Formula for turning decimal percentage to odds

Factual Questions
1

I suck hard at math - I have no trouble with the concepts of essential math, but I’m fairly clueless when it comes to whipping out the equations and formulas necessary to getting where I want to go. Recently I was trying to figure out the odds of being killed by a dog compared to the number of times dogs and humans encounter each other yearly, like so:

83 million dogs in the US.
365 days per year.
Assume all dogs encounter at least one human being at least one time on every one of those days. (A ridiculously conservative assumption, obviously)

So that gives us 30,295,000,000: 30.3 billion human/dog encounters yearly.

Last year, there were 34 fatalities caused by dogs.

Because these numbers happen to be pretty simple, it’s easy to just ballpark the obvious: 34 deaths, 30.4 billion encounters, fair to call it 1 in a billion.

But what if they weren’t so obviously easy to ballpark or I needed a more precise answer? What is the actual formula for odds?

I tried at first to divide 34 by 30.3 billion, and I got a wacky decimal percentage: 0.0000000011223…I believe this means I can state that there is a 0.0000000011223% chance of being killed by a dog in any given encounter with one.

But what is the formula for turning 0.0000000011223% into an expression of the odds? I feel like the answer might be to divide the larger number by the smaller, but it also feels like that isn’t entirely accurate. If I divide 30.3 billion by 34, the answer I get is 891,029,411.76470588235294, which I guess is close enough to “one in a billion” for me to think that might be right, but I rarely trust myself when it comes to this stuff.

I think this breaks my brain because the percentage is so much less than 1. When I’m working with percentages larger than zero, it’s pretty easy, but when the percentage is a teensy fraction of 1… my head breaks.

Assuming I effectively conveyed what I am trying to learn, I thank anyone who will enlighten me about how to do this. And again: if it is possible, PLEASE just give me the barest boned, super-simplest “add X to Y, Divide by Z, the result is 1 in _____” because if it gets too complex my head starts to hurt really badly. :slight_smile:

2

I didn’t check your math, but your division method seems correct to me…

If you divide 30.295/34 - the ratio should be the same (start with 0.89…)

3

Note that some would not consider these odds persay - more probability. Often odds are expressed as chance it will : chance it won’t

Not a big deal with 1bill:1

Odds of coin being heads 1:1
Probabilty of same 1 in 2

4

When you divided 34 by 30.3 billion, the number you came up with is a probability estimate. To convert to odds, you subtract the numerator from the denominator, then compare that number with the numerator.

In a simple example, if the probability was 1/10 or 10%, the odds would be 1 to 9. Or you could say that as 9 to 1 against.

In your example, the probability is just a rough estimate, and is so close to zero that there’s not much point in doing the subtraction step, so you would just say a billion to one, which is more or less what you did.

5

So, formally… If there is one chance in a billion, the odds are 999,999,999 to 1?

What if there’s 817 chances in a billion?

(Gads, I used to know this stuff…)

6

Its as accurate as the numbers you started with.

There is a process for turning a % into a "1 in X " odds…

Start with P %

So its "1 in 100/P "

P=5% ? 1 in 20. P= 0.1% ? 1 in 1000

7

Percentage is (number of hits) / (number of possibilities) = decimal percentage

Odds are (number of hits) : (number of failures), where the two numbers must add up to the total number of possibilities.

Thus, rolling a six on a standard die is 0.16667 percent probability, and 1:5 odds. It’s easier if you remember that probabilities are “in” and odds are “to” - that is, you have a one in six chance but one to five odds.

8

As Amateur Barbarian pointed out, "1 in X’ is not a statement of odds, but of probability.

9

This wiki link does most of the probability statistics for you and provides breed specific breakdown.

10

I wasn’t looking for that, but thanks anyway.

11

Ahem… I feel a migraine coming on…

Peeps, thank you for your time and effort. 'preciated. But I was deadly serious when I asked for a formula or equation as simple as possible. Y’all have me wandering around in a forest of vernacular that’s kinda making me wanna cry.

