Points, Percentages, and Stock-Market Plunges

Monday’s stock-market plunge brought plenty of headlines like this: “Dow plummets record 777 as financial rescue fails.”

That was from the Associated Press. The article’s subhead said, “Dow dives 777 points, biggest single day fall ever, as House rejects financial bailout package.”

The “biggest single day fall” sounds more dramatic and newsworthy than the “18th biggest single day fall.” Yet they are both true for Monday: By points, it was the largest single-day fall; by percentage, it was only 18th.

If these rankings are both true, can one be truer? I’d say yes if “truer” means a fairer comparison.

Let’s start with an axiom: If you are comparing daily changes to the Dow over the time frame “ever”—as in “biggest single day fall ever”—you should consider every trading day since the Dow’s inception.

The Dow debuted in 1896 at 40.94 points. It did not reach 777 points until the 1960s. So if you compare Monday’s drop to the past using points, you effectively eliminate from consideration any day before then—and, from a practical point of view, most days until the very recent past.

Too bad, because eight of the ten largest percentage drops occurred before 1935. The Great Depression years account for five of them, but the all-time winner for percentage losers is December, 12, 1914, when the Dow lost more than 24%. [Update: While technically true that the Dow lost more than 24% that day, it turns out this was due to a recalculation of the Dow, not a plunge of the overall market. The Wall Street Journal’s “The Numbers Guy” explains.]

A close second is 1987’s Black Tuesday, when the Dow lost 22%. But even with that relatively recent event, 22% of the Dow was only 508 points then. In contrast, yesterday’s drop was around 7%, less than a third of Black Tuesday by percentage but 219 points more.

So, to the issue of fairness, it’s not fair to compare point changes when the point scale is different, as it is with a Dow of 40 points versus a Dow of 10,000 points. In contrast, percentages can factor-out the magnitudes of different point scales, thus making changes more comparable.

Megapixels Begone (Comparative Metrics That Won't Go Away)

When you see a digital camera for sale, the first thing listed is usually the megapixel count: the camera’s maximum resolution in millions of pixels.

It’s the most important attribute because more megapixels means better pictures, right? With today’s digital point-and-shoot cameras, the answer is somewhere between “not necessarily” and “no.”

I noticed this issue last year when shopping for a point-and-shoot digital camera. Various roads led to the Fuji FinePix F30/31 series, which Digital Photography Review described like so:

In the fast-moving, ‘bigger better faster’ world of the digital compact the Fujifilm FinePix F30 will be one of the rare few that are remembered after they have gone (the nearest this throwaway business gets to a ‘classic’). The reason this unassuming, blocky little camera stands out from the scores of other cameras launched last year - and why it has a mantelpiece covered in industry awards - is simple; image quality, or more specifically, high ISO performance. The F30’s low light capabilities come from a combination of clever technology (Super CCD and Real Photo Processor) and a ‘swimming against the tide’ attitude to specification, which means a bigger sensor with fewer pixels. The F30 also, against all the odds, actually sold pretty well, going against the conventional wisdom that consumers buy on pixel counts alone. Although it has its share of faults the F30 became the benchmark by which all compact cameras in the 6-8 megapixel sector were judged.

But at the time I was shopping, Fuji had moved on to the F50 series. Here is what DP Review had to say about it:

Fujifilm has finally caved under the pressure and joined the mainstream with the F50fd, doubling the F30/F31fd’s pixel count to squeeze a whopping 12 megapixel on the tiny 1/1.6in sensor....

The good news is that - forgetting the F31fd for a moment - the F50fd is an excellent point and shoot camera that deserves a place near the top of its class. Sure, Fujifilm listened to its marketing department and installed a 12MP sensor, but the F50fd’s high ISO performance is still surprisingly good. On a per-pixel basis it is certainly not on a par with its predecessor but on an output level, i.e. on a print of the same size or a computer monitor the difference isn’t huge. Of course it would have been a lot better with 8 million larger pixels, but I’m afraid even Fujifilm isn’t brave enough to launch a premium compact camera so ‘under powered’ in today’s market....

