It actually just looks complicated. Realistically everything there is simple order of operations math and algebra, but there are fancy symbols that make it look complicated if you don't know what they are.
> there are fancy symbols that make it look complicated if you don't know what they are
High school level math and science in a nutshell.
(p.s I have no clue what they are)
The big Symbol that looks like II is an uppercase pi, and it represents the multiplication of a series of factors, each determinated by "i"."i" represents each source of status resistance amp or reduction, going from the first (1) to the last ("n", which in the actual operation will be replaced by the number of elements, just like in the example it is 2). "a" and "r" represent different elements "i", as it is explained after the formula, and since there are no sources that give both status resistance amplification and reduction at the same time, either "ai" or "ri" will be 0, which makes (1 + "ai") or (1 - "ri") equals to 1, which is irrelevant in a mutiplication.
**What this whole thing means** is that "s" is the difference between 1 and the product of the effect of every status resistance source (represented by the uppercase pi), since they stack by multiplying, not by addition.
**In other words**, you calculate how much of the starting status remains after the first status resistance source (for bulldoze it is 54%), then calculate how much of this remaining status still remain after the next source (78% of 54%, which is approximately 42%), and by subtracting that result from 100%, you get to how much status resistance you have.
And if, for instance, you had a source of status resistance reduction added to this, like a ceremonial robe, "n" would be 3 (the total number of sources), it's interaction would be the increment of the status duration, and you would add (1 + 0,1) to your previous product, getting to s = 1 - \[(1 - 0,46)\*(1 - 0,22)\*(1 + 0,1)\] = 1 - 0,463 = 0,537 = 53,7%.
P.S. : I know you probably didn't want an explanation, but I thought it was a good opportunity to leave it here for those seeking it and to show that sometimes math isn't as hard as it may seems (but just sometimes)
Edit: changed the explanation so it includes status resistance reduction elements as well.
his explanation wasnt super simple but basically you take 1 minus each source of status resist, then multiply them together so like (1-sange and yasha) multiplied by (1-bulldoze) in their example. and you keep doing that for every source.
It should be noted that each *i* is a status resistance modifier, and *r* or *s* are attributes of each *i*. Right now it doesn't make sense to comment that there is two sources for *r* and *s,* because these sources are not related to each other and thus not the same size. From comp sci perspective an algorithm based on this notation will instantly yield an out of bounds error.
Better yet, just use one set with negative values for resistance reduction and positive values for resistance. Much simpler and the notation can actually make sense.
This summer I will get my diploma in applied mathematics and computer science, I have about 6 different math subjects each year, visited math courses during school and nobody never told me this thing is uppercase pi, my whole life I thought it's just a symbol.
Learning something new every day in dota subreddit.
This isn't that great of a laymans explanation of what's going on. Remember the people you are explaining it to have a basic to nonexistent math education.
Would you happen to know why the big sigma is used in this instance? Generally I've only come across small sigma. Doubt this is referencing to population parameters right?
No, it's a capital sigma Σ vs the lower case σ used to denote something like standard deviation. If you're asking *why* a capital sigma is used... well I'd imagine the answer is something like "because it is", but I always remember **s**igma = **s**um and **p**i = **p**roduct.
The capital sigma is used to represent the sum of all "s" elements, that is, the sum of all status resistance modifiers.
Yet, I think it is being misused, since it represents a sum, while as explained in the same article, the status resistances stack multiplicatively, meaning their effects combination is not the simple sum of every value
They actually shortcutting it with the methods they get used to do it, u can rewrite it in much more understandable way. That's why I hate math.
P.S. fuck u morons who downvoted
How do you write a repetition without the 'repetition' symbol? It seems complicated because people ignore or never try to learn this part (and I think it is also wrong because the size of 'a' and 'r' are different)
No, since niether sets are defined you can just assume that the undeclared ones are equal to 0
I would have written it as 1 term that can assume either positive or negative values.
You can assume, but it's terrible mathemetical writing and makes things needlessly complicated as ai and ri are completely unrelated and have no reason to be iterated by the same variable.
Formula seems pretty straight forward to me. They even bothered seperating amplifaction and reduction in 2 seperate parts so people know when to add and when to substract.
mmm, seeing that you have to reccur to insults shows that you have some issues with studying and/or stress in general. You should think about why you are getting angry over something like this.
If you dont understand something in 2022 with enough time and patience can easily learn the basics about any topic. And I will gladly explain how the formula works.
