### Introduction

Throwing hard-earned cash down for computer purchases is never an easy task. Computer hardware can be a particularly tricky purchase, considering the sheer number of revisions, designs and price points at any one time. ATI and NVIDIA have over 100 cores combined for the AGP video market on shelves today. Yet, somewhere in that haystack of video cards lies the perfect video card, equally balanced in performance and price. Finding it can be a bit of a pain though. What we have decided to do today is step away from the specific type of guide format and look at buying components on a more general basis using mathematical modeling and historical data. We aren't going to tell you which hardware to buy per se, but we will show you the same methodology that we use when determining our picks for the week. We get really theoretical for the first few introductory pages before we get into the historical data, so bear with us if we sound like a college text book for a little while.

Let us cut right to the chase. When buying computer hardware – at least with a sane perspective – there exist only two goals in mind: minimize the Price and maximize the performance. Performance can be somewhat ambiguous, so in this analysis, we will refer to performance and features as Quality. We find later that Price and Quality are both predictable, yet dynamic equations, but the most basic building blocks of any economic model for computer hardware exist as Price (P) and Quality (Q).

It is actually very easy to put a data type on Price - it's just the dollar/yen/euro amount that the component costs. Quality, Q, is a little harder to quantify in the general sense. Everyone has different computing needs, and thus, it's virtually impossible for us to put a numerical value on the performance of a processor or video card in every application – but fortunately, we have benchmarks to simulate a vast majority of real world scenarios. The most critical and difficult step when computing your next purchase cost comes when we attempt to quantify Q. Don't let the name "quality" fool you either. CPUs, for example, make it easy for us to quantify Quality in specific applications because one product is always arbitrarily faster than another. Video cards, on the other hand, make it a little harder, since we need to put a value on additional features like TV tuning or Image Quality. We will get more into these concepts on the following pages.

The million dollar question that we get asked every day, thousands of times a day is "When should I upgrade?" Actually, the questions are usually phrased like:
• "Should I wait six weeks to buy a Radeon X800 XL?"
• "Is it worth it for me to upgrade to an SLI motherboard?"
• "Should I buy more RAM?"

Finding the right time to upgrade shouldn't revolve around the next best thing or even a particular component. The right time to upgrade can usually be modeled around how Valuable additional Quality is to you. The moment when you feel your Athlon XP 1700+ has put you behind a performance curve is the most opportune moment to start calculating how valuable an upgrade is to you. However, this can actually be quantified as well, and we will get more into that in the next couple of pages.

Another thing that we stress in our Buyer's Guides and Price Guides is to look at the entire picture when upgrading and not just a single component. You may feel that your Athlon XP 1700+ is too slow and that you need a new processor, but perhaps we can achieve better performance or Quality for cheaper by upgrading the video card instead. The solution actually hinges on looking at everything in the picture and not just individual components.

On the next few pages, we are going to determine the Value and Quality of some components and determine where the best upgrade path exists. This should answer the few example questions above, but the methodology can be applied anywhere we like when buying new computer hardware.

Quantifying Price

• #### trexpesto - Tuesday, March 08, 2005 - link

Or you could just ask on the forums like everyone does..

#7 and others:
it is interesting to note that if you do have a fair degree of confidence in parts of an equation, the more factors you include, the more likely the errors will cancel out.

Unless you are consistently an optimist or pessimist!

I believe Enrico Fermi popularized this strategy, famously estimating the yield of an atomic blast by throwing torn-up strips of paper in the air. That part sounds suspiciously theatrical.

A classic one you hear about is a test question that asks the circumference of Earth. Well there are 3 one-hour time zones in the continental US, which is about 3000 miles across. Every thousand miles = 1 hour * 24 hours/day = 24000 miles.
Actually it's 24,901.55 miles at the equator but that's not toooo bad.
• #### Gioron - Sunday, February 06, 2005 - link

I'm a bit late commenting, but oh well.

Looking through this, its an interesting way to view upgrading, but I feel its a bit oversimplified and overcomplicated at the same time. Its oversimplified because you're just assuming a linear fit for most of the graphs, when things aren't really linear. Its overcomplicated because you're trying too hard to account for every single variable and making your explanations too complex for most people to really grasp. On the bright side, the basic concept you're trying to get across is something that a lot of people could really use and seem to overlook when making buying decisions.

I'll spare you the explanation for why I feel you're overcomplicating the issue, but suffice it to say that it shouldn't take that many pages and charts to explain when to buy. You might need the charts if you were trying for a definitive "buy X in Y weeks" article, but you're aiming for a general "this is what to consider when buying" article, and that can be done in a lot simpler words and with less graphs.

So... what would I recommend instead? A more relaxed approach, but one that considers some of the same things as the article. I guess the heart of what I would say is "don't forget that having something now compared to later has value", it seems to be the one thing many people overlook. Aside form that, I can't really think of a mathematical model that would give an accurate depiction of the many variables, so I guess I'll leave it at that.
• #### JarredWalton - Wednesday, February 02, 2005 - link

For what it's worth, I don't know that a full-blown model of all potential upgrades would really be feasible or terribly useful, PrinceGaz. There are *SO* many factors to consider, and while ceratin tests will show a difference in performance, otheres might not change much at all.

