3x as much storage space!
3x more storage space!
I thought “as much” meant you get that many times, e.g. 3 in the example above, and “more” meant you get the original + that amount, so 1+3=4. This seems to be true for quantities between 0 and 1:
50% as much fat!
50% more protein!
But for higher quantities, they seem to mean the same thing - same as “as much”. So if something has “150% more hamsters”, do they mean the final has 150% or 250% the original?
I think it means “two times more.”
I have a box that holds one cubic foot. I have another box that holds three times as much, i.e., three cubic feet. That’s two cubic feet more.
3 x as much = 2 x more.
ETA: 150% more hamsters means 250% of the original amount. I had 100 hamsters, but with 150% more, I now have 250 hamsters.
Messy little blighters…
For higher quantities, they asymptotically approach being the same thing.
Start with 10 hamsters.
2 times as many = 20; 2 times more = 30.
20 times as many = 200; 20 times more = 210.
200 times as many = 2000; 200 times more = 2010.
2000 times as many = 20000; 2000 times more = 20010.
The bigger the factors get, the closer (percentage-wise) the “times as much” gets to the “times more,” but they’re never equal.
If I was writing a math book, 3 times more than 100 would be 400 and 3 times 100 would be 300.
However, in everyday language - especially advertising - the two constructions seems to be interchangeable.
Welcome to one of my pet peeves. It seems the language of advertising deliberately obfuscates the meaning in these kinds of statements. As a result statements in common parlance lack precision and can be interpreted ambiguously or even actually be ambiguous. The mathematical idea is always pretty straightforward but the decoding from English to mathematics is problematic. In this context I am required to teach percentages to secondary school students with little mathematical nous. They regularly get drowned in the language.
“Up to three times less fat than regular margarine.” Meh. Has no precise meaning and the advertisers know it.
Yes, fer sure they do that on purpose. Another pet-peeveworthy bamboozlement is the use of the word “significant” in advertising. They use it in the scientific statistical sense, which may be technically accurate and truthful — but the technical meaning is very precise and specific, and not quite what the typical TV viewer understands the word to mean.
I’ve likewise always wondered what “X times less” is supposed to mean. 
Best guess (assuming it means anything at all), is “1/X[sup]th[/sup] as much”
As for the OP’s example of 250% more hamsters: Coming from an SDMB participant, that’s just wishful thinking.
In any case they would always add the magic words “Up to”. Thus allowing for any conceivable variation.
There was a case here concerning (I think) Farleys rusks (biscuits made for teething babies to chew on) which were advertised as having 50% lower sugar content, without specifying to what they were comparing the product. In fact there was more sugar in a single rusk than in a chocolate biscuit.
Newspaper Tour Guide: And each paper contains a certain percentage of recycled paper.
Lisa: What percentage is that?
Newspaper Tour Guide: Zero. Zero is a percent, isn’t it?
Or better yet, “up to [whatever] and MORE!” 
If someone told me I was getting 100% more flurm, I’d assume that’s twice as much flurm.
If someone told me I was getting 1 times more flurm, I’d think he was crazy.
It’s actually fairly consistent that, when you’re giving percent increases, it’s on top of the original amount, and when it’s not percentage, it’s just a straight multiplication. Just don’t ask me why that is.
There was a recent article in American Scientist calling for a ban on the word “significant”, even in technical writing. That wasn’t just a side comment–it was the whole point of the article.
Aye! That one is absurd! A recent issue of Science News tripped over that usage, and the editor acknowledged its awkwardness. If I have ten hamsters, and tomorrow I have “seven times fewer” – does that mean I now have negative sixty hamsters? That’s what it sounds like it should mean. But, yeah, in the (stupid!) common language of advertising, it would mean I have either 10/7 of a hamster…or maybe 3/7?
negative sixty hamsters seems about right for the boards at the moment.
This one used to piss me off, but now it kind of amuses me.
SAVE UP TO 60% OR MORE.
Lexically parsed, this means “It might be full price. It might be free. Or it might be anything in between. But 60% is what you’re going to remember!”
I read this:
“More than three times less salt”
I got nothin on that one.
Yeh, it’s the homonym “times” that is causing the confusion. Usually on purpose.
There’s the usage of “times”, as in “Wooo! Riding that shark was fun, let’s do that three more times!”. So, you’d be riding the shark 4 times total.
This isn’t the same as the mathematical operation of multiplication, which we call “times.” There would be no preceding measure of something, as in the first example, which would be compounded upon; so it’s pure multiplication, where you’re starting from pure quantities.
Marketing relies on crap like this, purposefully conflating these two words, to maximize whatever might sound like a better bargain to consumers.
For example, what sounds better?
**“200% more ChumBites!™” ** (50 oz of original-size ChumBites™ x 200% = 100 oz total)
or
**“Now with Two Times as Many ChumBites!™” **(50 oz of original-size ChumBites™ plus two more… +50 oz, +50 oz = 150 oz total).
If you were in the ChumBites™ Business, and were promoting 100 oz over the original 50 oz can for the same price, you could argue that “Two Times as Many” vs. 200% is just semantics, and argue for one over the other if you were ever called on it. So, being shrewd, you wouldn’t let a silly conflation like that get in the way of printing the latter example on every can, would you? No, you’d use it to your advantage.
Which is why I always buy my flurm in bulk. I save 100% more on two times as many flurms that way.
Dammit, that was the one that I was going to mention. Doesn’t piss me off, just makes me laugh as it’s essentially meaningless.
I don’t understand this - the last paragraph is saying “two times as many” is the same as “200%”, but the calculations say they’re different. Also, the calculations for times and percent seem mixed up (200% more should be 150 oz, two times as many should be 100 oz).