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

moogle · Mar 30, 2007

Yeah, pockyD's got it pretty much. The constant 70 is there so all the percents for all 26 characters add up to about 100%. If I change the base, the constant would change accordingly, so that the percents still add up to about 100%.

Now, where I'm using %usage, Wesley is using N. They're directly proportional. But, N doesn't have a restriction such as having to add up to 100, so the constant denominator won't matter there.

As for the effects of changing the base... I think the value we want is somewhere around 3 and 3.5. A higher value for the base means more skewed values of %usage (or N). Like Falco would be 25% instead of 20%, and Bowser would be 0.08% instead of 0.1%.

Side note: it's possible that something like P^3 could work, rather than 3^P. I guess it's worth testing.

This math is so much better than the math I've seen in the Pool Room. >_< (does .999999...=1?)

ArticulacyFTW · Mar 30, 2007

Wesley said:
Which numbers are you talking about? Sometimes arbitrary constant decisious must be made, but outside of those, all numbers in the process have a reason. If you're talking about moogle's numbers, some constants need to be used and a little guesswork is necessary. His process described above seems as reasonable as we could hope for.

I'm talking about the "3^P" and "/70". Yes, I agree that sometimes constants have to be selected that don't seem to emerge from the mathematics exactly, but I was trying to point out the fact that those numbers seem a bit arbitrary. The adoptance rate of higher powered characters shouldn't really be a random guess--it should be based on some sort of logic or factual research.

That being said, are we trying to simply recreate the tier list? If that's the case, then arbitrary away. If we're trying to create a "should be in a perfect world" tier list, then we should have a more definite basis.

EDIT: Oh, you posted up in the middle of me figuring out what I was going to say.

Err, well, my reasoning still applies a bit, but now I understand the 70 at least.

pockyD · Mar 30, 2007

e is the way to go!

Zankoku · Mar 30, 2007

pockyD said:
you should also scale up the power levels so that some of them can be OVER 9000

Mogwai · Mar 30, 2007

ArticulacyFTW said:
I'm talking about the "3^P" and "/70". Yes, I agree that sometimes constants have to be selected that don't seem to emerge from the mathematics exactly, but I was trying to point out the fact that those numbers seem a bit arbitrary. The adoptance rate of higher powered characters shouldn't really be a random guess--it should be based on some sort of logic or factual research.

That being said, are we trying to simply recreate the tier list? If that's the case, then arbitrary away. If we're trying to create a "should be in a perfect world" tier list, then we should have a more definite basis.

EDIT: Oh, you posted up in the middle of me figuring out what I was going to say.

Err, well, my reasoning still applies a bit, but now I understand the 70 at least.

Hmm, this is a tough one. The ultimate goal here is not to prove the current tier list correct, it's to use tangible means to calculate it out rather than opinions. That being said, I'm not sure how to best get the C from "C ^ P" or "P ^ C" we would need to exponentially scale how players select characters. Certainly something about the current method is wrong, and I firmly believe that some form of exponential scaling is necessary, but I don't think there's any way that this decision can be made in a non-arbitrary way. In the end, perhaps some nice mathematical constant would be best. . .

pockyD said:
e is the way to go!

e has nice properties and seems like as good a guess as any.

The only way that we could tie such a number to an aquirable number would be to take some factual data on how many people play each character, calculate what that would make their Powers be and then solve for the desired 'C', though it's not garaunteed to line up. Since this is unlikely to work out, I'm more in favor of picking e and just running with it. If anyone has a better idea on this one, we sure could use it. . .

ArticulacyFTW · Mar 30, 2007

I agree. Go with "e." It is the natural number to use.

HAH WHAT A PUN PWNZORZ TO TEH MAX

Mcscruff · Mar 30, 2007

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.

moogle · Mar 30, 2007

Mcscruff said:
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?

BigRick · Mar 30, 2007

I agree with McScruff, I see two major flaws here:

1.The match-up chart is not accurate (and this has already been pointed out)

2.The population shouldn't be simulated with an equation, especially if power level is a factor. Since Sheik has the highest estimated amount of power level, then he will simply remain at the top of the list after each cycle, because he will have the highest estimated amount of population.

