3w ago

Percentages

130 comments

Can't believe nobody has linked the relevant xkcd yet
- We appreciate your service.
  
  🫡
- 🫡
- Which of course is why people referred to points when discussing stocks/markets. Got to love an unambiguous term.

Having two possible outcomes does not mean it's a 50:50 chance.
"So if I aim the arrow at the 1cm square from 100m away and shoot, I either hit it or I don't. So basically I have a 50% chance of hitting it."
- My wife, father-in-law and I were playing a board game with my brother-in-law. In this game, we were playing as detectives who have to try to find his character, but each turn he could move in secret in one of several directions. We were a few turns in at one point and he could have been in any of dozens of places at this point. We drove him nuts by saying "he's either in this spot or he's not, it's a 50-50 chance." He kept arguing "I could be in a ton of places! It's not a 50-50 chance!" But we just kept pretending we didn't understand and arguing that there were only two possibilities, he's there or he's not, so it was clearly a 50-50 chance. He got quite angry.
  
  Scotland Yard or Letters from Whitechapel?
  
  Letters from Whitechapel?
  Either that or you buried the lede by failing to mention something rather significant about the hidden character, and you were playing Fury of Dracula. Or my boardgamegeek-fu isn't as strong as I hoped.
  
  you know, if you watched for tells, that could tilt the probabilities... and I bet with the frustration... he was flashing tells all over the place...
- Either I become president, or I don't.
  Therefore, the odds of me becoming president is 50%
  Brb committing 34 felonies.
  
  You've already failed.
  You have to commit hundreds of felonies. In broad daylight. And brag about it.
  Threaten witnesses. Delay everything.
  And only be convicted of 34.
  Then not get sentenced.
- Very weird fun fact about arrows/darts and statistics, theres 0% chance of hitting an exact bullseye. You can hit it its possible to throw a perfect bullseye. It just has a probability of zero when mathematically analyzed due to being an infinitesimally small point. Sound like I'm making shit up? Here's the sauce
  How can an outcome both be entirely possible and have 0% probability?
  
  Q.E.D
  
  Key word here is "infinitesimally." Of course if you're calculating the odds of hitting something infinitesimally small you're going to get 0. That's just the nature of infinities. It is impossible to hit an infinitesimally small point, but that's not what a human considers to be a "perfect bullseye." There's no paradox here.
  
  You must not be playing on a soft tip board.
- On the other hand: Half of my lottery tickets were jackpots. I never played and have (1/2 0 = ) 0 jackpots.
- The thing with that is that it's actually a useful generalization to make in a lot of scenarios.
  If you know nothing about the distinction between two possible outcomes, treating them as equally likely is a helpful tool to continue with the back of the envelope guess. Knowing this path needs 5 coin tosses to go right and this one needs 10 is helpful to approximate which is better.
  Your example is obviously outside the realm where you have zero information, so uniform distribution is no longer the reasonable default. But the idea is from a reasonable technique, taken to extremes by someone who doesn't fully get it.

That's not even a stat question, it is a english question. It is an increase by 80% not to 80%
Statistics only come to play to figure out our new chances.
- Maybe I'm wrong but by writing "increase by 80%" there is ambiguity you don't get if you instead spelled out:
  Increase by 80 percent
  Increase by 80 percentage points
  
  I'm not an expert either and your second option is definitly clearer than mine but I believe the % symbol doesn't have the meaning of percentage point.
  It is better to make things easier for people to understand but people should also make the effort of properly reading even when it is not fully dumbed down. These are prepositions, so basic english not scientist jargon.
- Or "by 80 percentage points"
  
  "By 80 percentage points" means add 80 more points to a number of percentage points, so 5% becomes 85%. "By 80 percent" means add 80 percent of the current value.

In game design, it has to be stated whether it’s multiplicative or additive. Sometimes a logarithmic function is used as well, with increases in efficiency as 1 / ( 1 + bonus ). This allows you to always add more bonus, but there’s diminishing returns.
- i wish it was more common to also indicate the precedence of a percentage increase, so that it’s easier to know if i’m dealing with (x + y ) * z or x + (y * z). although that’s admittedly a lot harder to communicate.
  
  Just include a glossary of formulas for figuring out stats/chances/whatever in your game. With clearly labeled variables. Then throw a reference to that glossary in your tooltips/helpful popups.
- This upgrade adds +100% critical chance.
  The weapon has a base critical chance of 10%, so the new critical chance is 20%, not 110%
  
  In game design +100% would be 10% + 100% = 110% crit.
  Increases by +100% = base + 100%
  Increases by 100% = base + base x 100%

When my son was about to be born my mother in law caught wind that we didn't plan on circumcising (before researching it I mostly felt it was just strange to do cosmetic surgery on a newborn) but her argument was mostly parroting the 50% reduction in this that and the other disease, missing the fact that it was going from a 0.5% chance to a 0.25% chance, but of course introduced new risks by nature of being a surgery.
Naturally after looking more into it I learned just how bonkers circumcision is so I was far more cemented in my position
- The fact that it is even allowed in so-called civilized countries is outrageous. In the US it common because some religious nut was obsessed with children's masturbation.
  