12

Subtract the numerator from the denominator and compare the result to the numerator. So if the probability is A/B, then the odds are A : (B-A). If you’re dealing with a percentage, the denominator is always 100, so if the probability is N%, the odds are N : (100-N).

13

I guess it’s kinda the same with math for you guys as language is for me: to you, it is simple, straightforward to say things like this. But no, it’s not for those of us who struggle.

Can someone PLEASE PLEASE PLEASE PRETTY PLEASE give me the formula in words that a THREE YEAR OLD could probably understand. Words like “bigger” “smaller” and sooooper simple equations, hopefully confined to +, -, X and / in place of the kind of divide symbol I grew up with.

I was a freakin’ genius kid in every subject up to about third grade, when I was confronted with multiplication. My brain froze and I was in remedial math for the rest of the time I was in school. I never took algebra (or anything that follows), because I couldn’t pass grammar school math. I know it was largely a psychological block, but that doesn’t matter, because it resulted in my missing out on BOATLOADS of basic math that everyone takes in grammar, middle, and high school. I have since educated myself about a lot of it, but it’s very piecemeal and focused on what interests me.

So throwing around terms that you think my brain should just instantly understand and be able to apply to what I’m trying to do…no. Yeah, I learned what a denominator and numerator were…multiple times. Because it didn’t stick. And that was decades ago. So expecting me to know which is which generally, much less how they apply to my formula…? No. Head hurt. Me no can do. Then to throw in odds vs. probability, expecting me to instantly recognize which is which and get all fancy with the algebraic stuff? I laugh til I cry.

So please… pretend I am a bright 5 year old.

Thanks.

14

But it would normally be quoted as “5:1”, “five to one”; when “the chances of anything coming from Mars are a million to one”, we mean it’s a million to one against.

For small probabilities, Stoid, you can figure that a one in a billion probability and one in a billion odds are the same thing within acceptable limits of accuracy.

Otherwise, if the percentage chance of something happening is x%, then the odds against it is (100 - x)% : x%, and then the % can be eliminated from both sides of the odds ratio (because it just means “divided by 100”, and if you’re dividing both sides of a ratio by 100 then you might as well divide neither side). Hence:

Percentage chance: x%
Odds against: (100 - x) to x

Example: “There is an 11% chance it will rain tomorrow”
Odds of rain tomorrow: 89 : 11 against, or 8:1 against in round numbers.

15

In other words, plain English vs. the vernacular of math. Because I understand what I’m trying to do but only if we stick to talking about it in the the most simplistic, common, Anglo-Saxon words, vs. the Latinate.

16

This is very close, and actually I pretty much already understand it. But once the percentage is LESS THAN ONE.… that’s where I lock up. Can you do the above showing me how it works if there is a .000349% chance of rain?

17

Then the chance it won’t rain is 100% - 0.000349% = 99.999651%

So the odds of rain are 0.000349 : 99.999651

You can divide both of those numbers by 0.000349 to simplify things. A number divided by itself equals 1, of course. 99.999651 divided by 0.000349 comes out very close to 286532. So, the simplified odds are 1 rainy day vs. 286532 non-rainy days.

18

Don’t use percentages; that’s just making things more complicated. When you divided 34 by 30.3 billion, you got 0.0000000011223, not 0.0000000011223%. Your probability of being killed by a dog is 0.0000000011223, it is not 0.0000000011223%. If you insist, you could say that it’s 0.00000011223% (that’s the result of moving the decimal point over a couple of places), but it’s not really useful to do so: Either way, it’s still a big ugly mess of numbers, so you didn’t really simplify anything, and all you accomplished was making it harder to do any further math with it.

19

This is really too complicated for you?

20

I’d round the numbers, for a start. 0.0004% is 0.000004, which is one quarter-millionth, and then I’m quoting the odds as a quarter million to one. (That’s not far from the more accurate figure that AGuy worked out, and the impact on the audience is about the same.) But as suggested, percentages weren’t really helping you in the first place, and you might as well have given them a miss.