League Math

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Verandure

Senior Member

02-03-2014

I need a bit of help working out the relative strengths of "MP", "MP+", "MP5", and "MP5+" from the champion statistics. Because there is a variety of resources presented by these stats, it is very difficult to find a fundamental value to measure everything around.

For the purposes of what I'm doing, I'm taking resourceless champions (Ones that don't use mana or energy) as having infinite resources instead of the 0 they have denoted in places like the LoL wikia. Things like Bloodwell, Rengar's Ferocity, and Yasuo's Flow wouldn't be considered resources in this model(even though Ferocity does represent a resource consumption, I will cover the power it gives him in his passive rather than in his base stats).

Right now, I'm thinking of taking the natural log of the champion stat divided by the minimum value (to get rid of the infinities) but I'm likely going to need a function to compare energy to mana.

It's also possible for me to treat the resources as completely separate and find their relative power by type, but the purpose of this is to find the power level of champions regardless of their resource.

Any people somewhat fluent in math who can help will be appreciated.


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Verandure

Senior Member

02-03-2014

Pls halp. I know there's more than one person who's at least semi-competent in math out there.


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CosmoVibe

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Senior Member

02-03-2014

Assuming we're not taking into consideration cases where current or maximum mana affects damage output or mechanics other than just cost, you're looking in the wrong direction. Mana doesn't affect a champion's combat ability (in this case) assuming they don't run out of mana, so it has no power value. Instead, its strength is determined by its application in sustained laning and sieges. In that case, you have a ton of other factors to consider, such as the champion's mana costs, cooldowns, and how those spells are used and what they do.

Trying to come up with a standard mathematical algorithm to evaluate the strengths of those stats is like trying to mathematically determine which fruit is the best. Some fruits are better than others for certain things, but each fruit has its unique combination of advantages and disadvantages that should be evaluated on a case by case basis.

This is why theorycrafting is so difficult and why game theory is so complex. There are way too many dimensions in which the game needs to be analyzed, and small changes in stats can result in entirely different strategies and equilibriums. The game needs to be looked at not only on the detailed mathematical level, but also on a higher, more general level.


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Verandure

Senior Member

02-03-2014

Quote:
Originally Posted by CosmoVibe View Post
Assuming we're not taking into consideration cases where current or maximum mana affects damage output or mechanics other than just cost, you're looking in the wrong direction. Mana doesn't affect a champion's combat ability (in this case) assuming they don't run out of mana, so it has no power value. Instead, its strength is determined by its application in sustained laning and sieges. In that case, you have a ton of other factors to consider, such as the champion's mana costs, cooldowns, and how those spells are used and what they do.

Trying to come up with a standard mathematical algorithm to evaluate the strengths of those stats is like trying to mathematically determine which fruit is the best. Some fruits are better than others for certain things, but each fruit has its unique combination of advantages and disadvantages that should be evaluated on a case by case basis.

This is why theorycrafting is so difficult and why game theory is so complex. There are way too many dimensions in which the game needs to be analyzed, and small changes in stats can result in entirely different strategies and equilibriums. The game needs to be looked at not only on the detailed mathematical level, but also on a higher, more general level.
I realize, I'm taking the base stats as just one term in a much larger equation encompassing the other variables. This is trying to reduce down costs to a simple (or complex) coefficient to use for proportionality equations later on. I'll likely end up separating them out by resource type and assign some arbitrary multiplier just to make my job a bit easier.

Taking the maximum mana and the mana regeneration are also key to determining how long a champion can stay in lane compared to another champion -- like you said; though, this is also reliant on mana costs, cooldowns, and spell effects (which I'll try to get to within the year).

Certainly I'm not saying that a champion is balanced or not balanced depending on their base statistics alone. Right now, I'm trying to build a model to better understand balance, and specifically how those small changes in stats or abilities completely rubber band a champion's perceived viability.

Although erroneous, there are some interesting results from just adding up the stats compared to how often the champion is played -- but again, it's erroneous due to the amount of 0's.


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Riot Reboot

Business Intelligence Manager

02-03-2014
1 of 4 Riot Posts

Just so I'm clear, are you thinking about mana regen or magic penetration? I've seen MP refer to both in various contexts, so just checking.


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CupcakeTrap

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Senior Member

02-03-2014

Quote:
Originally Posted by Verandure View Post
I need a bit of help working out the relative strengths of "MP", "MP+", "MP5", and "MP5+" from the champion statistics. Because there is a variety of resources presented by these stats, it is very difficult to find a fundamental value to measure everything around.
Could you try to rephrase what you're attempting to determine?

I like theorycrafting and may be able to help, but first I need to know what you're trying to quantify and why.

Quote:
Right now, I'm trying to build a model to better understand balance, and specifically how those small changes in stats or abilities completely rubber band a champion's perceived viability.
This makes it sound like you're trying to correlate changes in certain stats to changes in win rate or pick rate.


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Verandure

Senior Member

02-03-2014

Quote:
Originally Posted by Riot Reboot View Post
Just so I'm clear, are you thinking about mana regen or magic penetration? I've seen MP refer to both in various contexts, so just checking.
It's "mana points" in this context -- going off of the list of base champion stats from leagueoflegends.wikia.com. I don't consider CDR or penetrations to be "fundamental" stats, so I haven't factored them in yet =P

Quote:
Originally Posted by CupcakeTrap View Post
Could you try to rephrase what you're attempting to determine?

I like theorycrafting and may be able to help, but first I need to know what you're trying to quantify and why.