The best thing you could do would be to survey the tournament smash population in the best way possible in order to estimate the population of each character.

BigRick · Mar 30, 2007

Wesley said:
I have an idea for computing the tier list using a complex analysis of matchups in a given metagame and I'm curious if people would be interested in this. What I'd like to do with this is take an initially perfectly diverse metagame (equal number of players playing each character), and then evaluate the respective power levels of every character using the following formula

Sry for double post, but this is another thing that I don't like in your method. If your list is going to be about tournament viability, then you shouldn't start everything by assuming that the metagame is perfectly diverse, because you know it is very far from it.

If you make something out of something that was false, then I doubt that it will be true.

In order to make a tier list out of this, you should determine your first set of power values with estimated values of population, like I implied in my previous post. Then you start the cycle.

If the population of (Fox+Falcos+ICs) is so much higher than the population of the lower tiered chars, then you could expect something like Falco ending up number 1 (not Fox, since his scores are lower than what they should be on that chart).

EDIT: Btw, I expect SHEIK to end up at the top of this list if you follow these calculations... And it's very funny how some of the people in this thread try to play with the formulas just so that Fox/Falco comes out on top lololol.

Like my teacher once said to me, about 85% of scientific discoveries are false. That would a good example.

ArticulacyFTW · Mar 30, 2007

BigRick, I don't know if you read it, which you very well may not have, or I just wasn't clear enough, but I already made this point and Wesley stated his reason for opposition. The point of this exercise isn't necessarily to find out what the tier list should be now, because that wouldn't require reiterations of a mathematical loop. It would just require using the populations now and using the match-ups to determine their correct power level. While this also would be a very interesting thing to do, it's not what is being attempted.

However, I do agree that starting from the current metagame, so to speak, WOULD give this more accurate results--at least more accurate to the current tier list. Or perhaps starting from the stats from 2001 or whatever.

But again, that's not really the point. The point (as far as I can tell) is to find out what the tier list SHOULD be, taking out player bias for character.

Anyhow, numerous repetitions should largely even out the discrepancies we're talking about, even though the initial jump given to Sheik may be to difficult to overcome.

PS: While (I think) it's been determined that Fox and Falco are the most powerful characters, in terms of the raw capability to win when taken to the highest level, this may not mean that they are the best choice to play, just because their match-ups aren't as good as Sheik's. I'm sure there are numerous analogies that can be drawn to the sports teams of the past, and, because I'm actually familiar with it, (wow, I feel like a nerd, posting on a video game message board about a card game) Magic: the Gathering decks. It is very possible that the "Best" something might not be the best thing to play.

BigRick · Mar 30, 2007

Omg I'm very sorry I missed alot of elements. I understand the point of this now.

Maybe I'll post a few more of my ideas later.

Zankoku · Mar 30, 2007

Here's the list calculated with e^ and using a population based on Poll #1, over here:
http://smashboards.com/showthread.php?t=63399

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

Smash G 0 D · Mar 30, 2007

BigRick said:
I agree with McScruff, I see two major flaws here:

1.The match-up chart is not accurate (and this has already been pointed out)

2.The population shouldn't be simulated with an equation, especially if power level is a factor. Since Sheik has the highest estimated amount of power level, then he will simply remain at the top of the list after each cycle, because he will have the highest estimated amount of population.

The best thing you could do would be to survey the tournament smash population in the best way possible in order to estimate the population of each character.

Just wanted to point this out, Sheik is a girl.

Mogwai · Mar 31, 2007

Mcscruff said:
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.

Everyone has their opinions about how the Phanna chart should be changed to be more accurate, and I think everyone with these opinions should post on his thread and contribute to making it as good as possible. However, I honestly don't think that even a perfect Phanna chart gives us the precision necessary to model this accurately. For this to work out as well as I would like, I would really like a game winning percentage on each matchup, but this would be an even more difficult undertaking than what Phanna has gotten himself into. Currently, the best we can hope for is to get all the kinks out of the math and process for this so that if/when we have an accurate matchup chart, we can model the tiers according to it.

moogle said:
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?

Very well put. Our goal here is to get the math down so that when we have a satisfactory Phanna chart, the tiers are trivial.