  Which is nuts, as a circumcised individual (medically necessary, my parents aren’t monsters) I masturbated A LOT as a teen.
- it baffles me that anyone with a penis, or really anyone who knows what a penis actually is, would think it's a good idea
  would people remove a child's eyelids? NO OF COURSE NOT holy shit
  piercing flesh is generally to be avoided unless absolutely necessary, as is helpfully indicated to us by it being fucking painful

I play video games; I need to know if the percentage is additive or multiplicative.
"+100%" looks pretty good until you see what "×25%" actually gives you.
- ×25% gives you 1/4 the original value, whereas +100% is double the original value, let's say 8/4 to keep it consistent. ×125% (in case a 1 is missing) is still only 5/4 the original value.
  Is there a typo in your comment?
  
  In video games they commonly use that to mean they are multiplying by 25. We know it's not correct in stats. This is why game wikis commonly put the actual formula for things rather than the tooltip the developers wrote.
  
  I feel they might've left something out. If you're at base value still an additive 100% increase (1+1=2) is better than a multiplicative 25% (1×1.25=1.25) increase but in games where bonuses stack another additive 100% increase would raise the effective value by 50% instead (1+1+1=3) whereas another multiplicative 25% would still raise the total by that much (1×1.25×1.25=1.56) so if you're stacking a lot of bonuses, eventually the multplicative ones are more effective. As for how many steps it would take to be equal in our example... 1+1×X=1×1.25^X I'm not gonna do this in my bed on my phone but that equation should already tell you that the right side grows faster when X -> infinity

I work in a place full of statisticians, and we've had to unfortunately have numerous conversations with some of them about the difference between "a decrease" and "a decrease in the rate." Apparently "it's increasing slower" isn't clear enough for some.
- Maybe I'm understanding wrong but a decrease in the rate would be the derivative of a decrease. Aka the slope of the line. So if you are decreasing at -x. Rate of decrease is -1.
  Unless I follow your wording incorrectly. Obviously it isn't always so nice of a function in real stats. Is that what they are missing?
  
  I think it's more y=5x and then y=3x, so you're still increasing, but the rate of increase has decreased. Versus y=-x where the function is now decreasing.

It's really pretty simple - if something increases by 80%, you add 80% of whatever it already is... one dollar becomes $1.80... one percent becomes 1.8 percent.
Most people don't understand it because they've seen it done wrong so often, the wrong way seems right.
- I'm quite willing to bet that 70% of the population has no clue that percentages, fractions, and decimals are the same thing.
  
  https://www.snopes.com/news/2022/06/17/third-pound-burger-fractions/
  
  That's about 60% more than expected
  
  Then odds show up to the party and upend everything we thought we understood.
  
  I think you can increase that by about 7.5/10%

I've always wondered how to disambiguate multiplication and addition of percentages. I guess that's what percentage points are for?
- 10% of your people vote for a party.
  The votes increase by 10% => now 11%
  The votes increase by 200% => now 30%
  The votes increased by 50 percent points => now 60%
- The annoying part is that there is no well-known notation for showing percentage points, so people use % for both percentages and percentage points.
  
  In deep rock galactic survival, the color of the number is different for percentage and percentage points
  
  I like how some games use "increases by +10%" as percentage points and "increases by 10%" as percentage.
  Or how oath of exile does it, with "(base + base * increases by y%) * z% more"
  So with a base of 5%, chance increased by 20%, and chance increased by 30%, with a 40% more chance, you'd get:
  (5% + 5% x (20% + 30%)) x (1+40%) = 7.5% x 1.4 = 10.5%
- Exactly. Unfortunately, they aren't used widely and consistently enough. Even in the press. So you frequently have to second guess what you're reading.

Difference between increase of x% (old percentage + old percentage * x%)% and increase of x percentage points (old percentage and x)%

Wrong: I had a 1% chance, and I doubled my chances. Now my chances are 101%.
Right: I had a 1% chance, and I doubled my chances. Now my chances are 2%.
Wrighongt: I had a 1% chance, and I doubled my chances. Now my chances are 3%, because I'm a lucky person.
- Sleep deprived fraction lover: I had a 1% chance, and I doubled my chances. Now due to 1/100 * 1/100 I chances are 0.0001%.

People got this wrong about inflation as well. In 2020 there was actual deflation, and in 2021 there was very minimal inflation, meaning prices were still largely lower or similar as 2019. Then we saw 9% inflation in 2022. Total inflation in 2024 vs the 2019 benchmark was around 15%. Or 3% average per year, which is barely over the baseline. People just hear 9% inflation, completely missing the fact that this was a YoY number relative to the Trump recession.
- And then there was that bogus article that said Argentina had lowered it's inflation to 2% and you find out in the article that's monthly inflation and the yearly figure was like 190%.
  
