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The Mathematics of Value

Once again, I am very gratified at the thoughtful responses to last week's blog that were posted here and e-mailed to me. Clearly, UAV has many intelligent, articulate readers, and I thank you for sharing your insights, which will help me select the best products to review. Instead of posting inline replies to the comments left during the week (sadly, an activity I don't often have time for), I'll summarize my thoughts here, partly so I can devote some undivided attention to them and partly in the hopes that the discussion will continue...

When I posed the question—Which would you prefer, reviews of high-end or affordable products?—I was expecting simple binary responses, one or the other. This would have let me calculate a ratio of high-end to affordable products to review. A few of you did offer such a response, but many more pointed out that the question is more complex. As Paul noted, "I think it's tough, since 'affordable' is subjective." Mike Wilson echoed this idea, writing, "Define affordable. Over $1k [for one component] gets you out of the mainstream? Over $5k gets you out of affordable for most?"

Indeed, defining "affordable" is quite a challenge, especially since it is relative to the financial resources of each buyer. A $2000 TV is totally out of reach for some but pocket change for others. Still, I did discern some trends in this regard. For example, many respondents seem to favor products in the under-$10k range, with some specifying a $4k cap per product. Many want reviews of higher-end products, but not those with stratospheric prices—more than one mentioned $30,000 speaker systems as being too much.

A number of you suggested another way to look at the question—not from a "high-end" versus "affordable" perspective, but in terms of value or "biggest bang for the buck," which Ric Pascual from Australia dubbed "BBB." He pointed out that a Yamaha RX-Z11 should certainly sound better than an RX-V3800, but is the improvement worth three times the price? (David Vaughn just finished his review of the Z11, and he also reviewed the V3800, so we'll soon see his answer to that question.) On the other hand, Ric also noted that using some formula like

bang for the buck = (features x quality)/price

would tend to favor the least-expensive products, which would not satisfy enthusiasts. "Somewhere," he continued, "there is a quality point beyond which bang for the buck decreases dramatically, maybe following something like an exponential function."

Impressively astute, Ric—actually, I think the relationship between price and performance (including audio and video quality, features, etc.) is more like a logarithmic function, which is the first graph depicted at the top of this blog:

performance = log(price)

(There are various other factors not included in this formula, which is intended only to roughly indicate what I'm talking about to those with a bit of math background.) As price increases, so does performance. But at some point, higher prices start buying less and less increased benefit, reducing the bang for the buck, or BB (extending Ric's nomenclature).

"I know it is very hard to define BBB," he concludes, "but if you can not define it, there is no hope that we enthusiasts can." You're right—BBB is difficult to define, but I'll take a stab at it. I suspect the relationship between bang for the buck and price is more like a negative parabolic function, which is depicted in the second graph at the top of this blog:

BB = -price2

(Again, I'm leaving out various unknown factors for clarity.) The graph of this function looks like an inverted bowl, and BBB is located at the top of the curve.

If you don't understand the math presented here, don't worry. Our reviewers know BBB when they see—or hear—it. This is exactly where their subjective but educated judgment comes in, not to mention their experience and knowledge of the marketplace, which lets them put a given product in its proper context.

Speaking of context, many of you requested comparative reviews, pitting similar products in different price ranges against each other. Also popular was the notion of face-offs between online-sourced products and those from more traditional manufacturers. As I said last week, these are great ideas, and I will implement them when I can, but I don't currently have the resources to do such reviews on any sort of frequent basis.

Finally, I'd like to respond directly to Israel's comment: "Please tell me you are NOT going to make editorial decisions based on 30 self-selected responses. While this exercise may be interesting and a nice gesture, it has no validity. How many hundred's of thousands of people view this site? Thanks for asking. Please take all responses with a HUGE grain of salt."

Actually, I am going to take the responses I've gotten into significant account when selecting products to review—a perfectly valid approach in my opinion. Of course, my little informal poll is not a scientific survey with any real statistical significance, but I believe that even so small a sample does reveal something meaningful about the desires of our readership. It's well known that any request made to a company or media outlet represents the opinion of some number of constituents who didn't take the time to write. I don't know what that number is in this case, but I'm willing to bet that the responses I've gotten reflect the opinions of many more than the 30 or so respondents.

The bottom line is that I value any and all reader feedback. I can't promise to implement all e-mails and blog comments, but that does not mean I don't read and consider them carefully. In fact, my informal survey of last week yielded an important result—that I should focus our reviews on high-value products that sit near the top of the BB/price graph. This approach transcends the high-end vs. affordable question and addresses a more universal and price-independent concern, which will benefit all of our readers.

If you have an audio/video question for me, please send it to

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