I'm afraid the only general distinction is the one you have already named: do = perform and make = create.
But that is no more than a general tendency; as your examples show, in any specific instance either or both may be relevant, and at some point in the history of the language one has earned more favour than the other.
It's often possible to see a reason why one is used rather than the other in a particular situation, and that's useful for remembering which one is used; but it is of no value in predicting which one is used when you encounter a new situation. For instance:
You complete your homework assignments, which included writing down the answers to a series of questions. It seems that should be 'making' your homework, but in fact the proper phrase is doing your homework. You might remember this by considering that sometimes your homework doesn't call for you to 'make' anything: it might be reading a chapter in your textbook. The important thing is you did the tasks that were assigned.
You agree to act as the fourth person in a game of contract bridge. You would think this would call for 'do', since you are performing a role; but in fact you make a fourth. You can remember this by noting that what you are doing is “making” a complete table of players—would that have occurred to you before you encountered the phrase?
There's just no telling. You have to learn the right term case by case.
The form, X is [number] times the size of Y
always means X is [number] times bigger than Y
.
The form, [number] times smaller
is perfectly acceptable, clear (not ambiguous in any way), and is often more popular or even the only idiomatic form in common usage. I'll call this the Times Smaller Form. The preference (aka "popularity") for this usage (instead of the Fraction Form) grows as [number]
gets bigger. This is demonstrated in the following Google Ngrams.
Google Ngram Three, Four
In these Ngrams, positive values means the Times Smaller Form is more popular and negative values means the Fraction Form is more popular. (See footnote #1 for an explanation of the Ngram equations.1) Note above that the only instance (in this Answer) where the Fraction Form is more popular than the Times Smaller Form is "one third the size". In all other cases (in this answer), the Times Smaller form is more popular.
Google Ngram Five, Ten
Note that these are at about 50%, which is higher than three and four.
Google Ngram One Hundred, One Thousand
Again, these are higher than the prior ngrams. +100% here means all instances are in the Times Smaller Form. The Fraction Form is non-idiomatic in this case.
Google Ngrams for Ten Thousand and One Million also show +100% of usage is in the Times Smaller Form indicating this is virtually an idiomatic form. On the other hand, it's grammatically correct to say "ABC is one ten-thousandth the size of XYZ". Interestingly, the Fraction Form doesn't strike me as odd or wrong in any way, but the searches in Google Ngram (and various corpora at http://corpus.byu.edu/) suggests this usage is rare.
Also note that the Times Smaller Form has even more usage than shown here since it has two variants for large numbers: a hundred times smaller, one hundred times smaller, a thousand times smaller, one thousand times smaller, etc. For example, it's natural to say "This is a thousand times smaller than that." See Google Ngram Variants
FOOTNOTE 1: Normalizing Google Ngram results.
In these Google Ngrams (A - B)/(A + B)
shows a normalized difference from -1 to 1 (shown by Google Ngram as -100% to 100%).
- In all Ngrams,
A
= Times Smaller Form, B
= Fraction Form
- 0% means "no difference" in popularity between the two terms.
- Positive values mean the first term (
A
, the Times Smaller Form) is more popular.
(A value of +100% means there are only instances of A
.)
- Negative values mean the second term (
B
, the Fraction Form) is more popular.
(A value of -100% means there are only instances of B
.).
This method allows us to compare widely different result-counts on a common scale.
Even though Pair #2 is far more common than Pair #1, they both demonstrate that A
is more popular than B
, and in the same relative ratio. A potential weakness is that smaller result counts are less accurate. For example, A=3, B=1
, also results in 50%, but this would be too small to be reliable.
Best Answer
This is the sentence that you want to use:
This sentence should normally be avoided:
I can think of no real syntactical reason why for being is wrong, but it's not idiomatic and would not normally be used. (I've never encountered it before, but that doesn't mean it hasn't been used by somebody, somewhere.)
Unfortunately, I can't give a better answer than that.
I'm afraid it gets even more confusing.
Some things simply don't pair well with other things. However, it appears to mostly come down to common usage and what is used and sounds natural rather than there actually being specific rules in every case.
Following are all examples of things that do and don't sound right. If you look only at the syntax, there appears to be no objective pattern.
I would be happy if somebody else could come up with a more coherent explanation for all of this rather than "it just sounds right or wrong."