This makes it sound like you're trying to correlate changes in certain stats to changes in win rate or pick rate.
(Not sure why somebody downvoted you).

I'm trying to build an equation to determine the power level of a champion relative to all other champions. Right now, I'm working to reduce some of the variables by relating the base statistics of a champion to the fundamental (or lowest currently in the game).

It's a very hefty project to quantify every variable, which is why I'm quite sure it'll take several months to work out, but this isn't something too foreign to me.

The logarithmic scale is to try and get the numbers as close to 1 as possible, just so it looks nice. Since there are a good number of 0's in the statistics (which I'm considering to be infinities instead for previously explained reasons) it helps to still allow numbers to be seen, even if it's E-14 and other ridiculous magnitudes at the moment.


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Riot Reboot

Business Intelligence Manager

02-03-2014
2 of 4 Riot Posts

Ok, so total mana as a contributing variable in an equation of champion power. I get you.

One of the things that you may have done and not shared, or not done (idk) is define "champion power." That can change based on the role of the champion, and for certain champions, the build. The first thing I would advise is narrowing your scope to a super clear definition regarding what you mean by "champion power" then lining up variables that could potentially affect that. After that, some of these considerations you're fighting with now should be a bit clearer.


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CupcakeTrap

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Senior Member

02-03-2014

Quote:
Originally Posted by Riot Reboot View Post
Ok, so total mana as a contributing variable in an equation of champion power. I get you.

One of the things that you may have done and not shared, or not done (idk) is define "champion power." That can change based on the role of the champion, and for certain champions, the build. The first thing I would advise is narrowing your scope to a super clear definition regarding what you mean by "champion power" then lining up variables that could potentially affect that. After that, some of these considerations you're fighting with now should be a bit clearer.
I agree.

To me, the gold standard of "champion power" is "ability to make the enemy nexus explode", but that's quite hard to actually measure directly.

Further, there's a serious apples and oranges problem here: the units do not match up. Adding +5 max mana is very different from adding +5 AD. If you want to throw everything in and quantify a Champion's total "power", you need to establish a unit of comparison and summation.

One way to try to quantify "power" based on stats would be to use the gold price of stats in the shop, and say, for each Champion, what's the gold value of the stats they start with / get as they level, relative to a hypothetical "baseline Champion"? Gold value helps to roughly compare stats in the same units, and incorporates Riot's implicit valuation of the power level of each point of each stat.

Of course, there are issues here. Stats can have synergistic power and offer above-linear returns in combination with certain other stats. As a result, stats are not always truly "worth" their price in the shop. Extreme example: AA staff is worth basically 0g on Garen. A more ordinary example: AD is great on champs with a ranged basic attack and high attack speed, and ADC DPS increases at a markedly non-linear rate due to the multiplicative effects of damage stats. You don't actually kill your opponents with gold value, you kill them with DPS. That said, gold value does roughly reflect usefulness even given the availability of synergistic stats. Crit is priced on the assumption that the buyer is an ADC who can use it to get non-linear DPS scaling.

Champions also have different kits that influence the true significance of their stats. For example, Cho'gath has a very high base AD, but arguably the power he (as a tanky mage with a melee attack and low AS) derives from that AD is rather lower than the gold price of AD would suggest.

Still, I think a gold-valuation metric might be one way to get started. You could even limit the universe of stats you're considering to make it more relevant. For instance, we could assume that mages are willing to pay "sticker price" for MP5 and maximum mana. Then, you could look at how much gold-value of mp5 and max mana each mage starts with, and how much they acquire per level.

Here, too, there would be complications. For example, Veigar's passive effectively multiplies the value of mana regen (and to some extent maximum mana). Also, champ mana costs vary significantly.

But that would be my advice: think very hard about what you're trying to measure. Sometimes narrowing it down can produce more enlightening information than an attempt to generate a Grand Unified Theory of champion power. Think about who might want to read your conclusions and why. Maybe they want to know what Champions are likely to thrive in a solo lane with lots of XP, so they want to see which champs get the most power from leveling. (In that example, another confounding example arises: a big part of level-up power is gaining and ranking up abilities. You'd want to try to address that, perhaps by measuring raw magic damage output from ability base damage. Comparing CC and utility would be difficult but not impossible by reference to shop items that grant similar utility.)

That said, sometimes it's fun and even useful to throw everything into the mix and crunch the numbers. In that case, I think gold value would be a reasonable way to start.


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Verandure

Senior Member

02-03-2014

Quote:
Originally Posted by Riot Reboot View Post
Ok, so total mana as a contributing variable in an equation of champion power. I get you.

One of the things that you may have done and not shared, or not done (idk) is define "champion power." That can change based on the role of the champion, and for certain champions, the build. The first thing I would advise is narrowing your scope to a super clear definition regarding what you mean by "champion power" then lining up variables that could potentially affect that. After that, some of these considerations you're fighting with now should be a bit clearer.
The equation is to define champion power. While some champions are more suited to certain situations, a balanced game would still have all of their "relative power levels" without too much deviation. A tank will have higher MR, scaling MR, Armor, scaling Armor, HP, HP5, steroids for those stats, or all of the above. This means that, in a balanced universe, they'd have lower ad, scaling ad, base damage, and damage scaling (only in a perfect world).

While I'm "modeling" champion power, I'm not trying to do it for only the ideal case. While that's where I'm starting, hopefully I can get something that's a little closer to the nuance and reality of the game.

(Was in a game with Pendragon, sorry for the delay).


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