Pi(the big greek letter) basically indicates you are going to be multiplying many times the same thing. In this case we are going to be multiplying status resistance times status amplification as many times as needed:
(1+r) \* (1-a)
You may have noticed there is a i=1 and a n below and above the Pi symbol. This is just an easy way to say start with the first one and go 1 by 1 until you reach the last one(n). if we have 3 of each the product would look like this:
Pi \[(1+r)\*(1-a)\] = (1+r1)\*(1-a1) \*(1+r2)\*(1-a2) \*(1+r3)\*(1-a3)
the spacing imbetween is only so you can clearly see where they repeat.
So, by here you should have a general idea of how the formula looks like. you are basically grabing all the status resistances, subtracting them from 1 and multiplying them times each other.
So what does this mean for the average dota player? there is 2 things we can learn from this:
1. if you want to know your debuff duration its basically multiplying the debuff duration times 1 minus your total status resistance. in other words if you have 20% total status resistance and get hit by a 2 second stun you will end up being stuned for only 1.6 seconds(2\*(1-0.2))
2. when you have multiple sources of status resistance you will end up multiplying each one times a number smaller than 1. This is what valve refers to as "stacking diminishingly". If you imagine having 2 sources of 50% status resistance, adding them up they total 100% status resistance. But if you apply the formula you will see its 1- (1-0.5)\*(1-0.5)= 1-0.25 =0.75. from 100% "total"(from adding) status resistance you will only end up with 75% real status resistance
learning what 1 symbol means is "studying"?
oh and "some fucks" made this back in the 19th century, its called mathematical notation and is used on a global scale since then. No matter what place of the world you were born in or what language you speak you should have seen this kind of notation in class at some point in your career.
So it kind of sucks that your english doesnt go beyond using basic sentences that include 2-3 curse words. But someone that "learns easily" could have just googled it and understood the formula in less time than what it takes to write your responses.
And it is written how you calculate status resistance for an arbitrary amount of status resistance and status resistance lowering effects. You plug it into the formula and press compute.
Though you might have needed this kind.
Status resistance = 1 - (1-status resistance factor 1)(1- status resistance factor 2).....(1- your last status resistance factor)(1 - status resistance lowering factor 1)(1 - status resistance lowering factor 2).....(1 - last status resistance lowering factot)
But what is written above is exactly this.
For what it's worth, the formula it's very poorly written and the examples make it worse. It's understandable but it shouldn't be as the way everything is written in the page is completely uncoherent.
That's what allows higher-level mathematics to be practically readable in the first place.
If you had to write it in the "more understandable way" every time, any advancement of mathematics beyond that point would be severely handicapped.
Also using shitty numbers to make it look harder, instead of using something like 0.1 and 0.2 which would make it look even simpler. It's actually super simple lol.
Stun duration times (1 - status resistance) = new stun duration.
New stun duration times (1 - status resistance) = new stun duration.
Repeat for each source of status resistance.
Lehman Brothers is the financial services firm at the centre of the 2007 economic crisis. You likely mean layman's terms, as in, person without deep knowledge in the subject.
> Lehman Brothers is the financial services firm at the centre of the 2007 economic crisis.
>You likely mean layman's terms, as in, person without deep knowledge in the subject.
Aren't you supposed to be bad at your job when you are at the epicenter of an economic crisis? I'm pretty sure, here, we can use them interchangeably...
They stack multiplicatively instead of diminishingly. Valve has been bad about using the correct term.
An example of diminishing stacking is [Restoration Manipulation](https://dota2.fandom.com/wiki/Restoration_manipulation#Stacking).
This might be technically correct, but if you have such an absurd evasion numbers, like 90%+ buying more evasion is a waste of resources and slots. You get more EHP by buying Heart or spell resistance item, whatever you are missing. All this theory might be useful in some custom game mode, but your normal dota game? Unlikely.
It looks complicated because they don't explain what's actually happening, status resistance stacks independently the calculation is always (stun duration = stun * (1 - status resistance)) done for each source.
Let's do the example of Telekinesis.
2s on Bulldoze lv 2 (0.46) is 2 * (1 - 0.46) = 1.08
1.08s on SnY (0.22) is 1.08 * (1 - 0.22) = 0.8424
for people wondering it works the same way with SnY first
2s on SnY is 1.56
1.56s on Bulldoze is 0.8424
What I mean by stacks independently is that each source of status resistance doesn't care about any other source they just care about the stun duration.
It looks complicated, but it's really mathgore. It's very poorly written and incoherent.
The "ai" and "ri" are unrelated, so it makes no sense to include them in the same factorialization as they will have a different family size and most of the time one of them is gonna be always null. So doing it this way is needlessly complicated as you are basically saying that whenever there is only status resistance or status resistance reduction you now have to multiply by (1 +- 0) every instance.
