NHL teams strategize when to play for overtime

Here's an article I found a year ago in the Journal of Sports Economics, but didn't get around to writing about until now.

It's by Michael Lopez, and it's called "Inefficiencies in the National Hockey League Points System and the Teams That Take Advantage." 

As is well-known, NHL teams have an incentive to get games to go to overtime. If a game is settled in regulation, the winning team gets two standings points, while the loser gets none. However, if a game goes to overtime or a shootout, the winning team gets the same two points -- but the losing team gets one point too.

An overtime game is better for teams, in general, because they get to split three points between them instead of just two. So it's no surprise than NHL teams respond to the incentive. In the first thirteen seasons after the "loser point" rule was adopted, the frequency of overtime games jumped from 20.2 percent to 23.6 percent. (Coincidentally, it's the same 23.6 percent before and after the shootout was adopted.)

Lopez's paper was able to quantify two new additional findings:

1. Games are more likely to go to overtime later in the season than earlier; and

2. Games are more likely to go into overtime when teams are not in the same conference.

These make sense, intuitively. Later in the season, some teams are fighting desperately for a playoff spot, and the extra standings point is much more important for them in terms of leverage. And, whether a team makes the playoffs depends only on the other teams in its own conference, so sharing an extra point with an other-conference opponent doesn't cost anything at all. (Well, maybe it might, rarely, cost home-ice advantage in the finals, but that's highly unlikely.)

As mentioned, 23.6 percent of games went to overtime in the shootout era. But the overtime percentage varies substantially by situation:

25.4% Inter-conference games
23.2% Within-conference games 

22.0% September-December games
23.8% January-February games
25.6% March games
29.3% April games

The conference difference is only significant at p=.08, but the month difference is significant at p=.001.

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But, Lopez found, the differences are actually larger than those raw percentages, because the two situations aren't independent. As it turns out, the NHL tends to schedule within-conference games late in the season. That's for drama, so that the most meaningful, high-leverage games are likely to be against historical rivals.

Because of that, the two effects partially cancel each other out. The late-season effect tends to increase overtimes, but those games tend to be within-conference, which decreases them.

Lopez separated out those factors with a regression. Calculating from his coefficients, and assuming teams of equal talent, I get:

23.5% within conference, early in season
26.2% different conference, early in season
31.8% within conference, April
35.0% different conference, April

So, the differences are a lot bigger than the raw numbers show.

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Something else that's interesting: the "within conference" effect is very recent.

The overall conference effect was 2.7 percentage points (26.2 versus 23.5). But, almost the entire effect came from the last two seasons in the study. For the study's first twelve years, there was almost no difference at all, on average. But in 2010-11 and 2011-12, the conference effects were 4.7 and 5.8 percentage points, respectively.

It's like teams suddenly caught on to the idea that they don't want to give points away to conference opponents.

But ... well, it seems to me that strategy doesn't really make a whole lot of sense.

Yes, it's true that you don't get an advantage against your rival by playing for three points instead of two. It almost seems like it's worse -- if you win in overtime, you only gain one point on your opponent (you get two, they get one). But if you win in regulation, you gain two points!  Except that it's symmetrical ... if *they* beat *you* in overtime, they only gain one point on you. 

The disadvantage comes not from any negative expectation -- it's symmetrical, after all -- but that the other-conference games come with a *positive* expectation.  You share three points instead of two, but your opponent's gain is not your loss, so the more points to split, the better.

So, against that particular opponent, the inter-conference overtime game is much better for you, with 50 percent more points up for grabs, and no penalty for the points the other team takes, beyond your disappointment at not getting them yourself.

The problem, though, is: that's only true for the one team you're playing against. But, you're not just competing in the standings against this one particular opponent. You're also competing against the other 12 (West) or 14 (East) teams in the conference! If you can raise the expected payoff to 1.5 points each instead of 1.0, you break even against the one same-conference opponent, but gain an expected half point against at least 12 other teams!

Sure, there's *a bit* less incentive within conference, because you stand to gain on only 12 teams, instead of 13 teams when you win an inter-conference game. But, that's so small a drop in incentive that you shouldn't even see it. 

To repeat an analogy I've used in the past: If you see a $2 coin in the street, you'll pick it up. If it's only a $1 coin, sure, you're less likely to pick it up, in theory. But, in practice? You'll still pick it up so often that nobody will be able to tell the difference. It's like a 99.99% chance compared to a 99.98% chance, or something.

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Also: why should there be a March/April effect?  Every game counts equally in the standings. A November game is just as important for making the playoffs, on average, as an April game.

Of course, in April you *know* how important the game is, whereas for a November game, it might, in retrospect, turn out to have been meaningless. But, since games count equally, the overall leverages have to be the same. If that's the case, then for every absolutely crucial April game, there must be an offsetting meaningless one, in order for the April average to equal the November average.