BigRick said:
Sry for double post, but this is another thing that I don't like in your method. If your list is going to be about tournament viability, then you shouldn't start everything by assuming that the metagame is perfectly diverse, because you know it is very far from it.

If you make something out of something that was false, then I doubt that it will be true.

In order to make a tier list out of this, you should determine your first set of power values with estimated values of population, like I implied in my previous post. Then you start the cycle.

If the population of (Fox+Falcos+ICs) is so much higher than the population of the lower tiered chars, then you could expect something like Falco ending up number 1 (not Fox, since his scores are lower than what they should be on that chart).

EDIT: Btw, I expect SHEIK to end up at the top of this list if you follow these calculations... And it's very funny how some of the people in this thread try to play with the formulas just so that Fox/Falco comes out on top lololol.

Like my teacher once said to me, about 85% of scientific discoveries are false. That would a good example.

Who's playing with formulas to rig spacies? Every iteration has put sheik higher than fox, and most put her higher than falco.

As for the point about using the current metagame as a starting point, since we expect the system to stabalize, it really shouldn't make much of a difference where we start. To calculate the best character to use in the tournament scene of today, simply estimate the ratios of characters and then plug into the power equation here, it will find you the character with the best expected matchup by the Phanna chart.

ArticulacyFTW said:
BigRick, I don't know if you read it, which you very well may not have, or I just wasn't clear enough, but I already made this point and Wesley stated his reason for opposition. The point of this exercise isn't necessarily to find out what the tier list should be now, because that wouldn't require reiterations of a mathematical loop. It would just require using the populations now and using the match-ups to determine their correct power level. While this also would be a very interesting thing to do, it's not what is being attempted.

However, I do agree that starting from the current metagame, so to speak, WOULD give this more accurate results--at least more accurate to the current tier list. Or perhaps starting from the stats from 2001 or whatever.

But again, that's not really the point. The point (as far as I can tell) is to find out what the tier list SHOULD be, taking out player bias for character.

Anyhow, numerous repetitions should largely even out the discrepancies we're talking about, even though the initial jump given to Sheik may be to difficult to overcome.

PS: While (I think) it's been determined that Fox and Falco are the most powerful characters, in terms of the raw capability to win when taken to the highest level, this may not mean that they are the best choice to play, just because their match-ups aren't as good as Sheik's. I'm sure there are numerous analogies that can be drawn to the sports teams of the past, and, because I'm actually familiar with it, (wow, I feel like a nerd, posting on a video game message board about a card game) Magic: the Gathering decks. It is very possible that the "Best" something might not be the best thing to play.

Don't worry about nerdiness dude, you're posing on the "Mathematically Calculated Tier List" thread. I mean, I play magic too, and I know what you're talking about. In the right format, the best deck, might be something that's very janky and ghetto, but tears apart the weaknesses of the dominant decks. The same sort of thing can happen in smash when everyone starts playing sheik, just run ICs and the format is all yours. Nothing but Falcos in your area? Play Peach and **** their faces off. Metagaming is always important, so even with this list, it's important to understand how viable you are in your own tournament scene.

Smash G 0 D said:
Just wanted to point this out, Sheik is a girl.

Truer words have never been spoken.

Kwan · Mar 31, 2007

I really like the idea, but i think theres something wrong with your formulas. dont ask me how to fix em, but try plugging them into each other >.> I'm sure theres some relationship between "power" and "relative power" that just makes the while thing turn to poop. Something about your formulas just doesnt feel right. Cool idea, though.

Elen · Mar 31, 2007

Are you weighing the difference between higher tier matchups and lower tier matchups? In my opinion, having a higher matchup than shiek on the chart, should not be worth the same as having a higher matchup than bowser. Using the data you already have, you should go through the process again, weighing characters matchups based on their "power levels". If your already weighing match ups (I havn't looked too deeply into your forumula, as it's early

) please disregard this post. This is a really great idea btw, although it would be nice if we had a more solid 'match ups chart'.

ꓰspeon · Mar 31, 2007

Smash G 0 D said:
Just wanted to point this out, Sheik is a girl.