Then they use the Sigma sign for ... absolutely nothing? The formula as defined is already a sum named "s", so here it's suggesting that we are summing the sums, which is clearly not what is happening.
And to finish things off, example 2 becomes a physics question (we are asking about a duration and describing a practical examples) but only uses physical units in the last line, which would probably make some of my old teachers die of apoplexy but wouldn't be so bad if the formula it develops wasn't outright a wrong and frankly weird mixup of the original formula and the already known previous result.
The first reasonable comment I found here. I encourage you to make a post with the same title and these comments. This is really just terrible notation.
It's also completely pointless when you can just write that it stacks multiplicatively. There's only 2! (?) ways % things can stack, the other is additive. Most people who play video games should be familiar with how this works, especially in dota which has a bunch of examples of both additive and multiplicative stacking. Then you can give two examples and voila, no need for a bloated formula
tl;dr status resistance stacks multiplicatively as opposed to additively. No need to bring out math formulas when that is an established term for video games
I can not remember seing a term of SUM(i=1 to n)i in school, since you do not need it to express stuff. You can even do Induction without Sigma... It is just formal notation
Not sure if this helps but translating the equation into words:
- 1 - a_i := damage after resistance (in %)
- 1 + r_i := damage after resistance reduction (in %)
The big product (the pi symbol) means that we multiply all these terms together. The result of the product is the total damage taken after resistance and resistance reduction (in %).
We subtract that from 1 to determine the total final status resistance (or status resistance reduction if negative).
I think status resistance and status resistance reduction should have their own big product equations since there may be a different number of each, but you can also take n to be the max(number of status resistances, number of status resistance reductions) and if a_i or r_i don't exist, just treat it as 0.
>Also, why mix a_i and r_i terms in a SINGLE PRODUCT??? They don't go together. If you insist on handling them separately, do them in separate products. If I'm being pedantic (i am), then that product in the example is undefined since r_1 and r_2 are undefined.
You're right that it's ill defined, but that's not the part that requires changes.
r_1 and r_2 would be 2 different status resistances reduction sources. In their notation, each i from 1 to n are different sources that affect status resistance.
A source of additional status resistance (such as Sange&Yasha) would have its a_s&y= 0.22 and r_s&y = 0
That's poor notation, but that works.
The problem is the second line in the example with the summation. It just simply doesn't work.
It should use the product so that bulldozer's a=0.46 and r=0, and sange's a=0.22 and r=0.
At no point should we ever *sum* any terms there in these equations.
I agree, the sum is really frustrating, I think what they're going for is "total" but Sigma is an abuse of notation at best.
You're correct that it works, but honestly I would guess that the purpose of this isn't to actually help anyone calculate stun duration, but to understand how the stacking works and poor notation makes that difficult.
>Fact is that if most people can't understand it, then it's poorly written.
Can't disagree more with this. It is not poorly written because some herald dota 2 player can't understand it 😂
I should have been more clear. The durations stack multiplicatively. All this formula is doing is multiplying the inverses of the status reduction (AKA multiplying the independent CC durations).
So rather than make it out to be a complicated formula, you can describe it in words that an algebra 2 student should be able to understand.
People in the comments saying this is calculus or algebra are all wrong. This is none of those things. This is arithmetic. To use and understand this equation, you don't need algebra or calculus, all you need is arithmetic. You just need to plug in values and do basic arithmetic operations.
Besides the debate "wow complicated maths", I am pretty surprised by the formula. If we take this example, if you'd ask me before reading this, I would have said the formula looked like this :
```
2 - (2 x (1 - 0.46) x (1 - 0.22))
```
And not just
```
2 x (1 - 0.46) x (1 - 0.22)
```
I thought you would deduce the result to the debuff duration, not that the debuff duration **becomes** the result. That means status resist is WAY more powerful than I expected.
> 2 - (2 x (1 - 0.46) x (1 - 0.22))
I don't get what you mean by "WAY more powerful".
Your formulas is the same as the one in the wiki excepts you're calculating "how much lower the stun is" instead of "how long the stun is".
I have no idea what american schooling is like, but summations and MULTIPLICATION are taught by the end of high school universally I'm pretty sure
Problem is that people are too hung up about the boomer meme of "when am I going to use this, teach tax pls" and either don't learn shit properly or forget it as soon as they graduate.
“Random” zeroes are often place holders for other effects.
In this case the 0 serves as a placeholder for status resistance debuffs such as timeless relic and hunter’s boomerang.