I wonder if the April effect applies only to the most important games. Maybe teams are thinking, "well, we feel a bit weird lowering our intensity to play for the regulation tie, so we're only going to do it when it's really, really important."  In other words, the probability of overtime doesn't increase smoothly with leverage -- instead, it takes a big jump when the pressure to gain points is exceptionally high. 

Maybe I'm 100% willing to steal food if I'm on the brink of starvation, but I'm not 50% willing to steal food if I'm only halfway to starving. In the latter case, the risk isn't worth it.

It could be the same thing here. Maybe teams aren't willing to play a less intense strategy (or whatever they do to play for overtime) when it's an ordinary, early-season game. But, when it's *really* important, that's when it's worth the trouble.

Do stock buybacks enrich CEOs at the expense of the economy?

Are share buybacks hurting the economy and increasing income inequality? 

Some pundits seem to think so. There was an article in Harvard Business Review, a while ago, which might have been an editorial (I can't find a byline). That followed a similar article from FiveThirtyEight, that concentrated on the economic effects. When I Googled, I came across another article from The Atlantic. I think it's a common argument ... I'm pretty sure I've seen it lots of other places, including blogs and Facebook.

They think it's a big deal, at least going by the headlines: 

-- "How stock options lead CEOs to put their own interests first" (Washington Post)

-- "Stock Buybacks Are Killing the American Economy" (The Atlantic)

-- "Profits Without Prosperity" (Harvard Business Review)

-- "Corporate America Is Enriching Shareholders at the Expense of the Economy" (FiveThirtyEight)

But ... it seems to me that neither the "hurt the economy" argument nor the "increase inequality" argument actually makes sense.

Before I start, here's a summary, in my own words, of what the three articles seem to be saying. You can check them out and see if I've captured them fairly.

"Corporations have always paid out some of their earnings in dividends to shareholders. But lately, they've been dispersing even more of their profits, by buying back their own shares on the open market. 

"This is problematic in several ways. For one, it takes money that companies would normally devote to research and expansion, and just pays it out, reducing their ability to expand the economy to benefit everyone. In addition, it artificially boosts the market price of the stock. That benefits CEOs unfairly, since their compensation includes shares of the company, and provides a perverse incentive to funnel cash to buybacks instead of expanding the business.

"Finally, it makes the rich richer, boosting the stock values for CEOs and other shareholders at the expense of the lower and middle classes."

As I said, I don't think any part of this argument actually works. The reasons are fairly straightfoward, not requiring any intricate macroeconomics.

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1. Buybacks don't increase the value of the shares

At first consideration, it seems obvious that buybacks must increase the value of your stockholdings. With fewer shares outstanding, the value of the company has to be split fewer ways, so your piece of the pie is bigger.

But, no. Your *fraction* of the pie is bigger, but the pie is reduced in size by exactly the same fraction. You break even. That *has* to be the case, otherwise it would be a way to generate free money!

Acme has one million (1 MM) shares outstanding. The company's business assets are worth $2 MM, and it has $1 MM in cash in the bank with no debt. So the company is worth $3 a share.

Now, Acme buys back 100,000 shares, 10 percent of the total. It spends $300,000 to do that. Then, it cancels the shares, leaving only 900,000.

After the buyback, the company still owns a business worth $2 million, but now only has $700,000 in the bank. Its total value is $2.7 million. Divide that by the 900,000 remaining shares, and you get ... the same $3 a share as when you started.

It's got to be that way. You can't create wealth out of thin air by market-value transactions. 

The HBR author might realize this: he or she hints that buybacks increase stock prices "in the short term," and "even if only temporarily."  I'm not sure how that would happen -- for very liquid shares, the extra demand isn't going to change the price very much. Maybe the *announcements* of buybacks could boost the shares, by signalling that the company has confidence in its future. But that's also the case for announcements of dividend increases.

One caveat: it's true the share price is higher after a buyback than a dividend, but that's not because the buyback raises the price: it's because the dividend lowers it. If the company spends the $300,000 on dividends instead of buybacks, the value of a share drops to $2.70. The shareholders still have $3 worth of value: $2.70 for the share, and 30 cents in cash from the dividend. (It's well known, and easily observed, that the change in share price actually does happen in real life.)

If the CEO chooses to spend the cash on buybacks, then, yes, the stock price will be higher than if he chose to spend it on dividends. It won't just be higher in the short term, but in the long term too. 

Are buybacks actually replacing dividends? The FiveThirtyEight article shows that both dividends and buybacks are increasing, so it's not obviously CEOs choosing to replace one with the other. 