Oh, and props for the mathematical tier attempt. I'll try to give my 2 cents later.

Virgilijus · Mar 31, 2007

Well, here is my two cents:

The formula for how effective a character is in an average tournament should mean (this is very obvious, but I'll state it anyway), a match up >5 should benefit them, a match up <5 should hurt them, and =5 match up should not hurt them at all. So, I took what every characters advantage supposedly is (based on Phanna's chart) and subtracted five from
each one (making the good one's positive, the bad one's negative, and the even one's zero). I will now call this number m.

How well a character does in the tournament is not just dependent on every character match up, but what characters (their match ups included) that they are most likely to face, i.e. Fox's matchup to someone is more important than Luigi's because you are more likely to face more Foxes than Luigis. So, using Moogle's approximations for what percentage of characters are used at big tournaments(let's call this n), I multiplied this by m; this shows (on a scale from 5 to -5), the chance of doing well in a tournament against a certain character q given the probability of actually fighting q.

Now, because tournaments can be composed of every character, the results are all inclusive and can be summed: Σ(m*n). This leads to a number on a scale from 27 to -27 of the character's overall likelyhood of placing well/winning at a tournament with the average number of each character used.

Following this template I came up with this:

Sheik 4.45
Falco 4.1
Fox 3.6
Marth 3.35
Peach 1.35
IC 0.3
Samus 0.15
Doc -0.38
J Puff -1.9
Ganon -2.5
C.Falcon -2.85
Mario -5.85
Luigi -6
Y. Link -6.8
Link -7.9
DK -8.75
Ness -9.5
Roy -9.65
Pikachu -10.65
Zelda -11.1
Yoshi -11.25
Kirby -12.2
Mr. G&W -13.05
Mewtwo -15.35
Pichu -15.65
Bowser -18

It seems to follow the already assumed order rather well and does have quite a large margin between best and last. The only smudging I really see right now is the approximate percentages of how much a character is used in an average high level tournament isn't anywhere close to exact (aka, Moogle's approximation).

You can also really do anything with these numbers, like make a scale from one to ten that holds them all or something of the sort.

Anyways, any comments or things that I did wrong?

pockyD · Mar 31, 2007

i'm not reading half the posts, but the original formula produces a power level which is equivalent to the expected value of any matchup for that character (i.e. you enter a match playing sheik; your EV on the phanna chart (calculated by a weighted average) is 6.81 or whatever)

and the populations are directly proportional to the power levels (basically power level / total number of characters), which has since been decided isn't a great thing because they all stay too close together

Mogwai · Mar 31, 2007

Kwan said:
I really like the idea, but i think theres something wrong with your formulas. dont ask me how to fix em, but try plugging them into each other >.> I'm sure theres some relationship between "power" and "relative power" that just makes the while thing turn to poop. Something about your formulas just doesnt feel right. Cool idea, though.

I appreciate your concern, but I'm really confused about what you're trying to say. "Power" and "Relative Power" are more or less used interchangably. I just use the phrase "Relative Power" to make sure people know I'm talking about powers relative to a specific metagame. The formulas are fine as far as we can tell, they do exactly what we hoped they would:

Step 1 : Find the powers of everyone in a given metagame.
Step 2 : Use these powers to change the metagame to favor stronger characters.
Step 3 : Repeat from Step 1 using the new metagame.

If it's not clear enough, I'm using the term "metagame" to refer to the number of players playing each character. If you see a specific problem, great, let us know, but we know what we're doing (sorta), so if it just seems "fishy" to you, trust us, it has a sound foundation for everything it's doing.

Virgilijus said:
How well a character does in the tournament is not just dependent on every character match up, but what characters (their match ups included) that they are most likely to face, i.e. Fox's matchup to someone is more important than Luigi's because you are more likely to face more Foxes than Luigis. So, using Moogle's approximations for what percentage of characters are used at big tournaments(let's call this n), I multiplied this by m; this shows (on a scale from 5 to -5), the chance of doing well in a tournament against a certain character q given the probability of actually fighting q.

Now, because tournaments can be composed of every character, the results are all inclusive and can be summed: Σ(m*n). This leads to a number on a scale from 27 to -27 of the character's overall likelyhood of placing well/winning at a tournament with the average number of each character used.