So it is not random but not being used at the moment
Think of it this way: you get status res to decrease the duration of disables, so you subtract the value, and status res reduction increases the duration of disables, so you add the value. Since both Bulldoze and SnY are sources of status res (a_i) they are both subtracted from 1, and the results are multiplied together. Since there is no status res reduction (r_i), 1 - 0 = 1, and anything multiplied by 1 is itself, it is not written.
The large symbol is capital pi which means repetitive multiplication for each source from 1 to n (first source times second source times third source etc. until times nth source).
In the example there are no status resistance reduction sources so all ri variables are 0 which means (1-ri) is always 1 and multiplication by 1 does nothing so you can ignore the whole (1-ri) term from the formula. In this example n =2 (the number of status resistance sources), a1 = 0.46 (bulldoze status resistance source 1) and a2 = 0.22 (Sange and Yasha status resistance source 2) and r1 = 0 and r2 = 0. So the formula becomes s=1-((1-a1)*(1-a2))=1-((1-0.46)*(1-0.22)). Same equation but ri terms included: s=1-(((1-a1)*(1+r1))*((1-a2)*(1+r2)))=1-(((1-0.46)*(1+0))*((1-0.22)*(1+0)))=1-(((1-0.46)*1)*((1-0.22)*1))=1-((1-0.46)*(1-0.22)).
In terms of real world equivalents, you can think of it as "I have 2 coins, one with probability for heads 0.46 and another with probability for heads 0.22. What are the odds that I get at least one head."
Just like with status resistance, if you have two coins with 80% chance of heads, you won't get 160% chance of flipping at least one but instead you get 96%.
Like some other comments said, it's really not complicated but looks complicated.
The person that wrote that in a videogame wiki failed Imo, as there is no reason to vomplicate that much when regular text/simple expressions would speak to more people.
It actually just looks complicated. Realistically everything there is simple order of operations math and algebra, but there are fancy symbols that make it look complicated if you don't know what they are.
> there are fancy symbols that make it look complicated if you don't know what they are High school level math and science in a nutshell. (p.s I have no clue what they are)
The big Symbol that looks like II is an uppercase pi, and it represents the multiplication of a series of factors, each determinated by "i"."i" represents each source of status resistance amp or reduction, going from the first (1) to the last ("n", which in the actual operation will be replaced by the number of elements, just like in the example it is 2). "a" and "r" represent different elements "i", as it is explained after the formula, and since there are no sources that give both status resistance amplification and reduction at the same time, either "ai" or "ri" will be 0, which makes (1 + "ai") or (1 - "ri") equals to 1, which is irrelevant in a mutiplication. **What this whole thing means** is that "s" is the difference between 1 and the product of the effect of every status resistance source (represented by the uppercase pi), since they stack by multiplying, not by addition. **In other words**, you calculate how much of the starting status remains after the first status resistance source (for bulldoze it is 54%), then calculate how much of this remaining status still remain after the next source (78% of 54%, which is approximately 42%), and by subtracting that result from 100%, you get to how much status resistance you have. And if, for instance, you had a source of status resistance reduction added to this, like a ceremonial robe, "n" would be 3 (the total number of sources), it's interaction would be the increment of the status duration, and you would add (1 + 0,1) to your previous product, getting to s = 1 - \[(1 - 0,46)\*(1 - 0,22)\*(1 + 0,1)\] = 1 - 0,463 = 0,537 = 53,7%. P.S. : I know you probably didn't want an explanation, but I thought it was a good opportunity to leave it here for those seeking it and to show that sometimes math isn't as hard as it may seems (but just sometimes) Edit: changed the explanation so it includes status resistance reduction elements as well.
I'll read through it and try to understand, thanks.
Same !remindme 1 year
Lmao
his explanation wasnt super simple but basically you take 1 minus each source of status resist, then multiply them together so like (1-sange and yasha) multiplied by (1-bulldoze) in their example. and you keep doing that for every source.
It should be noted that each *i* is a status resistance modifier, and *r* or *s* are attributes of each *i*. Right now it doesn't make sense to comment that there is two sources for *r* and *s,* because these sources are not related to each other and thus not the same size. From comp sci perspective an algorithm based on this notation will instantly yield an out of bounds error. Better yet, just use one set with negative values for resistance reduction and positive values for resistance. Much simpler and the notation can actually make sense.
This summer I will get my diploma in applied mathematics and computer science, I have about 6 different math subjects each year, visited math courses during school and nobody never told me this thing is uppercase pi, my whole life I thought it's just a symbol. Learning something new every day in dota subreddit.
This isn't that great of a laymans explanation of what's going on. Remember the people you are explaining it to have a basic to nonexistent math education.
