# 150%, 1.5 times, 1.5× or 1.5-fold

If some measure of quality improves to 150 % of its original value in a study from condition A to condition B, would it be most appropriate, in terms of scientific writing (computer science specifically), to describe that as:

• a 1.5-fold improvement

• a 1.5× improvement

• performing 1.5 times better

• "150% improvement" would typically mean a 150% increase. That is, if it used to be 100, now it is 250. So these don't all mean the same thing. Apr 28, 2016 at 5:17
• You really shall use a comparison, as you do in the first line of your question. Another option (looking less good) is: "Our method performs 50% better than XYZ".
– yo'
Apr 28, 2016 at 6:46
• This is a good question; I see misuses of numbers in attempts to communicate performance improvements all the time. Of course typically people choose the option that puts the biggest number on the page; you always want to say "150% of previous" because that's obviously HUGE compared to "improvement by half", regardless of what makes more sense in context. :) Apr 28, 2016 at 12:42
• I recommend avoiding percents above 100%. If a stock price doubles (2x), that means it goes up 100%. In the first case you're using a "2" and in the second case you're using a "1". Similarly, a stock that triples (3x), goes up 200%. For whatever reason, percents feel unnatural in these usages. I say avoid them. (I realize this doesn't quite answer your question) Apr 28, 2016 at 16:03

## 4 Answers

The following may seem a bit nitpicking, but such details are what separates the wheat from the chaff:

• a 1.5-fold improvement

Bad. This implies that the improvement – not the quality measure – is 1.5 of something else, that is reasonably comparable, e.g., another improvement. This would make sense in a context like:

We compared different performance boosters and found that contrafibulaties yielded a 1.5-fold improvement compared to the improvement by pericombobulations.

(Note that I do not consider the above sentence an example of good writing as it is bound to be misunderstood by somebody, but it’s at least technically correct.)

• a 1.5× improvement

Very bad. If I am benign, I read this as “1.5-fold improvement” (see above). If I am not, this does not make any sense at all. Replacing words with mathematical symbols just because they have some semantic relation is a very bad habit as it almost never yields a clear meaning, is bad style, and is indicative of deficiencies in basic mathematical concepts.

• performing 1.5 times better

Meh. If we are being literal, it has problems similar to “a 1.5-fold improvement”: Does 1.5 times apply to better or something else? Now, linguistically, this is a fixed idiom with a clear meaning, so the situation is not that bad, but I would guess that some non-native speakers misunderstand it. Moreover, idioms do not stylistically mix very well with accurate, quantitative descriptions.

• performing 50 % better

Almost Good. Similar to the above, but better, since 50 % is by far not as likely to be understood to apply to better than 1.5 times.

• performing 1.5 times as well
performing 150 % as well

Good. These leave no room for misunderstanding as you make clear what 1.5 times or 50 % refer to, and it’s the correct thing, namely “goodness”, i.e., your measure of quality.

• an improvement by 50 %
an improvement to 150 %

Good (with sufficient context). Again, it is clear, what the numbers actually refer to.

• performing 50 % better than A
performing 1.5 times as well as A
performing 150 % as well as A
an improvement by 50 % in comparison to A
an improvement to 150 % of A’s performance

Very Good. By naming the actual reference, you avoid misunderstandings. However, with sufficient context, the expressions I labelled good may be preferable for brevity and avoiding unnecessary redundancy.

Note that all this assumes a measure of quality that increases with quality. If your measure decreases with quality (e.g., runtime), it’s probably best to directly talk about the measure, e.g.:

A’s runtime was 50 % of B’s.
A runs twice as fast as B.

• In my opinion it sounds like "an improvement to 150 %", without context, would usually be meaningless. `150%` of what? An apple? It only works if the value that improved was actually a percentage, as in "My grade improved to 90%". "an improvement by 50%" works because the context is made relative by "by".
– Paul
Apr 28, 2016 at 8:35
• I think even "50 % better than" without precise explanation can be ambiguous in some cases. If an algorithm A is 50 % better than algorithm B (in a case where the only difference can be in speed/running time), is the running time of A for a given input 50 % or 67 % of that of B for the same input? I honestly wouldn't know; speed is usually measured by something divided by time, but speeds of algorithms are often expressed by running times for certain inputs.
– JiK
Apr 28, 2016 at 8:45
• @JiK I don't find that ambiguous. A is 50% better than B means that A ran in half the time that B did. So A is 50% better than B and B is 100% worse than A.
– Paul
Apr 28, 2016 at 9:02
• @Paulpro This implication is not guaranteed, if something like durability is the objective: 'A is 50% better than B means that A ran in half the time that B did' might well be false. It might mean that A achieved 3/2 times B's time. Apr 28, 2016 at 10:45
• @Paulpro: "50% better/faster" is ambiguous. Say B takes 6 seconds to run, meaning it can run 10 times a minute. If we say "A is 50% faster than B," does that mean A takes 3 seconds to run (so it runs 20 times a minute, a 100% increase), or that it can run 15 times a minute (so it takes 4 seconds to run, a 33% decrease)? Apr 28, 2016 at 16:00

In my opinion, the expression

1.5 times better

is to be avoided at all cost. It doesn't have any linguistic meaning. That is because "better" (like "bigger", "more") implies an addition to whatever thing is being measured:

this car goes 10 km/h faster than the other one

while "1.5 times" implies a multiplication.

(If we were to assign a meaning to it, because of the "additional" meaning, "1.5 times better" would mean "2.5 times as good").

Furthermore, if "1.5 times better" were to be allowed, what would "50% better" mean? When following the reasoning that would make "1.5 times better" mean "1.5 times as good", this would imply that it meant "50% as good". Which it of course never meant.

My suspicion is that the incorrect phrasing "1.5 times better" got into usage because people are unsure how to write "1.5 times as good as" and connecting it to the thing they are comparing.

• This is a major peeve of mine as well. People routinely say "__ times more" when they mean "__ times as much", not realizing the literal meaning of "__ times more" is "+1 times as much". And don't get me started on " times less", which makes no sense at all. Apr 28, 2016 at 21:02

I usually clarify that like this:

Condition A's performance was 1.5 times that of condition B.

That gets the condA = 1.5 × condB thing across, without the ambiguity of “improvement times x”.

Or draw them. There's no shame in being too clear.

In general, it's preferable to use the same arithmetic form when discussing relative change in processes of any kind. Consistency shows consideration for the reader. Where I live and translate, the typical writing style tends to like the "x times more than" and the "x-fold" forms mixed with percentages, which is not that easy to interpret as we can see from the discussion here. Percentages not only are more obvious but they also allow comparison with other percentages. So,

• Rule #1, use the same form to compare across your entire discussion or report out of consideration for readers.

• Rule #2, use percentages in preference to "times more/less than" or "-fold" forms, which are not as precise and require interpretation.