But, sure, if the company does replace expected dividends with buybacks, the share price will indeed sit higher, and the CEO's stock options will be more valuable.

To avoid conflicts of interest, it seems like CEOs should be compensated in options that adjust for dividends paid. (As should all stock options, including the ones civilians buy. But they don't do that, probably because it's too complicated to keep track of.)  But, again: the source of the conflict is not that buybacks boost the share price, but that dividends reduce it. If you believe CEOs are enriching themselves by shady dealing, you should be demanding more dividends, not decrying buybacks.


2. The buyback money is still invested

The narratives claim that the money paid out in share buybacks is lost, that it's money that won't be used to grow the economy.

But it's NOT lost. It's just transferred from the company to the shareholders who sell their stock. 

Suppose I own 10 shares of Apple, and they do a buyback, and I sell my shares for $600 of Apple's money. That's $600 that Apple no longer has to spend on R&D, or advertising, or whatever. But, now, *I have that $600*. And I'm probably going to invest it somewhere else. 

Now, I might just buy stock in another company -- Coca-Cola, say -- from another shareholder. That just transfers money from me to the other guy -- the Coca-Cola Corporation doesn't get any of that to invest. But, then, the other guy will buy some other stock from another guy, and so on, and so on, until you finally hit one last someone who doesn't use it to buy another stock.

What will he do? Maybe he'll use the $600 to buy a computer, or something, in which case that helps the economy that way. Or, he'll donate the $600 to raise awareness of sexism, to shame bloggers who assume all CEOs and investors are "he". Or, he'll use it to pay for his kids' tuition, which is effectively an investment in human capital. 

Who's to say that these expenditures don't help the economy at least as much as Apple's would?

In fact, the investor might use the $600 to actually invest in a business, by buying into an IPO. In 2013, Twitter raised $1.8 billion in fresh money, to use to build its business. It's quite possible that my $600, which came out of Apple's bank account, eventually found its way into Twitter's.

Is that a bad thing? No, it's a very good thing. The market judged, albeit in a roundabout way, that there was more profit potential for that $600 in Twitter than in Apple. The market could be wrong, of course, but, in general, it's pretty efficient. You'd have a tough time convincing me that, at the margin, that $600 would be more profitable in Apple than in Twitter.

The economy grows the best when the R&D money goes where it will do the most good. If Consolidated Buggy Whip has a billion dollars in the bank, do you really want it to build a research laboratory where it can spend it on figuring out how to synthesize a more flexible whip handle? 

At the margin, that's probably where Apple is coming from. It makes huge, huge amounts of profit, around $43 billion last year. It spent about $7 billion on R&D. Do we really want Apple to spend six times as much on research as we think is appropriate? It seems to me that the world is much better off if that money is given back to investors to put elsewhere into the economy.

That might be part of why buyback announcements boost the stock price, if indeed they do. When Apple says it's going to buy back stock, shareholders are relieved to find out they're not going to waste that cash trying to create the iToilet or something.


3. Successful companies are not restrained by cash in the bank

According to the FiveThirtyEight article, Coca-Cola spent around $5 billion in share repurchases in 2013. But their long-term debt is almost $20 billion.

For a company like Coca-Cola, $20 billion is nothing. It's only twice their annual profit. Their credit is good -- I'm sure they could borrow another $20 billion tomorrow if they wanted to.

In other words: anytime the executives at Coke see an opportunity to expand the business, they will have no problem finding money to invest. 

If you don't believe that, if you still believe that the $5 billion buyback reduces their business options ... then, you should be equally outraged if they used that money to pay down their debt. Either way, that's $5 billion cash they no longer have handy! The only difference is, when Coca-Cola pays down debt, the $5 billion goes to the bondholders instead of the shareholders. (In effect, paying off debt is a "bond buyback".)

The "good for the economy" argument isn't actually about buybacks -- it's about investment. If buybacks are bad, it's not because they're buybacks specifically; it's because they're something other than necessary investment.

It's as if people are buying Cadillac Escalades instead of saving for retirement. The problem isn't Escalades, specifically. The problem is that people aren't using the money for retirement savings. Banning Escalades won't help, if people just don't like saving. They'll just spend the money on Lexuses instead.

Is investment actually dropping? The FiveThirtyEight article thinks so -- it shows that companies' investment-to-payout ratio is dropping over time. But, so what? Why divide investment by payouts? Companies could just be getting rid of excess cash that they don't know what to do with (which they also get criticized for -- "sitting on cash"). Looking at Apple ... their capital expenditures went from 12 cents a share in 2007, to $1.55 in 2014 (adjusted for the change in shares outstanding). A thirteen-fold increase in research and development doesn't suggest that they're scrimping on necessary investment.