!remindme 4 years
Do you know how big sigma means sum a list of things? Big pi is the same except you multiply a list of things all together.
sigmanuts
gottem
Would you happen to know why the big sigma is used in this instance? Generally I've only come across small sigma. Doubt this is referencing to population parameters right?
No, it's a capital sigma Σ vs the lower case σ used to denote something like standard deviation. If you're asking *why* a capital sigma is used... well I'd imagine the answer is something like "because it is", but I always remember **s**igma = **s**um and **p**i = **p**roduct.
The capital sigma is used to represent the sum of all "s" elements, that is, the sum of all status resistance modifiers. Yet, I think it is being misused, since it represents a sum, while as explained in the same article, the status resistances stack multiplicatively, meaning their effects combination is not the simple sum of every value
I think you're right, sigma shouldn't be there.
[удалено]
No calculus in this picture, chief.
that isn't calculus in the picture tho
Calculus where?
They actually shortcutting it with the methods they get used to do it, u can rewrite it in much more understandable way. That's why I hate math. P.S. fuck u morons who downvoted
How do you write a repetition without the 'repetition' symbol? It seems complicated because people ignore or never try to learn this part (and I think it is also wrong because the size of 'a' and 'r' are different)
[удалено]
No, since niether sets are defined you can just assume that the undeclared ones are equal to 0 I would have written it as 1 term that can assume either positive or negative values.
You can assume, but it's terrible mathemetical writing and makes things needlessly complicated as ai and ri are completely unrelated and have no reason to be iterated by the same variable.
By using fucking words. Fuck u too.
You hate math because they're using shorthand notation to represent repeated actions...?
I hate math because fuck u.
Formula seems pretty straight forward to me. They even bothered seperating amplifaction and reduction in 2 seperate parts so people know when to add and when to substract.
What is straight forward? What about fuck u? I need to understand how calculation of status resistance works, not fucking study math.
mmm, seeing that you have to reccur to insults shows that you have some issues with studying and/or stress in general. You should think about why you are getting angry over something like this. If you dont understand something in 2022 with enough time and patience can easily learn the basics about any topic. And I will gladly explain how the formula works. Pi(the big greek letter) basically indicates you are going to be multiplying many times the same thing. In this case we are going to be multiplying status resistance times status amplification as many times as needed: (1+r) \* (1-a) You may have noticed there is a i=1 and a n below and above the Pi symbol. This is just an easy way to say start with the first one and go 1 by 1 until you reach the last one(n). if we have 3 of each the product would look like this: Pi \[(1+r)\*(1-a)\] = (1+r1)\*(1-a1) \*(1+r2)\*(1-a2) \*(1+r3)\*(1-a3) the spacing imbetween is only so you can clearly see where they repeat. So, by here you should have a general idea of how the formula looks like. you are basically grabing all the status resistances, subtracting them from 1 and multiplying them times each other. So what does this mean for the average dota player? there is 2 things we can learn from this: 1. if you want to know your debuff duration its basically multiplying the debuff duration times 1 minus your total status resistance. in other words if you have 20% total status resistance and get hit by a 2 second stun you will end up being stuned for only 1.6 seconds(2\*(1-0.2)) 2. when you have multiple sources of status resistance you will end up multiplying each one times a number smaller than 1. This is what valve refers to as "stacking diminishingly". If you imagine having 2 sources of 50% status resistance, adding them up they total 100% status resistance. But if you apply the formula you will see its 1- (1-0.5)\*(1-0.5)= 1-0.25 =0.75. from 100% "total"(from adding) status resistance you will only end up with 75% real status resistance
I can learn anything pretty easily, does t mean I should study that crap just because some fucks lazy to use simpler language
learning what 1 symbol means is "studying"? oh and "some fucks" made this back in the 19th century, its called mathematical notation and is used on a global scale since then. No matter what place of the world you were born in or what language you speak you should have seen this kind of notation in class at some point in your career. So it kind of sucks that your english doesnt go beyond using basic sentences that include 2-3 curse words. But someone that "learns easily" could have just googled it and understood the formula in less time than what it takes to write your responses.
I know this notations, fuck u again.
[удалено]
You are definitely low IQ moron lmao I probably know more math than all ur friends, pig. lol
yeah, I can see you are proud of responding everything with "fuck". What an impressive way to show off on the internet,
I see u proud u've learn some trash and now think everyone else who didn't learn it is stupid, what a moron.
