Beating the System: The AnandTech Guide to Economic Upgrading
by Kristopher Kubicki & Jarred Walton on January 30, 2005 5:59 PM EST- Posted in
- Guides
Building the Model
Before we get too carried away with variables and equations, it's time that we put something down on paper (or computer screen, in this instance). Without taking into account Time - when to buy - a simple plot of a set of products along the interval $150 to $250 dollars looks like this:
| Product | Price |
| Video Card A | $150 |
| Video Card B | $175 |
| Video Card C | $200 |
| Video Card D | $225 |
| Processor A | $175 |
| Processor B | $200 |
| Processor C | $225 |
| Processor D | $250 |
This chart is pretty useless. The reason why we introduced products deviating by $50 from our set allowance of $200 is to account for fluctuations in price once we introduce Time into the model. If all hardware devalues at the same dollar amount, exposing time to the equation is pointless. Generally processors take a dip in price every few weeks, so let's see what would happen if we put a 3% price cut on the products every four weeks on video cards, and a 4% price cut on processors. This discrete model doesn't make a lot of sense, since hardware generally devalues at a discrete rate, but in the meantime, we will use it for this example.
Here comes the important step - how much is your time worth? An easy way to visualize this is if you had a computer at work, and six minutes of your day every day was wasted waiting for Outlook to load up. Your company is paying you two hours a month on lost productivity. You can put any value per hour on this number, but let's say the Cost of not upgrading your existing hardware comes down to $0.25 per day; each day you don't upgrade it costs you another 25 cents on the resale value of your old hardware, or in lost productivity, or something else along those lines. The actual Cost to Not Upgrade (per day) can actually be something more abstract as well. Perhaps in the few hours per day that I play World of Warcraft, the frustration that I get while waiting for the screen to render is worth $0.25 per day. For the purposes of this example, we will just say that we value a new computer upgrade at $0.25 per day. This skews our graphs slightly.
Things have changed a little bit on this graph. Notice that it actually gets more expensive to wait six months before buying Video Card C, even though the vendor sells it for slightly less. Putting this quantitative value on how much our time is worth per day gets us out of the perpetual waiting cycle that we had mentioned earlier. It becomes real easy to say "I can just wait six months for the cost to drop $200," but if that's your mentality, then why upgrade at all? The upgrade isn't needed if there is no cost associated with waiting.
And finally, just to make things really interesting, let's take the Quality of each component and base it on a fictional benchmark like a video game. Each component's relative quality is listed as a percentage of base performance. Just by taking the price variable P and dividing by Q, we've changed our graph enough to give a pretty realistic representation of what a generic model looks like.
| Product | Price | Quality |
| Video Card A | $150 | 200.00% |
| Video Card B | $175 | 240.00% |
| Video Card C | $200 | 260.00% |
| Video Card D | $225 | 280.00% |
| Processor A | $175 | 235.00% |
| Processor B | $200 | 270.00% |
| Processor C | $225 | 305.00% |
| Processor D | $250 | 340.00% |
Click to enlarge.
What we are seeing in this graph is that we will get best return on our investment at different times for different parts, assuming the constant rate of decline in price and a 25 cents per day cost to not upgrade. For example, we get the the most out of a dollar by buying Processor D in six months - in fact, looking at the curve in the graph, it would be better to continue to wait even longer! If our time is only worth $0.25 per day, it apparently isn't worth it to buy any of the new processors today - only the "budget" processor A is a good buy. Otherwise, we would be overpaying for the Quality. Of course, Processor D is a little bit out of our price budget too. We maximize our price to quality by week 12 for Processor B, and Processor C looks to be leveling off towards week 24. All of the video cards, on the other hand, will actually maximize our performance for our dollar if we buy right now.
To demonstrate the entire process that we just described above, we created a simple Excel workbook. By modifying the assumptions highlighted in yellow, we can create a dynamic graphical process to easily verify two things: whether or not it makes sense to upgrade now, and the relative Price and Quality of each product in our set. The idea is to purchase the hardware that gives us the largest Price to Quality ratio while taking in account the Cost to Not Upgrade (we refer to this as CNU). If the maximum ratio exists at some other date than the start date of the model, then either our CNU per Day doesn't reflect our need to upgrade accurately, or the part in question is too expensive for its relative quality.
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trexpesto - Tuesday, March 8, 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 6, 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.
As an example of how you're oversimplifying things, consider your "cost to not upgrade" that you're considering a flat $0.25. In reality, the cost to not upgrade is going to increase every day you wait. Its more of an exponential increase instead of a linear line, but there are large steps in the value as you start running into more things your current computer just can't do. As an example of this, my computer 3.5 years ago was fairly high end, it could play all the games, ran the current windows version well, and there wasn't a whole lot out there that was better. Sure, I could upgrade it, but the cost to me would only be about $0.01 a day, mainly from bragging rights. A year later, it was still a good computer, but new games had come out, a new version of windows had come out, and it was being asked to do new things. The games still ran at decent frame rates, but they could be better, windows didn't spend too much swapping out its now medium amount of RAM, but it was noticable now. At that point, upgrading the computer would be worth about $0.05 a day for me. The next year, new games came out where its performance dropped, new software came out that taxed it a bit, and I would definately see an improvement if I upgraded. At that point, it would be worth $0.25 for me to upgrade. A year later, you start hitting things is just plain _cannot_ handle. Can't run the latest games, processor can't handle real time video encodes that I wanted, etc. If I were still using it, it would be worth at least $2.50 a day for me to upgrade it. This is not a linear trend, but over the short term you can fool yourself into thinking that it is one. Assuming tomorrow is like yesterday, turning down the graphics in unreal tournament is worth the same amount of money, but once HL2 comes out the price suddenly jumps, and they'll constantly be coming out with more new software that is more and more taxing on the system. The same can also be said for some of the prices, since the "next best thing" you keep telling people not to wait for tends to push prices down suddenly, but in between prices fall at a slower rate. The period of time you're looking at for video cards and processors is really farily stable, but that doesn't mean its like that all the time.
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 2, 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. :)
MadAd - Wednesday, February 2, 2005 - link
#11 Hahahaha, right on - statistics sux huh :-)LordConrad - Wednesday, February 2, 2005 - link
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.PrinceGaz - Tuesday, February 1, 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 1, 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.
PrinceGaz - Monday, January 31, 2005 - link
http://images.anandtech.com/reviews/buyersguide/20...they put a space in front of cost_continuous.xls in the link on page 3
malikarshad - Monday, January 31, 2005 - link
The link for excel worksheet is not working. Can somebody post a valid link