4. Companies offset their buybacks by issuing new shares

As I mentioned, the FiveThirtyEight article notes that Coke bought back $5 billion in shares in 2013. But, looking at Value Line's report (.pdf), it looks like, between 2012 and 2013, outstanding shares only dropped by about half that amount.

Which means ... even while buying back and retiring $5 billion in old shares, Coca-Cola must have, at the same time, been issuing $2.5 billion in *new* shares. 

I don't know why or how. Maybe they issued them to award to employees as stock options. In that case, the money is part of employee compensation. Even if the shares went to the CEO, if they didn't issue those shares, they'd have to pay the equivalent in cash.

So if you're going to criticize Coca-Cola for wasting valuable cash buying shares, you also have to praise it, in an exactly offsetting way, for *saving* valuable cash by paying employees in shares instead. Don't you?

I suppose you could say, yes, they did the right thing by saving cash, but they could do more of the right thing by not buying back shares! But: the two are equal. If you're going to criticize Coca-Cola for buying back shares, you have to criticize other companies that pay their CEOs exclusively in cash. 

But the HBR article actually gets it backwards. It *criticizes* companies that pay their CEOs in shares!

Suppose Coca-Cola is buying back (say) a million shares for $40 MM, which is presumably bad. Then, they give those shares to the employees, which is also presumably bad. Instead, the Harvard article says, they should take the $40 MM, and give it to the employees directly. 

But that's exactly the same thing! Either way, Coca-Cola has the same amount of cash at the end. It's just that in one case, the original shareholders have shares and the CEO has cash. The other way, the original shareholders have the cash and the CEO has the shares.

What difference does that make to the economy or the company? Little to none.


5. Inequality is barely affected, if at all

Suppose a typical CEO makes about $40 million. And suppose half of that is in stock. And suppose, generously, that the CEO can increase the realized value of his shares by 5 percent by allegedly manipulating the price with share buybacks.

You're talking about $1 million in manipulation. 

How much does that affect inequality? Hardly at all. The top 1% of earners in the United States are, by definition, around 3 million people. That includes children ... let's suppose the official statistics use only 2 million people.

The Fortune 500 companies are, at most, 500 CEOs. Let's include other executives and companies, to get, say, 4,000 people. 

That's still only one-fifth of one percent of the "one percenters."

The average annual income of the top 1% is around $717,000. Multiply that by two million people, and you get total income of around $1.4 trillion.

After the CEOs finish manipulating the stock price, the 4,000 executives earn an extra $4 billion overall. So the income of the top 1% goes from

$1,400,000,000,000

to 

$1,404,000,000,000

That's an increase of less than one-third of one percent. Well, yes, technically, that does "contribute" to inequality, but by such a negligible amount that it's hardly worth mentioning. 

And that .00333 percent is still probably an overstatement:

1. We used very generous assumptions about how CEOs capitalize on stock price changes. 

2. When the board offers the CEO stock options, both parties are aware of the benefits of the CEO being able to time the announcements. Without that benefit, pay would probably have to increase (for the same reason you have to pay a baseball player more if you don't give him a no-trade clause). So, much of this alleged benefit is not truly affecting overall compensation.

3. Price manipulation is a zero-sum game. If the executives win, someone loses. Who loses? The investors who buy the executives' shares when they sell. Who are those investors? Mostly the well-off. Some of the buyers might be pension funds for line workers, or some such, but I'd bet most of the buyers are upper middle class, at least. 

We know for sure it isn't the poorest who lose out, because they don't have pension funds or stocks. So it's probably the top 1 percent getting richer on the backs of the top 10 percent.

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Here's one argument that *does* hold up, in a way: the claim that buybacks increase earnings per share (EPS).

Let's go back to the Acme example. Suppose, originally, they have $200,000 in earnings: $190,000 from the business, and $10,000 from interest on the $1 MM in the bank. With a million shares outstanding, EPS is 20 cents.

Now, they spend $300K to buy back 100,000 shares. Afterwards, their earnings will be $197,000 instead of $200,000. With only 900,000 shares remaining outstanding, EPS will jump from 20 cents to 21.89 cents.

Does that mean the CEO artificially increased EPS? I would argue: no. He did increase EPS, but not "artificially."

Before the buyback, Acme had a million dollars in the bank, earning only 1 percent interest. On the other hand, an investment in Acme itself would earn almost 7 percent (20 cents on the $3 share price). Why not switch the 1-percent investment for a 7-percent investment? 

It's a *real* improvement, not an artificial one. If Acme doesn't actually need the cash for business purposes, the buyback benefits all investors. It's the same logic that says that when you save for retirement, you get a better return in stocks than in cash. It might be right for Acme for the same reason it's right for you.