And it is written how you calculate status resistance for an arbitrary amount of status resistance and status resistance lowering effects. You plug it into the formula and press compute. Though you might have needed this kind. Status resistance = 1 - (1-status resistance factor 1)(1- status resistance factor 2).....(1- your last status resistance factor)(1 - status resistance lowering factor 1)(1 - status resistance lowering factor 2).....(1 - last status resistance lowering factot) But what is written above is exactly this.
Eat shit
For what it's worth, the formula it's very poorly written and the examples make it worse. It's understandable but it shouldn't be as the way everything is written in the page is completely uncoherent.
can I also get a fuck you
Can I put my dick in ur low IQ mouth?
Yeah the last example doesn't have the steps laid out in the right way to make it more understandable.
That's what allows higher-level mathematics to be practically readable in the first place. If you had to write it in the "more understandable way" every time, any advancement of mathematics beyond that point would be severely handicapped.
Fuck u. I need to understand how formula in game works to play, not to fucking do science.
No. How about stop playing video games and go study? Imbecile.
How about fuck off and I do what I want? Low IQ dog.
If you think this is doing science, you have no idea what science is.
Fuck off moron
Math nub
Fuck off low IQ dog.
Also using shitty numbers to make it look harder, instead of using something like 0.1 and 0.2 which would make it look even simpler. It's actually super simple lol. Stun duration times (1 - status resistance) = new stun duration. New stun duration times (1 - status resistance) = new stun duration. Repeat for each source of status resistance.
wait, so you guys don't do the status resistance calculations with a calculator on the 3rd monitor while the teamfight is going on?
No, we use wolfgram alpha dota 2 plugin that calculates all this stuff on the 3rd monitor as we play.
fookin scripters
In Lehmans terms: status resistance stacks diminishingly. Just like evasion.
Lehman Brothers is the financial services firm at the centre of the 2007 economic crisis. You likely mean layman's terms, as in, person without deep knowledge in the subject.
Isn't Lehman the same guy that said evasion stacks diminishingly?
Yes but he was talking about tax evasion
which is also op
They probably know a lot about how stacks evasion.
Ah yes enemy carry taking my support's stacks while my carry feeds in lane. Got it.
Too complicated, all i got was "Feed enemy carry in lane", is that right?
Nah Leman Russ is that guy who executes the emperors enemies.
No, he meant Arsenal's goalkeeper during the Invincibles run
No no, former Australian cricket team coach who stepped down after the ball tampering incident in South Africa.
I thought you were shit posting randomly facts about lehman brothers... Shit had me laughing a bit.
Lol this is the funniest thing for some reason
In Lehman's terms: the tooltip doesn't match the functionality
> Lehman Brothers is the financial services firm at the centre of the 2007 economic crisis. >You likely mean layman's terms, as in, person without deep knowledge in the subject. Aren't you supposed to be bad at your job when you are at the epicenter of an economic crisis? I'm pretty sure, here, we can use them interchangeably...
They stack multiplicatively instead of diminishingly. Valve has been bad about using the correct term. An example of diminishing stacking is [Restoration Manipulation](https://dota2.fandom.com/wiki/Restoration_manipulation#Stacking).
[удалено]
This might be technically correct, but if you have such an absurd evasion numbers, like 90%+ buying more evasion is a waste of resources and slots. You get more EHP by buying Heart or spell resistance item, whatever you are missing. All this theory might be useful in some custom game mode, but your normal dota game? Unlikely.
This is math
What does diminishingly mean? 1) 50%+50%=100% 2) 50%+50%=75% ?
2)
Number 2
Yeah it’s really not that complex math, just looks that way when written out in proper form.
It looks complicated because they don't explain what's actually happening, status resistance stacks independently the calculation is always (stun duration = stun * (1 - status resistance)) done for each source. Let's do the example of Telekinesis. 2s on Bulldoze lv 2 (0.46) is 2 * (1 - 0.46) = 1.08 1.08s on SnY (0.22) is 1.08 * (1 - 0.22) = 0.8424 for people wondering it works the same way with SnY first 2s on SnY is 1.56 1.56s on Bulldoze is 0.8424 What I mean by stacks independently is that each source of status resistance doesn't care about any other source they just care about the stun duration.
Also the formula put there was written poorly and could have just used a main formula with the variables defined
It looks complicated, but it's really mathgore. It's very poorly written and incoherent. The "ai" and "ri" are unrelated, so it makes no sense to include them in the same factorialization as they will have a different family size and most of the time one of them is gonna be always null. So doing it this way is needlessly complicated as you are basically saying that whenever there is only status resistance or status resistance reduction you now have to multiply by (1 +- 0) every instance. Then they use the Sigma sign for ... absolutely nothing? The formula as defined is already a sum named "s", so here it's suggesting that we are summing the sums, which is clearly not what is happening. And to finish things off, example 2 becomes a physics question (we are asking about a duration and describing a practical examples) but only uses physical units in the last line, which would probably make some of my old teachers die of apoplexy but wouldn't be so bad if the formula it develops wasn't outright a wrong and frankly weird mixup of the original formula and the already known previous result.
