= 0%
Match-up 1= 7.4074074%
Match-up 2= 19.8250729%
Match-up 3= 31.6406250%
Match-up 4= 41.7009602%
Match-up 5= 50%
Match-up 6= 58.2990398%
Match-up 7= 68.3593750%
Match-up 8= 80.1749271%
Match-up 9= 92.5925926%
Match-up 10= 100%


These numbers are more easily graded than the others (and thus more forgiving), which may not be what is actually desired.

Who knows?

 

[Shai Hulud]

For those of you who don't think it makes a difference which percentages you use--

Unadjusted--------2/3----------3/5
1) Sheik------------Falco--------Falco
2) Falco------------Sheik--------Sheik
3) Fox--------------Fox----------Marth
4) Marth-----------Marth-------Fox
5) Peach-----------Peach-------Peach
6) ICs--------------Samus-------ICs
7) Samus----------ICs----------Samus
8) J. Puff-----------J. Puff-------J. Puff
9) C. Falcon--------Ganon-------Ganon
10) Ganon---------C. Falcon-----C. Falcon
11) Doc------------Doc----------Doc
12) Mario----------Mario--------Luigi
13) Luigi-----------Luigi---------Mario
14) Y. Link---------Y. Link-------Y. Link
15) Link------------Link---------Link
16) Ness-----------Ness---------DK
17) Pikachu-------DK------------Ness
18) DK-------------Pikachu------Zelda
19) Zelda----------Zelda---------Roy
20) Roy------------Roy----------Pikachu
21) Yoshi----------Yoshi---------Yoshi
22) Mr. G&W------Kirby---------Kirby
23) Kirby----------Mr. G&W-----Mr. G&W
24) Mewtwo------Mewtwo------Pichu
25) Pichu---------Pichu----------Mewtwo
26) Bowser-------Bowser--------Bowser

I find it very interesting how the tier list varies depending on whether you're playing one game, a regular set, or a finals set.

 

[Shai Hulud]

As Shai Hulud has already pointed out his methods (which, I think, are not accurate to the intents of Phanna's chart, but may be more accurate in reality) I won't correct you on that point. If you wanted to get the correct values for the method that you started (1 is a 1/6, 2 is 2/7 and so on) then the numbers I posted actually do turn out to be correct. Shai Hulud ( I believe) said mine were incorrect because I used a similar method to yours to actually calculating the individual game percentages, rather than each number out of 10.

Hmm...I may have been interpreting the chart incorrectly. An 8 doesn't mean 8-2 but 5-2. ****ing confusing.

 

[The_NZA]

Im glad ness finally got the position he rightfully deserves

 

[3GOD]

I have been playing with the idea of making the actual tiers a factor in how many people play a certain character. For instance, I can scale my power (P) to 100 max and have say 90-100 be Top Tier; 80-90 for High Tier; etc. I was thinking of have maybe 5 or 6 tiers and seeing how things work out.

I'll implement it by having N = P * e^(some function of tier #).

The key is going to be finding the arbitrary ranges for each Tier.

 

[Gimpyfish62]

Im glad ness finally got the position he rightfully deserves

Ness is worse than bowser

I dont know why i checked this thread again, i'll leave ;P

 

[Wave⁂]

No, seriously. Are we talking overall, potential, speed, or power, or what?

 

[Nakamaru]

You've got one hell of a project Wes. Looks really sweet, but to make it a little more accurate i think you should use Shai Hulud's method of single game, best 2/3, and best 3/5. You'll end up with 3 different tier lists, but you will have a more accurate stand on where each character places when it comes to a tournament standpoint.

Edit-I dont know if someone already said that or not, but i just didnt feel like reading the last 7 pages of posts. Again nice project wes.