We really only looked at two of the major components in a computer, as they are often the bottleneck. RAM capacity is really the only other major factor. If we were to try to add in HDD, motherboards, PSUs, etc. then the model quickly becomes something that not even a mathlete would properly understand without staring for a while.

As for the Quality to Price topic, for upgrading it becomes very difficult to model properly while including your present Quality to Price. If you assume your current system as 100% performance with 0 cost, you get a divide by zero error. In fact, any price for your current hardware other than its original price is going to skew a graph heavily in favor of not upgrading. Which leads to my take on the situation.

The impetus for an upgrade has to be that you're unsatisfied with the current level of performance. If you're more or less happy, don't bother upgrading! Once you decide to upgrade, however, Forget about selling old hardware, forget about all the other stuff, and just pretend you're going to ditch what you have and buy something new. If you try to take all of the other variables into account, you again end up with a confusing model.

If you want to be "fair" in the model, you can always take the price for all hardware and add the MSRP for your current hardware to it. So if you have a \$100 9600 Pro, rather than saying it's "free" (and getting divide by zero), say it costs \$100 but the 9800 Pro costs \$300. Three times the price for maybe double the performance. The 25 cents per day CNU then changes as well, I think. If you want to play a game like Doom 3 and it runs poorly on your 9600 Pro, CNU is going to be more than 25 cents each day.

My final comment (for now) is that the hypothetical system we were going to upgrade was chosen for a reason: we could forget motherboard, RAM, and many other components for an upgrade. A more realistic upgrade would have an older mobo, PSU, RAM, etc. and would need more than \$200 to get a lot better performance. If you actually have an A64 2800+ with a 9600 Pro, you're probably going to be quite happy with it. :)

#11 Hahahaha, right on - statistics sux huh :-) Reply

I think this article should have been called "The Mathletes Guide to Upgrading". As this article proves, it is certainly possible to overcomplicate things. For those of you (like me) who hate calculating and charting stuff, check out posts 31-32 for a much simpler way to accomplish the same tasks. Reply
• #### PrinceGaz - Tuesday, February 01, 2005 - link

Thanks for the explanation. Perhaps the article should be retitled "The Economic Guide to Building a New System", instead of the misleading "Economic Guide to Upgrading" as it most certainly isn't about upgrading.

The only part of the article which even considers what you might upgrade from is where you set the quality of that at 100% and every option is relative to that. The graphs would be identical (except for the scale) if you just suggested people put the raw framerate from benchmarks in, as setting an arbitrary level to 100% (what you are upgrading from) doesn't affect the results at all.

I was under the impression this was a guide to economic upgrading, and it could so easily have been if you'd deducted the quality and (optionally) the second-hand value of whatever you upgrade from. Upgrading is about replacing something old with something better, and the quality and price of an upgrade is therefore the quality of what you buy minus what you have, and the price is the cost of the upgrade minus what you can sell what you have for.

"I actually modeled the "Quality - 100%" approach, and while the Quality to Price graphs changed in terms of numbers, the overall slopes were about the same.". Did you try that with the example I gave, or anything approaching a wide-range of upgrade options? The slopes might be similar but where they are on the graph are totally different. Your current sheet could very easily recommend someone to upgrade to something slower, and this is an article about upgrading! In fact I'm sure it would recommend a low-end Sempron as the best upgrade choice for someone with a fast Barton or Athlon 64. You really need to make it clear that the quality and value of what you have must be deducted from any upgrade option.

I'm sorry to go on about this, but whilst it was a very interesting (if heavy going) article, it was so flawed from being "The AnandTech Guide to Economic Upgrading" that it really needs correcting. Either change what the article addresses (new system builds instead of upgrades), or correct it to reflect upgrading.
• #### JarredWalton - Tuesday, February 01, 2005 - link

38 - PrinceGaz, the current model does actually reflect more of a "what part should I purchase" mentality as opposed to an upgrade. So if you consider that the model is based off of that, the charts are still valid. The simple approach would be to take the spreadsheet and plug in your own quality, price, and depreciation values along with your own CNU to see how things look.

There are a myriad number of ways to model the situation, and only the individual can readily determine how important an upgrade is to them. The idea behind the article is still sound, even if some of the graphs don't necessarily look right. I actually modeled the "Quality - 100%" approach, and while the Quality to Price graphs changed in terms of numbers, the overall slopes were about the same.
• #### CrapONez - Monday, January 31, 2005 - link

Good article that makes you think about cost/benefit rationalization to upgrades - for those who need it or simply are curious.

The problem I had with this article was in determining the cost of not upgrading. So the game/encode/compile runs slowly on your computer. Where's the bottleneck? Processor? Amount of memory? Memory speed/bandwidth?

Anandtech has plenty of reviews where various components are upgraded to determine the effect of each upgrade on total performance. We don't have that luxury. Determining which component to upgrade is often more difficult than selecting which model to upgrade to.