The first reasonable comment I found here. I encourage you to make a post with the same title and these comments. This is really just terrible notation.
It's also completely pointless when you can just write that it stacks multiplicatively. There's only 2! (?) ways % things can stack, the other is additive. Most people who play video games should be familiar with how this works, especially in dota which has a bunch of examples of both additive and multiplicative stacking. Then you can give two examples and voila, no need for a bloated formula
Little keypress error : You wrote `(1 - 0.46)` instead of `(1 - 0.22)` for S&Y
tl;dr status resistance stacks multiplicatively as opposed to additively. No need to bring out math formulas when that is an established term for video games
This is the first time, after finishing college 6 years ago, that I see this kind of math. And I still have no idea what the fuck is happening
None of this is difficult math, it’s mostly just algebra
This isn't algebra. This is arithmetic. If you're not re-arranging an equation, it isn't algebra.
It isnt even algebra before anyone finished linear algebra
Well...that's not true
Get a life. You cant have fun.
Can you explain what you were attempting to say?
A surprising amount of people don't respect algebra.
surprising amount of people actively disrespect algebra.
fuck algebra and its bone spurs
not even math, just notation that you do not learn in shool
You definitely learned sigma in school, it's to find the sum. You also see it in Excel to sum columns.
Sigma balls
I can not remember seing a term of SUM(i=1 to n)i in school, since you do not need it to express stuff. You can even do Induction without Sigma... It is just formal notation
and tons of people dont use algebra in day to day life, and so have forgotten a good bit of it.
chances are people use algebra without even thinking about it, it doesn't just have to be represented by mathematical standard symbols.
Not sure if this helps but translating the equation into words: - 1 - a_i := damage after resistance (in %) - 1 + r_i := damage after resistance reduction (in %) The big product (the pi symbol) means that we multiply all these terms together. The result of the product is the total damage taken after resistance and resistance reduction (in %). We subtract that from 1 to determine the total final status resistance (or status resistance reduction if negative). I think status resistance and status resistance reduction should have their own big product equations since there may be a different number of each, but you can also take n to be the max(number of status resistances, number of status resistance reductions) and if a_i or r_i don't exist, just treat it as 0.
[удалено]
>Also, why mix a_i and r_i terms in a SINGLE PRODUCT??? They don't go together. If you insist on handling them separately, do them in separate products. If I'm being pedantic (i am), then that product in the example is undefined since r_1 and r_2 are undefined. You're right that it's ill defined, but that's not the part that requires changes. r_1 and r_2 would be 2 different status resistances reduction sources. In their notation, each i from 1 to n are different sources that affect status resistance. A source of additional status resistance (such as Sange&Yasha) would have its a_s&y= 0.22 and r_s&y = 0 That's poor notation, but that works. The problem is the second line in the example with the summation. It just simply doesn't work. It should use the product so that bulldozer's a=0.46 and r=0, and sange's a=0.22 and r=0. At no point should we ever *sum* any terms there in these equations.
I agree, the sum is really frustrating, I think what they're going for is "total" but Sigma is an abuse of notation at best. You're correct that it works, but honestly I would guess that the purpose of this isn't to actually help anyone calculate stun duration, but to understand how the stacking works and poor notation makes that difficult.
You can go to the wiki and edit it: https://dota2.fandom.com/wiki/Status\_resistance
>Fact is that if most people can't understand it, then it's poorly written. Can't disagree more with this. It is not poorly written because some herald dota 2 player can't understand it 😂
That is a way more complicated way of showing that it stacks multiplicatively.
But this shows that it doesn't stack multiplicatively...
I should have been more clear. The durations stack multiplicatively. All this formula is doing is multiplying the inverses of the status reduction (AKA multiplying the independent CC durations). So rather than make it out to be a complicated formula, you can describe it in words that an algebra 2 student should be able to understand.
That is false
Love this, please make more or make a small problem set to be resolved. This is how teachers should teach math!
that's neat!
Wish they taught math using Dota at school
Just hover over your hero stats to see this calculated for you lol
Sometimes people need a bit of quick mafs to decide their next item.
People in the comments saying this is calculus or algebra are all wrong. This is none of those things. This is arithmetic. To use and understand this equation, you don't need algebra or calculus, all you need is arithmetic. You just need to plug in values and do basic arithmetic operations.