Following this template I came up with this:

Sheik 4.45
Falco 4.1
Fox 3.6
Marth 3.35
Peach 1.35
IC 0.3
Samus 0.15
Doc -0.38
J Puff -1.9
Ganon -2.5
C.Falcon -2.85
Mario -5.85
Luigi -6
Y. Link -6.8
Link -7.9
DK -8.75
Ness -9.5
Roy -9.65
Pikachu -10.65
Zelda -11.1
Yoshi -11.25
Kirby -12.2
Mr. G&W -13.05
Mewtwo -15.35
Pichu -15.65
Bowser -18

It seems to follow the already assumed order rather well and does have quite a large margin between best and last. The only smudging I really see right now is the approximate percentages of how much a character is used in an average high level tournament isn't anywhere close to exact (aka, Moogle's approximation).

You can also really do anything with these numbers, like make a scale from one to ten that holds them all or something of the sort.

Anyways, any comments or things that I did wrong?

What are the moogle aproximations. . ? the only stuff I'm seeing from him about how many people should play each given character based on their relative power level using an exponential scale. If this is the case, they what values are you using in the first place to determine power level.

Honestly, I'm pretty confused by your process here. First of all, subtracting 5 from the matchup value is trivial, it will just shift data, so I don't really understand why it's necessary. Second of all, how is this ending up on a -27 to 27 scale? There are 26 characters, so I suppose I could understand a -26 to 26 scale, but still, m ranges from 5 to -5, so the only way you can end up at -26 to 26 is if the n in the "Σ(m*n)" term maxes out at 0.2. (also, how did you make the sigma? I <3 sigmas!) Since this is representing amount of people playing a character, I'm confused, unless you're talking percentages, in which case, I'm curious where the numbers are coming from. Regardless, this apears to me to just be calculating powers (on a slightly different scale) in some set metagame, which, while helpful at times, doesn't do much unless that metagame is accurate.

Virgilijus · Mar 31, 2007

Wesley said:
What are the moogle aproximations. . ? the only stuff I'm seeing from him about how many people should play each given character based on their relative power level using an exponential scale. If this is the case, they what values are you using in the first place to determine power level..

What I was using his guesses as were in a large, highly competitive tournament, this character is used this % of the matches. I know it is horribly approximate due to counter picks and what not, but if they were taken over a very large sample they should be smooth enough. I didn't used them based on power (although Moogle's view may have put them there), just as the chance each match you will face this character. As I said before, this is the only part I am not confident at all because the percents (being vague approximates), do not equal one, even though they are in the correct order (assumedly). If some one wants to try to find out what it is actually like, I will love you <3.

Honestly, I'm pretty confused by your process here. First of all, subtracting 5 from the matchup value is trivial, it will just shift data, so I don't really understand why it's necessary.

Well, when I was trying to think of a summation expression for how much each matchup accounts for, I realized that a completely neutral matchup (Fox v. Fox) should neither contribute or detract since it is neutral. Since Phanna's chart goes from 0->10, subtracting five just made it so when eventually they needed to be summed, an absolutely neutral character would come out as zero. It is a shift, as you said, but I thought it would make the results more vivid.

Second of all, how is this ending up on a -27 to 27 scale?

I took a perfect character (10's in every matchup) and the worst possible character (- 10's in every matchup) and used them as the limits of the scale: they turned out to be +27, -27. Problem is this is dependent on the Moogle's percentage earlier, so it is liable to change with better numbers (which is one of the reason's I didn't use the absolute value of the scale for ratios).

(also, how did you make the sigma? I <3 sigmas!)

Microsoft Word-->Insert-->Symbols-->Sigma-->Insert-->Copy-->Paste to your hearts content!

Regardless, this appears to me to just be calculating powers (on a slightly different scale) in some set metagame, which, while helpful at times, doesn't do much unless that metagame is accurate.

Everything we do is dependent on the metagame, which we all know is never set in stone, so small deviations will always be a part of it. And the list basically says, if all mindgames and technical skill are equal between players and an infinitely large tournament is held consisting of the the average percentages of characters played in most high level tournaments, then characters above 0 will (given a completely random draw) most likely advance (more so with increasing magnitude above zero) while the opposite also holds true.