Does the improvement in EPS boost the share price? Probably not much -- the stock market is probably efficient enough that investors would have seen the cash in the bank, and adjusted their expectations (and stock price) accordingly. A small boost might arise if the buybacks are larger, or earlier, than expected, but hardly enough to make the CEO any more fabulously wealthy than he'd be without them.

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There's another reason companies might buy back shares -- to defer tax for their shareholders.

Suppose Coca-Cola has money sitting around. They can pay $40 to me as a dividend. If they do, I pay tax on that -- say, $12. So, now, I have $12 less in value than before. The value of my stock dropped by $40, and I only have $28 in after-tax cash to compensate.

Instead of paying a dividend, Coke could use the $40 to buy back a share. In that case, I pay no tax, and the value of my account doesn't drop.  

Actually, the buybacks are just deferring my taxes, not eliminating them. When I sell my shares, my capital gain will be $40 more after the buyback than it would have been if Coke had issued a dividend instead. As one of the linked articles notes, the US tax rate on capital gains is roughly the same as on dividends. So, the total amount is a wash -- it's just the timing that changes.

Maybe that tax deferral bothers you. Maybe you think the companies are doing something unfair, and exploiting a loophole. I don't agree; for one thing, I think taxing corporate profits, and also dividends, is double taxation, a hidden, inefficient and sometimes unfair way to raise revenues. (Companies already have to pay corporate income tax on earnings, regardless of whether they use it for buybacks, dividends, reinvestment, or cash hoards.)

You might disagree with me on that point.  If you do, then why aren't you upset at companies who don't pay dividends at all? If share buybacks are a loophole because they defer taxes, then retained earnings must be a bigger loophole, because they defer even *more* taxes!

Keep in mind, though, the deferral from buybacks is not quite as big as it looks. When the company buys the shares, the sellers realize a capital gain immediately. If the stock has skyrocketed recently, the total tax the IRS collects after the buyout could, in theory, be a significant portion the amount it would have collected off the dividend. (For instance, if all the selling shareholders had originally bought Coca-Cola stock for a penny, the entire buyback (less one cent) would be taxed, just as the entire dividend would have been.)

There's another benefit: when Coca-Cola buys shares, it buys them from willing sellers, who are in a position to accept their capital gains tax burden right now. That's the main advantage, as I see it: the immediate tax burden winds up falling on "volunteers," those who are able and willing to absorb it right now.

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In my view, buybacks have little to do with greedy CEOs trying to enrich themselves, and they have negligible effect on the economy compared to traditional dividends. They're just the most tax-efficient way for companies to return value to their owners.




UPDATE: Finance writer Michael Mauboussin explains buybacks in more detail in a FAQ here.  (Mauboussin has also written about sports and luck.)

Consumer Reports on unit pricing

Consumer Reports (CR) wants government to regulate supermarket "unit pricing" labels because they're inconsistent. Last post, I quoted their lead example:

"Picture this: You're at the supermarket trying to find the best deal on AAA batteries for your flashlight, so you check the price labels beneath each pack. Sounds pretty straightforward, right? But how can you tell which pack is cheaper when one is priced per battery and one is priced per 100?"

The point, of course, is that CR must be seriously math-challenged if they don't know how to move a decimal point.

I laughed at their example, and I thought maybe they just screwed up. But ... no, they also chose a silly example as their real-life evidence. 

In the article's photograph, they show two different salad-dressing labels, from the same supermarket. The problem: one is unit-priced per pint, but the other one is per quart. Comparing the two requires dividing or multiplying by two, which (IMO) isn't really that big a deal. But, sure, OK, it would be easier if you didn't have to do that.

Except: the two bottles in CR's example are *the same size*.

One 24-ounce bottle of salad dressing is priced at $3.69; the other 24-ounce bottle is priced at $3.99. And CR is complaining that consumers can't tell which is the better deal, because the breakdowns are in different units!

That doesn't really affect their argument, but it does give the reader the idea that they don't really have a good grip on the problem. Which, I will argue, they don't. Their main point is valid -- that unit pricing is more valuable when the units are the same so it's easier to compare -- but you'd think if they had really thought the issue through, they'd have realized how ridiculous their examples are.

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The reason behind unit pricing, of course, is to allow shoppers compare the prices of different-sized packages -- to get an idea of which is more expensive per unit.

That's most valuable when comparing different products. For the same product in different sizes, you can be pretty confident that the bigger packs are a better deal. It's hard to imagine a supermarket charging $3 for a single pack, but $7 for a double-size pack. That only happens when there's a mistake, or when the small pack goes on sale but the larger one doesn't. 

When it's different products, or different brands ... does unit pricing really mean a whole lot if you don't know how they vary in quality?

At my previous post, a commenter wrote,

"What if some batteries have different life expectancies?"

