Calculating percentages correctly

 It depends on the direction

 

I love checking numbers, and so I was interested when Dell joined Autodesk in announcing a new study. It said that you would be more efficient if you just would spend more money with them. (Had the study found the opposite, it would not have been released, naturally.)

Here's what part of the press release that interested me the most:

The two companies just released a joint study that outlines the productivity gains that can result from upgrading your hardware and design software -- and results found that by moving from AutoCAD 2010 to 2015 and upgrading from a Dell Precision T1600 to a T700 tower workstation, customers can achieve a productivity improvement of 92 percent!

Autodesk has over the years released other studies that "proved" increased efficiency by upgrading to a newer release. Someone once added up all the percentages, and we would now be completeing drawings in something like seconds, if true.

The most infamous one claimed that the ribbon made AutoCAD users 40% more efficient than using menus and toolbars; later, when the Mac version came out, it had no ribbon. I insolently asked Autodesk marketing if this meant that Mac users were 40% less efficient than Windows users, but never received an answer.

When I work through the math in the study, I find that the percentage changes are less dramatic. The study timed drawing activies on AutoCAD 2010 and an older Dell workstation, and then did the same tasks on AutoCAD 2015 and a newer Dell workstation.

Converted to decimals, the timings were 10.18 hours (for the old system) and 5.32 hours (new system). Just by eye-balling it, we can see that the fastest system takes about half the time of the slowest one. Calculating the percentage, it is 48% better. 

 

The study says the improvement is 92%. If the fastest system truly were 92% faster, then its timing should be around 1/10th that of the slowest one. 

I think the error resulted from the order in which the results were graphed. The fastest system was graphed first, but was the last result; the slowest system was graphed last, but was the first result. 

Percentages are tricky to calculate, because their value depends on the direction of the calculation. It appears the study author calculated up (from 5.32 to 10.18 hours) instead of down (from 10.18 to 5.32). 

Here is a site that helps perform the tricky percentage calculations:  www.percentagecalculator.net.

Comments

[Sepp Bauer]

Productivity is inverse function of time spent so the claimed increase is correct (mathematically).

[Daniel]

Apparently they calculate like this: (10.18-5.32)/5.32=0.913, so it can be said "more than 90 percent".

What I am interested is the number itself. Is it true that the same thing done by a same guy in ACAD 2010 needs 10 hours work, and only 5 hours in ACAD 2015 with newer hardware? I can accept the hardware makes the a lot of contribution to this, but I really don't the ACAD version helps too much. (Unless they designed a specific drawing that takes a lot of advatange of v2015 on purpose)

[TonyT]

No, they calculated wrong. You can choose:
1. Go from AutoCAD 2015/Dell 2015 to AutoCAD 2010/Dell 2010 means doing these tasks will take 92% more time (on their carefully selected set of drawings, which probably aren't typical) OR
2. Go from ACAD 2010/Dell 2010 to ACAD 2015/Dell 2015 means doing these tasks will take 48% less time.

AutoDesk/Dell tried to combine 1&2 -> FAIL!

[Nancy Johnson, Cadalyst]

I think Sepp Bauer is correct. The 92% claim relates to "productivity gained," not time spent. If you can do something in half the time (48% of the time in this case), that makes you TWICE as productive (or 92% more, in this case) because you can double the amount of work you do in the same amount of time spent.

[Stey99]

www.percentagescalculator.co.uk is what i use.