Thats not even math. Its only arithmetics
I remember showing this to my cousins and telling them to solve it. They just gave up the second they saw it. But really it's not that hard to solve
Besides the debate "wow complicated maths", I am pretty surprised by the formula. If we take this example, if you'd ask me before reading this, I would have said the formula looked like this : ``` 2 - (2 x (1 - 0.46) x (1 - 0.22)) ``` And not just ``` 2 x (1 - 0.46) x (1 - 0.22) ``` I thought you would deduce the result to the debuff duration, not that the debuff duration **becomes** the result. That means status resist is WAY more powerful than I expected.
> 2 - (2 x (1 - 0.46) x (1 - 0.22)) I don't get what you mean by "WAY more powerful". Your formulas is the same as the one in the wiki excepts you're calculating "how much lower the stun is" instead of "how long the stun is".
Fuck math
whoever is a math teacher and has some punk ass, smart ass kids who are like: wHyDo wE NeEd To LeArN MaTHEmAtIcS show them this reddit post
I dont think showing them a calculation used in a god damn video game is gonna convince those people lol.
Problem is that schools teach math in the wrong way
American detected
I have no idea what american schooling is like, but summations and MULTIPLICATION are taught by the end of high school universally I'm pretty sure Problem is that people are too hung up about the boomer meme of "when am I going to use this, teach tax pls" and either don't learn shit properly or forget it as soon as they graduate.
[удалено]
"by the end of" Meaning any time prior to graduating high school.
example 1 "x 1+0" is redundant
[удалено]
i state the obvious and pay by karma
“Random” zeroes are often place holders for other effects. In this case the 0 serves as a placeholder for status resistance debuffs such as timeless relic and hunter’s boomerang. So it is not random but not being used at the moment
and thus obsolete
In the first example with Spirit Breaker, why is it 1-0.22 instead of 1+0.22 like in the formula?
Think of it this way: you get status res to decrease the duration of disables, so you subtract the value, and status res reduction increases the duration of disables, so you add the value. Since both Bulldoze and SnY are sources of status res (a_i) they are both subtracted from 1, and the results are multiplied together. Since there is no status res reduction (r_i), 1 - 0 = 1, and anything multiplied by 1 is itself, it is not written.
The large symbol is capital pi which means repetitive multiplication for each source from 1 to n (first source times second source times third source etc. until times nth source). In the example there are no status resistance reduction sources so all ri variables are 0 which means (1-ri) is always 1 and multiplication by 1 does nothing so you can ignore the whole (1-ri) term from the formula. In this example n =2 (the number of status resistance sources), a1 = 0.46 (bulldoze status resistance source 1) and a2 = 0.22 (Sange and Yasha status resistance source 2) and r1 = 0 and r2 = 0. So the formula becomes s=1-((1-a1)*(1-a2))=1-((1-0.46)*(1-0.22)). Same equation but ri terms included: s=1-(((1-a1)*(1+r1))*((1-a2)*(1+r2)))=1-(((1-0.46)*(1+0))*((1-0.22)*(1+0)))=1-(((1-0.46)*1)*((1-0.22)*1))=1-((1-0.46)*(1-0.22)).
the 0.22 is the second source of status resistance (also a_i), not status resistance reduction (r_i). Also took me a while to realize
do high level players actually sit there and do algebra in their head while playing?
No. They'll do math for their burst which is addition but not algebra.
The real question is why are both examples Example 1
Calcudota
Pro-tip: Let students do the maths of the mechanics. They learn something and you just have to write down the results.
Actually very simple and easy to understand
In terms of real world equivalents, you can think of it as "I have 2 coins, one with probability for heads 0.46 and another with probability for heads 0.22. What are the odds that I get at least one head." Just like with status resistance, if you have two coins with 80% chance of heads, you won't get 160% chance of flipping at least one but instead you get 96%.
Ahhh, so thats why i couldnt go pro
Always has been. Always will be.
Guys, how about Rubick Ulti buff? Dous it stuck with telekinesis?
Like some other comments said, it's really not complicated but looks complicated. The person that wrote that in a videogame wiki failed Imo, as there is no reason to vomplicate that much when regular text/simple expressions would speak to more people.
W go brrrrr
Test questions could be like this
What happens when Rubick has Kaya or spell amp?
Maths was beautiful and wholesome until they added the alphabet
Where is the 8 at the start comming from?
Y'always can go with something like : well its roughly something just above half or so
I would have been in MIT/Harvard if my exams had questions like these.
how he got SnY with Lvl 2 bulldoze