Ha! Excellent point. 

There's an 18-pack of HappyPower AA batteries for $5.99, and a 13-pack of GleeCell for $4.77. Which is a better deal? I guess if the shelf label tells you that each HappyPower battery works out to 33 cents, but a GleeCell costs 37 cents, that helps you decide, a little bit. If you don't know which one is better, you might just shrug, go for the HappyPower, and save the four cents.

Except ... there's an element of "you get what you pay for."  In general (not always, but generally), higher-priced items are of higher quality. I'd be willing to bet that if you ran a regression on every set of ratings CR has issued over the past decade, 95 percent of them would show a positive correlation between quality and price. There certainly is a high correlation in the battery ratings, at least.  (Subscription required.)

So, at face value, unit price isn't enough. The question you really want to answer is:

If someone chose two random batteries, and random battery A cost 11 percent more in an 18-pack than random battery B in a 13-pack, which is likelier to be the better value?

That's not just a battery question: it's a probability question. Actually, it's even more complicated than that. It's not enough to know whether you're getting more than 11 percent better value, because, to get that 11 percent, you have to buy a larger pack! Which you might not really want to do. 

Pack size matters. I think it's fair to say that, all things being equal, we almost always prefer a smaller pack to a larger pack. That must be true. If it weren't, smaller sizes would never sell, and everything would come in only one large size! 

To make a decision, we wind up doing a little intuitive balancing act involving at least three measures: the quality of the product, the unit price, and the size of the pack. The price is just one piece of the puzzle. 

In that light, I'm surprised that CR isn't calling for regulations to force supermarkets to post CR's ratings on the shelves. After all, you can always calculate unit price on the spot, with the calculator app on your phone. But not everyone has a data plan and a CR subscription.

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Here's another, separate issue CR brings up:

"[Among problems we found:] Toilet paper priced by '100 count,' though the 'count' (a euphemism for 'sheets') differed in size and number of plies depending on the brand."

So, CR isn't just complaining that the labels use *inconsistent* units -- they're also complaining that they use the *wrong* units. 

So, what are the right units for toilet paper? Here in Canada, packages give you the total area, in square meters, which corrects for different sizes per sheet. But that won't satisfy CR, because that doesn't take "number of plies" into account. 

What will work, that you can compare a pack of three-ply smaller sheets with a pack of two-ply larger sheets?

I guess they could do "price per square foot per ply."  That might work if you're only comparing products, and don't need to get your head around what the numbers actually mean.

They could also do "price per pound," on the theory that thicker, higher-quality paper is heavier than the thinner stuff. But that seems weird, that CR would want to tell consumers to comparison shop toilet paper by weight.

In either case, you're trading ease of understanding what the product costs, in exchange for the ability to more easily compare two products. Where is the tradeoff? I don't think CR has thought about it. On the promo page for their article, they do an "apples and oranges" joke, showing apples priced at $1.66 per pound, while oranges are 75 cents each. Presumably, they should both be priced per pound. 

Now, I have no idea how much a navel orange weighs. If they were $1.79 a pound, and I wanted to buy one only if it were less than, say, $1, I'd have to take it over to a scale ... and then, I'd have to calculate the weight times $1.79.

According to CR, that's bad: 

"To find the best value on the fruit below, you'd need a scale -- and a calculator."

Well, isn't that less of a problem than needing a scale and calculator *to find out how much the damn orange actually costs*?

I think CR hasn't really thought this through to figure out what it wants. But that doesn't stop it from demanding government action.

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In 2012, according to the article, CR worked with the U.S. Department of Commerce (DOC) to come up with a set of recommended standards for supermarket labels. (Here's the .pdf, from the government site.)

One of the things they want to "correct" is a shelf label for a pack of cookies. The product description on the label says "6 count," meaning six cookies. The document demands that it be in grams.

Which is ridiculous, in this case. When products come in small unit quantities, that's how consumers think of them. I buy Diet Mountain Dew in packs of twelve, not in agglomerations of 4.258 liters. 

It turns out that manufacturers generally figure out what consumers want on labels, even if CR is unable to. 

For instance: over the years, Procter and Gamble has made Liquid Tide more and more concentrated. You need less to do the same job. That means that the actual liquid volume of the detergent is completely meaningless. What matters is the amount of active ingredient -- in other words, how many loads of laundry the bottle can do.

Which is why Tide provides this information, prominently, on the bottle. My bottle here says it does 32 loads. There are other sizes that do 26 loads, or 36, or 110, or ... whatever.

But, under the proposed CR/US Government standards, that would NOT BE ALLOWED. From the report:

"Unit prices must be based on legal measurement units such as those for declaring a packaged quantity or net content as found in the Fair Packaging and Labeling Act (FPLA). Use of unit pricing in terms of 'loads,' 'uses,' and 'servings' are prohibited."