In some ways I think this list is very accurate: There is no character that completely dominates while there are some that are completely dominated (all of this in tournament play) which most of us can agree with from observed tournament results.

Hopefully I explained that well.

choknater · Mar 31, 2007

front page: i was skeptical to this at first, but i find the results pretty accurate considering how objective it is. only... there are problems with fox, link, and/or falcon being too low. this is where we might need some subjective opinions. but that's how the SBR tier list is made... so nice attempt at a mathematically calculated one.

Mogwai · Mar 31, 2007

Virgilijus said:
Everything we do is dependent on the metagame, which we all know is never set in stone, so small deviations will always be a part of it. And the list basically says, if all mindgames and technical skill are equal between players and an infinitely large tournament is held consisting of the the average percentages of characters played in most high level tournaments, then characters above 0 will (given a completely random draw) most likely advance (more so with increasing magnitude above zero) while the opposite also holds true.

In some ways I think this list is very accurate: There is no character that completely dominates while there are some that are completely dominated (all of this in tournament play) which most of us can agree with from observed tournament results.

Hopefully I explained that well.

Yup, you did explain it well. I don't particularly like the reasoning for the -5 scale, as presenting an average expected matchup on the Phanna chart makes more sense to me. But that's entirely subjective, so I won't get hung up on that.

I'm aiming at not needing a correct metagame at the start of this. I expect the numbers to naturally develope into the current metagame, and possibly beyond. I understand how that seems shady, so let me explain the reasoning for not even trying to get a read on the current metagame for this project.

Assume that it is possible to get the metagame, and we have a value for how many people play each character. Once we have these values, There's no need for any complexity, powers are easily calculated by the power formula in the first post, and you could easily find which character is the theoretical best to play if you were to play against any random player in the world.

While this would be a worthy endevor, the math is simple and the real challenge lies is getting accurate numbers for how many people play each character. Honestly, I have no idea how to go about doing something like this and would rather model this in a perfect world where everyone starts playing a random character (equal players playing each character), and then adapts to who's the best in the current metagame. Eventually, the numbers should stabalize, and I honestly think it will roughly model the current metagame fairly well and the theoretical best characters should rise to the top. I understand the flaws of this process, but until someone finds out how many people play each character, I don't think there's a better way to do this.

choknater said:
front page: i was skeptical to this at first, but i find the results pretty accurate considering how objective it is. only... there are problems with fox, link, and/or falcon being too low. this is where we might need some subjective opinions. but that's how the SBR tier list is made... so nice attempt at a mathematically calculated one.

Thanks. Most of the problems are boiling down to poor ratings on the Phanna chart IMO. Fox vs. Marth being a 4 screws Fox over a bit, as well as his highly underestimated low tier matchups. Link is given strictly worse numbers than Y. Link for the most part, which rails him. Falcon on the other hand, I think is getting pretty accurately represented. Samus and ICs do seem to be better against the top tiers and due to that, I'm pretty sure they should be higher than CF. If there is a problem for him, it's again in the Phanna chart, but I don't actually think his numbers are that poorly represented. I will refine the math as best I can, and then all efforts should go towards making the Phanna chart as good as possible.

MaskedMarth · Mar 31, 2007

I have two suggestions. I don't understand all the mathematics behind the process, but I've looked at the numbers and have fiddled with this type of weighted list before.

One, expand the weights of high tier vs. low tier matches even more. A match against Fox, for instance, should be more important than the entire bottom and low tier.

Two, it seems to me that 6-4 matches are often used for matchups that are considered equal or near-equal, so perhaps don't give so much weight to 6-4 or 4-6 (use a flatter scale for matchups). 7-3 is where we really get into the realm of significant advantages.

Also, the matchup list itself has problems, but that's another matter.

tarheeljks · Mar 31, 2007

@maskedmarth: many people have issues w/the chart; there will always be discrepancies. this is as close as it will get b/c there is variation in the strenght of a given matchup. I do agree w/you about weighting matchups according to the strength of a character; however, how do you determine the absolute strength? referencing the current tier list isn't helpful b/c the data becomes biased. I'm not sure there is anyway to do this.