  If they managed to decrease from 190%/year to 2%/month (which is 27%/year) that's still an impressive result. Not as impressive to publish when you want to make a click bait.
  I'm not sure how to put that to percentages thought, is it 86% and 143 percent points decrease?
- Drag doesn't know exactly what the problem is, but the official inflation figures cannot be right. Housing is so much more expensive. Food is more expensive. And it's not 9% more expensive. Drag knows they say the math takes into account the price of rent, but they've gotta be lying somehow. It's impossible that the cost of living is rising so much faster than inflation. Those should be the same. If they're not the same, someone's math is wrong.
  
  I keep track of my grocery bills going on 10 years now and 14-15% is spot on for what I buy.

So you're telling me there's a chance?

well it's ambiguous. Its also a sloppy way of expressing an increase by 80 percentage points.
- That's not sloppy, that's simply wrong
  
  Fair enough, I'm inclined to agree. It's a relatively common error though, still leaving it ambiguous outside of circles where you expect people to express themselves with mathematical precision.

That's why when presenting numbers at work, we always distinguish a movement of X % (percent) from a movement of X ppts (percentage points)

Dark Souls cleared this up for me real quick.

I know all this. I play DPS!

Why lying with maths is so easy, the average person, even in developed countries is practically innumerate (massive hyperbole, but the fact lying with numbers is easy, still stands)

In the same vein, if the volume on your phone is on 1, and you increase it to 2, it has increased by 100%
- Kinda. Logarithms are weird
- i think

Convert percentage to fraction, i.e, 80% become 0.8 Then multiply with initial value
If it says 80% more use initial + (initial80) or simply initial1.8
Or if it says 80% less, use - in above calculation or multiply by 0.2
I find percentages more neat when used as fractional number Edited to escape the multiplication symbol
- It's really not even converting, as percent is literally "1/100" (per-cent = per 100). It's purely convenient shorthand.
  
  Yeah, the math straight up works in the fractional form
- I said that to a friend of mine how to get percentage by creating fraction. They were flabbergasted at the sorcery.
  The friend is a Doctrate of biological sciences and a professor. Where as I am just an engineer.
- Convert percentage to fraction, i.e, 80% become 0.8
  That's not a fraction.
  ⅘ is a fraction.
  
  You know we say "a fraction of something" with a number(usually between 1 and zero) often denoted by letter epsilon. 4/5 equals 0.8 so there is nothing wrong in calling that a fraction too
  Edit: Its called Decimal Fractions
  
  This is just annoying pedantry you know what they meant.

Even more confusing when you hear that the odds of catching a disease have increased by a %. In many ways odds can be more intuitive, but we're so used to working with simple probability that it's a total nightmare to wrap your head around at first.

Did this turn into an /iamverysmart thread ?

The different ways in which numbers slide up, down, sideways, diagonally.
Is the example in the post part of the fifth type of arithmetic?
Addition +
Subtraction -
Multiplication x
Division /
Modulo %
The first time I learned about modulo as its' own branch of arithmetic was long out of school already, I had only hazily heard of it, on a PBS Nova documentary in the 1990s about Fermat's famous theorem and when it was proven after centuries of failed tries.
- No it's not modulo, it's how to talk about increasing a number by a percentage of the number.
- Yeah we just learned "by" was a standard term for multiplication. So increased by 80% was just 1.8 times whatever you started with. "Divide by" meaning multiply inversely
  Language translating to artithmetic. I'm sure it doesn't always line up, as we change language quite often.

hopeful-weirdo just needs to be told to consider what increasing by 500% means and it'll click.

huh, this feels pretty well established here in sweden: whenever people talk about stuff like elections it's consistently percentage points

I think it's ambiguous and the 90% actually makes more sense. If you increase something by 5m you are taking the original value and adding 5m to it. For multiplication you should probably avoid the word increase and say scaled by instead. 10% scaled by 180% is 18%.

Ever seen girl math?
"If I preload my Starbucks account with $25 and I go to Starbucks the following week, my order was free."
"Spending money abroad doesn't count because it's a different currency."
Things aren't mathing as they should.
- What makes this “girl” math?
  
  Sexism 👉👉
  
  Stupid people standing on soapboxes saying stupid shit.
  Back in my day, people had to dedicate years of their life before they were given the opportunity to stand in front of hundreds of people and tell them things.
  
  Anecdotally, I've only heard women use that sort of argument IRL. Kinda falls in the, "This widget is 80% so I'm saving money!"
  Well, no, not if you didn't have to purchase the widget in the first place.
  Men are hardly immune, but in my experience it's more so women.
- ah yeah girl math where
  "common irrational human psychology" + "deepseated hatred of women" = whatever the fuck this take is
- As I recently learned,
  "If I return clothes to the store (store credit), but then buy new clothes (using that store credit), those new clothes are free. (No new money spent)"
  
  They aren't free but they are a sunk cost so you might as well

130 comments