CR, and the DOC, believe that the best way for consumers to intelligently compare the price of a bottle of Tide to some off-brand detergent that's diluted to do one-quarter the loads ... *is by price per volume*. Not only do they think that's the right method ... they want to make any other alternative ILLEGAL.

That's just insane.

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I have a suggestion to try to get CR to change its mind. 

A standard size of Tide detergent does 32 loads of laundry. The premium "Tide with Febreze" variation does only 26 loads. But the two bottles are almost exactly the same size. 

I'll send a letter. Hey, Consumer Reports! Procter and Gamble is trying to rip us off! The unit price per volume makes it look like the two detergents are the same price, but they're not! The other one is watered down!

I bet next issue, there'll be an article demanding legislation to prohibit unit pricing by volume, so that manufacturers stop ripping us off.

I'm mostly kidding, of course. For one thing, P&G isn't necessarily trying to rip us off. The Febreze in the expensive version is an additional active ingredient. (And a good one: it works great on my stinky ball hockey chest pad.) Which is "more product" -- 32 regular loads, or 26 enhanced loads? P&G thinks they're about the same, which is why they made the bottle the same size, to signal what it thinks the product is worth.

Or, maybe they diluted both products similarly, and it just works out that the combined volume winds up similar.

Either way, unit pricing by volume doesn't tell you much. Unless you want to think that, coincidentally, a load with Febreze is exactly 32/26 as valuable a "unit" as a load without. But then, what will you do when Tide changes the proportions?

It makes no sense.

------

Anyway, I do agree with CR that it's better if similar products can be compared with the same unit. And, sometimes, that doesn't happen, and you get pints alongside quarts.

But I disagree with CR that the occasional lapse constitutes a big problem. I disagree that supermarkets don't care what consumers want. I disagree that CR knows better than manufacturers and consumers. And I disagree that the government needs to regulate anything, including font sizes (which, yes, CR complains about too -- "as tiny as 0.22 inch, unreadable for impaired or aging eyes"). 

CR's goal, to improve things for comparison shoppers, is reasonable. I'm just frustrated that they came up with such bad examples and bad answers, and that they want to make it illegal to do it any way other than their silly wrong way. 

If their way is wrong, what way is right?

Well, it's different for everyone. We're diverse, and we all have different needs. 

What should we do, for, say, Advil? Some people are always take a 200 mg dose, and will much prefer unit price per tablet. Me, I sometimes take 200 mg, and sometimes 400 mg. For me, "per tablet" isn't that valuable. I'd rather see pricing per unit of active ingredient. In addition, I'm willing to take two tablets for a higher dose, or half a tablet for a lower dose, whichever is cheaper. 

It's an empirical question. It depends on how many people prefer each option. Neither the government nor CR can know without actually going out and surveying. 

-----

Having said all that ... let me explain what *I* would want to see in a unit price label, based on how I think when I shop. You probably think differently, and you may wind up thinking my suggestion is stupid. Which it very well might be. 

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A small jar of Frank's Famous Apricot Jam costs 35 cents per ounce. A larger jar costs 25 cents per ounce. Which one do you buy?

It depends on the sizes, right? If the big jar is ten times the size, you're less likely to buy it than if it's only twice the size. Also, it depends on how much you use. You don't want the big jar to go bad before you can finish it. On the other hand, if you use so much jam that the small jar will be gone in three days, you'd definitely buy the bigger one. But what if you've never tried that jam before? Frank's Famous Jam might be a mediocre product, like those Frank's Famous light bulbs you bought in 1985, so you might want to start with the small jar in case you hate it.

You kind of mentally balance the difference in unit price among all those other things.

Now, I'm going to argue: the unit price difference, "35 cents vs. 25 cents" is not the best way to look at it. I think the unit prices seriously underestimate the savings of buying the bigger jar. I think the issue that CR identified, the "sometimes it's hard to compare different units," is tiny compared to the issue that unit prices aren't that valuable in the first place.

Why? Because, as economists are fond of saying, you have to think on the margin, not the average. You have to consider only the *additional* jam in the bigger jar.

Suppose the small jar of jam is 12 ounces, and the large is 24 ounces (twice as big). So, the small jar costs $4.20, and the large costs $6.00.

But consider just the margin, the *additional* jam. If you upgrade to the big jar, you're getting 12 additional ounces, for $1.80 additional cost. The upgrade costs you only 15 cents an ounce. That's 58 percent cheaper! 

If you buy the small jar instead of the big one, you're passing up the chance to get the equivalent of a second jar for less than half price. And that's something you don't necessarily see directly if you just look at the average unit price.