Smash bro pro · Mar 31, 2007

Ok... you confused me until i read it over three times and how did you come up with the formula you must spend along time doing so explain! t :dk:

Corigames · Apr 1, 2007

Now I know why I'm having problems against Cpt. Falcon as Samus.

Icetrash · Apr 1, 2007

I dont get one thing on your formula, what does N mean? "Number of players playing a given character"???? What does that mean. If what I think it means is true how does a players power level have to do with how many people play the character?

Wave⁂ · Apr 1, 2007

And this is why Ness is so low. his matchups against Upper Tiers are crap, but against lower tier, he rocks.

Are you accounting for possible potential?

pockyD · Apr 1, 2007

this is meant to be completely objective with the exception of the matchup values taken from the phanna chart

also, it is assumed that the amount of people playing a character is proportional in some way to its relative power level; whether or not this is a safe assumption, there's not really a better, clearly mathematical way to do this

vidjogamer · Apr 1, 2007

This is a terrible idea...

Virgilijus · Apr 1, 2007

vidjogamer said:
This is a terrible idea...

I don't think so; they are just statistics born out of ennui. I know that even my own calculations are nothing more than something some what amusing to look at; nothing more, nothing less.

The terrible thing would be people using any mathematical list as proof or evidence, but that is the blame of the user, not the object.

tarheeljks · Apr 1, 2007

pockyD said:
this is meant to be completely objective with the exception of the matchup values taken from the phanna chart

also, it is assumed that the amount of people playing a character is proportional in some way to its relative power level; whether or not this is a safe assumption, there's not really a better, clearly mathematical way to do this

based on the assumption that players are playing to win/be successful in tournies, the assumption that P~N is reasonable. My concern is that M is probably more important than N.

Zankoku · Apr 2, 2007

I disagree. A character is viable if it has a distinct advantage over the present environment; not the full range of characters, used or not.

Gimpyfish62 · Apr 2, 2007

let the intelligent people make the tier list XD

pockyD · Apr 2, 2007

i don't understand what's with the hostility

as far as i can understand, this isn't an attempt to replace the current tier list or anything; it's more of an attempt to determine what it would look like with alternate criteria

instead of thinking he's trying to overthrow the tier list, think of this more like the "recovery tier list" or whatever other random lists are floating around; it's just a different way of judging characters

Gimpyfish62 · Apr 2, 2007

the recovery tier list is garbs and horribly inaccurate, tahts why i posted what i posted before

innaccurate lists that newer or uneducated people believe aren't good for the community

Sky2042 · Apr 2, 2007

Gimpyfish62 said:
the recovery tier list is garbs and horribly inaccurate, tahts why i posted what i posted before

innaccurate lists that newer or uneducated people believe aren't good for the community

What does the BR think of this attempt at a different tier list? I certainly can't say this idea isn't enchanting; I love math naturally, and having a slightly more objective way of saying "this is how it is" just tickles my statistics nose.

Corigames · Apr 2, 2007

Can someone make a list out of Character VS Level to see where each character is good? I think that would also be an interesting chart. 0 - 26 wins (for each character they verse; 0 being they have no chance for a win, 26 meaning the HAVE to win)

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

Smash Ace

Smash Cadet

Smash Legend

Never Knows Best

Smash Gizmo

Smash Cadet

Smash Ace

Smash Ace

Smash Master

Smash Master

Smash Cadet

Smash Master

Never Knows Best

Leave Luck to Heaven

Smash Gizmo

Smash Cadet

Smash Lord

Sun Pokemon

Nonnulli Laskowski praestant

Smash Legend

Smash Gizmo

Nonnulli Laskowski praestant

Smash Obsessed

Smash Gizmo

Smash Ace

Smash Lord

Smash Rookie

Smash Hero

Smash Journeyman

Smash Legend

Smash Legend

Smash Master

Nonnulli Laskowski praestant

Smash Lord

Never Knows Best

Banned (62 points)

Smash Legend

Banned (62 points)

Smash Apprentice

Smash Hero

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