The replacement of the F31fd means the end of the line for a sensor that over four generations of Fujifilm compact cameras has shown that there is an alternative to pointless megapixel increases and noisy results at anything over base ISO. Whilst the F50fd still has a lead over its conventional CCD competitors that advantage has been cut down to little more than a whisker, and this is a regrettable and slightly depressing indication of where the compact camera manufacturers’ priorities lie.

In other words, the F50fd was among the best point-and-shoot cameras of its time for image quality. However, the cameras of its time all had taken the same step backward by squeezing too many pixels into a given size of sensor. Thus, all the newer models were inferior to the F30’s image quality, especially in less than perfect lighting.

So what happened? Over to photography blogger Micah Marty, from late 2007:

Here’s a first: a digital camera that has appreciated in value. That’s right: if you had bought a truck full of new Fuji F30/31 cameras and just parked it in a warehouse for a year before selling them, you’d have no problem paying those holiday bills. Contrary to conventional wisdom (“Digital cameras always decrease in value when the successor model is introduced”) those two discontinued Fujis have almost doubled in value since they were current.

This happened, of course, because a few months ago Fuji decided to forgo its primary edge over the competition (“Less noise”) in favor of being more like the competition (“More megapixels!”). As a result, discontinued-but-new F30s that once could be bought new for $230–260 are now up as high as $400 on eBay, while the discontinued-but-new F31s that once could be bought new for $250–275 are now approaching the $500 mark on the same auction site. Those two cameras each have six megapixels; their shiny new successor (the F50), with twice as many megapixels but also more noise—and, by the way, a shorter-lived battery—currently is selling for $228 new at B&H.

The persistence of megapixels as digital cameras’ key advertised feature is a case study in a particular flavor of numbers abuse: the comparative metric that won’t go away. Such metrics typically made sense at some point in the past but, as with megapixels, outlived their usefulness as descriptions of quality. Yet they remain because, like kids studying to the test rather than learning the subject, manufacturers keep designing products to excel at the metric—after all, it’s what the market (thinks it) wants.

Having designed their cameras for more megapixels, the manufacturers are then obliged to tout their new cameras’ excellence on that metric, thereby reinforcing the metric in consumers’ minds.

It’s a vicious cycle, and the fate of the Fuji FinePix line demonstrates how hard it is to stop.

[Sidenote: Technically, the megapixels issue is not about an absolute limit. It’s about the number of pixels in relation to the size of the sensor. Thus, digital SLRs (the pro-looking cameras with swappable lenses) can get better quality from, say, 12 megapixels rather than 8 megapixels because the 12-megapixel sensor is typically larger in the digital SLR. In contrast, point-and-shoot cameras’ smaller bodies resist larger sensors, so manufacturers have packed more pixels into the same sensor size—despite the evidence that, above 6 megapixels, it hurts more than helps. For more details, see Image Engineering’s 6 Megapixel site, a public-interest plea in the name of 6-megapixel point-and-shoot cameras.]

The Inverse Out-of-Office Message

A few weeks ago at work, one of my team members was on vacation. He had left the office physically, but his mind was partly still there.

Now I’ll be the first to salute someone who takes time out of a vacation to address an emergency, but otherwise a vacation is for getting away. I had made that point to the team member, yet he was dashing-off emails from the Mexican seaside along the lines of, “Hey, how did that meeting go?”

By mid-week, the rest of the team decided an intervention was necessary. So I took our vacationer’s out-of-office message, changed some words, and sent it to him in response to one of his messages, autoresponder-style.

From: Steve Krause
Sent: Wednesday, August 27, 2008 2:03 PM
To: XXXXXXXXXXXX
Subject: RE: seller_update/verify_run_metis_client

Thank you for your E-Mail,

You are out of the office August 25th through September 1st, returning Tuesday, September 2nd. In the meantime, if you have temptation to contact the Intelligent Cross-Sell team, please resume your normal vacation activities instead.

