# Are processor upgrades worth it?

Most computer companies allow you to choose which processor you get when buying a new computer - oftentimes there are a number of architecture and speed options for any given model. Based on a strict set of assumptions, are these upgrades worth it?

## Thought experiment

Let's say your line of work is a series of jobs, each of which takes around 10 hours and pays $500. All of this work is done on a computer, and the only time you use your computer is when you're doing these jobs. Let's say that you spend 10% of your time doing “processor-intensive” tasks. In other words, 90% of the time is spent doing work (coding, sending emails, word processing, etc) that could be done just as quickly on a computer that was made 5 or 10 years ago, which can't be done any faster or slower. This is probably true for a lot of jobs (even coding jobs - the only really processor-intensive task is compiling and perhaps testing) and not others (video/image/audio editing, for example), but is a good baseline. So, for that 10% of the time, if you use a processor which is twice as fast, you'll get twice as much work done during that one hour - meaning that 10% of the job would take you half as long. Using Apple's 2011 15" MacBook Pro update as an example, the base model has a 2.0 GHz processor, and upgrades are available for 2.2 GHz (+$300) and 2.3 GHz (+$550). The processors are otherwise equal (same number of cores and threads, same cache, etc). If the 10% of your work day takes 1 hour on the 2.0 GHz processor, then it would take 2.0/2.2 = .91 hours of work with the 2.2 GHz processor and 2.0/2.3 = .86 hours of work on the 2.3 GHz processor. That's an extra 5.4 and 8.4 minutes, respectively, per-task that you have to work on the next task. In order to make up for the upgrade cost to 2.2 GHz, you'd have to work 6 hours (6 hours *$50/hour = $300). In other words, you'd have to do about 67 of these “tasks” in order to make up for the extra cost. For the 2.3 GHz, you'd have to work 11 hours, or about 79 “tasks”. After doing 200 tasks (what the average person would do in a work year), you will have saved 18 hours with the 2.2 GHz and 28 hours with the 2.3 GHz. That's$900 and \$1400 respectively, at your current pay rate.

## Reality

As it turns out, based on Geekbench scores, the 2.3 GHz model is only marginally faster than the 2.2 GHz model - if that. In many cases, otherwise equivalent 2.2 GHz models actually score higher than the 2.3 GHz version. Most of the time, the 2.0 GHz models are a small amount slower. Based on these results, the assumption above about time time required for computationally intensive tasks scaling linearly with processor speed falls apart. Furthermore, I don't know of any jobs that work in quite that way! I'd also be interested in comparing otherwise equivalent computer's performance using Matlab's bench function, because that might give more insight into real-world speed differences for those of us who do signal processing.