If this is an emergency—defined as “I can’t stop myself from using this Blackberry thing”—please call your own voicemail and leave yourself a message.

Thank you and have an ICS-free week,
The ICS Team

And thus was born the Inverse Out-of-Office Message. May you be so fortunate to have an employee so enthusiastic that he or she needs it.

The Metrics of High Gas Prices

In the United States, gas prices hit all-time highs this year, even in inflation-adjusted dollars. This new reality has motivated some rethinking about metrics related to cars, gas, and money.

Total Cost of Ownership for Cars

Total Cost of Ownership (TCO) is a metric that includes not only the purchase price of a car but also the costs to run and maintain the car over time. While a business would likely use TCO to evaluate buying a fleet of cars, relatively few consumers use it when buying their own cars.

However, new-car buyers are increasingly doing a rough form of TCO as they abandon gas-guzzling SUVs and trucks in favor of fuel-efficient cars. Moreover, according to this New York Times article, many consumers are using their future savings at the pump to load up on options like leather seats and fancy car stereos.

In this new math for the auto industry, gas mileage often trumps sticker price for consumers.

“Affordability is not so much the issue as fuel economy,” said George Pipas, Ford’s chief sales analyst. “Just because you want more fuel efficiency doesn’t mean you don’t want a moonroof or leather interior.”

Gallons Per Mile

Earlier this summer, a pair of Duke University professors published research that suggests people often misinterpret the “miles per gallon” metric when comparing different cars. For example, which of the following saves the most gas?

(a) Replacing a 20-MPG car with a 40-MPG car

(b) Replacing a 10-MPG car with a 20-MPG car

(c) The previous two choices will have an equivalent effect

Many people don’t realize the answer is (b). However, if you flip the metric to be gallons per mile—or better, gallons per 10,000 miles—things clarify. (Gallons per 10,000 miles just means the number of gallons of gas necessary to drive 10,000 miles.)

Per this spreadsheet...

...a 10-MPG gas guzzler requires 0.10 gallons to go a mile; that is 1,000 gallons for 10,000 miles. In comparison, the 20-MPG normal car takes 500 gallons to go 10,000 miles. And the 40-MPG efficient car takes 250 gallons to go 10,000 miles. So switching from the gas guzzler to the normal car saves double the gas as switching from the normal car to the fuel-efficient car. At $4 per gallon, that’s a $2,000 versus $1,000 savings.

This result is worth considering in light of government policies that simply promote ownership of fuel-efficient cars. Such policies might instead want to base the subsidy on the fuel-inefficiency of the owner’s previous car, thereby creating greater incentives to get the worst gas guzzlers off the road.

We Feel It Because We See It

Behavioral economist Dan Ariely, author of Predictably Irrational, had a recent piece about why there’s so much angst about gas prices. He argues that we care more about gas prices than the prices of other necessities because when we buy gas, the cost adds up right before our eyes.

Looking back at my family’s expenses over the past few years, I see big increases in our health care costs and in how much we pay for food. The rise in what we spend on gas is not nearly as extreme as our increases in categories like electricity and telephone. So why does the amount we spend on gasoline feel so enormous? I think it is because of the way we buy gas.

For the several minutes that I stand at the pump, all I do is stare at the growing total on the meter — there is nothing else to do. And I have time to remember how much it cost a year ago, two years ago and even six years ago.

Yet I have no such memory about the prices of items in any other category. I have no idea how much milk was six years ago, how much bread was three years ago or how much yogurt was a week ago. But I suspect that if I stood next to the yogurt case in the supermarket for five minutes every week with nothing to do but stare at the price, I would also know how much it has gone up — and I might become outraged when yogurt passed the $2 mark.

I like the spirit of the example, but I don’t know anyone who buys $50 worth of yogurt per week or whose livelihood relies on eating yogurt. In contrast, large numbers of people have those situations with gas.

I would have rather seen Ariely use health care as the example. At various points in people’s lives, it’s an absolute necessity, yet few people understand exactly how much they pay (through some combination of direct, employer, and insurer payments) or how that amount has changed over time.