-----

I think that's a much more relevant comparison: 35 cents vs. 15 cents, rather than 35 cents vs. 25 cents. 

Don't believe me? I'll change the example. Now, the small jar is still 35 cents an ounce, but the large jar is 17.5 cents an ounce. Now, which do you buy?

You always buy the large jar.  It's the same price as the small jar! At those unit costs, both jars cost $4.20. 

That's obvious when you see that when you upgrade to the bigger jar, you're getting 12 ounces of marginal jam for $0.00 of marginal cost.  It's not as obvious when you see your unit cost drop from 35 cents to 17.5 cents.

------

So, that's something I'd like to see on unit labels, so I don't have to calculate it myself: the marginal cost for the next biggest size. Something like this:

"If you buy the next largest size of this same brand of Raisin Bran, you will get 40% more product for only 20% more price. Since 20/40 equals 0.5, it's like you're getting the additional product at 50 percent off."

Or, in language we're already familiar with from store sales flyers:

"Buy 20 oz. of Raisin Bran at regular price, get your next 8 oz. at 50% off."

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Unit price is a "rate" statistic. Sometimes, you'd rather have a bulk measure -- a total cost. If I want one orange, I might not care that they're $3 a pound -- I just want to know that particular single orange comes out to $1.06.

In the case of the jam, I might think, well, sure, half price is a good deal, but I'm running out of space in the fridge, and I might get sick of apricot before I've finished it all. What does it cost to just say "screw it" and just go for the smaller one?

In other words: how much more am I paying for the jam in the small jar, compared to what I'd pay if they gave it to me at the same unit price as the big jar?

With the small jar, I'm paying 35 cents an ounce. With the big jar, I'd be paying 25 cents an ounce. So, I'm "wasting" ten cents an ounce by buying the smaller 12 ounce jar. That's a cost of $1.20 for the privilege of not having to upgrade to the bigger one.

That flat cost is something that works for me, that I often calculate while shopping. I can easily decide if it's worth $1.20 to me to not have to take home twice as much jam. 

-------

So here's an example of the kind of unit price label I'd like to see:

-- This size: 12 ounces at $0.35 per ounce

--Next larger size: 12 extra ounces at $0.15 per extra ounce (58% savings)

--This size costs $1.20 more than the equivalent quantity purchased in the next larger size.

I'd love to see some supermarket try this before CR makes it illegal.

Do rich people ignore declines in their wealth?

Here's a recent article at FiveThirtyEight that didn't make sense to me. It's called "Why the Housing Bubble Tanked the Economy and the Tech Bubble Didn't."  It's by two guest writers, Amir Sufi and Atif Mian, both professors of economics.

Their argument goes like this (my words):

----

In 2007, the housing bubble wiped out $6 trillion in real estate values. Coincidentally, in 2000, the tech stock bubble dropped stock prices by roughly the same $6 trillion. 

But, from 2007-2009, there was a bad recession, with consumer spending dropping 8 percent. In 2000, by contrast, consumer spending actually grew. 

Why the difference?

Sufi and Mian argue that it's because the tech stock losses fell on mostly the rich, while the housing bubble hurt poor homeowners' nest eggs more severely. In a series of charts, they show how the richest quintile of home owners lost only about 25% of their total wealth in the housing crash, while the poorest 20 percent -- with their mortgage barely paid off, resulting in high leverage -- lost about 90% of their net worth. (This is dramatically illustrated in their second chart, where the bottom-quintile line dives to almost zero. Hey, embedding a tweet is fair use, right?  In that case, here's the graph.) 

This graphic on the housing bust, from economists Amir Sufi and Atif Mian, is striking. http://t.co/RdJJL57UFA pic.twitter.com/xQyZEss53l
— Nate Silver (@NateSilver538) May 12, 2014

The authors write,

"The poor cut spending much more for the same dollar decline in wealth ... If Bill Gates loses $30,000 in a bad investment, he's not going to cut back his spending. If a household with only $30,000 suffers a similar loss, they're going to massively slash spending."

So, that's their argument for why 2007 was so much worse than 2000: because it wasn't just the rich who took a huge hit. 

----

The article's facts make sense to me, but I don't think the conclusion follows. 

While the poorer homeowners did indeed suffer a larger percentage loss, that's not directly relevant. The *dollar* loss is the better measure of what affects the broader economy. When the local coffee shop goes out of business, it doesn't matter if it's because its 200 poorest customers stopped spending entirely, or its 800 richer customers cut spending by a quarter.

The authors implicitly acknowledge that, when they note that the less wealthy are more sensitive to changes on a dollar-for-dollar basis, their $30,000 to Bill Gates' $30,000. But the bottom quintile didn't lose more on a dollar for dollar basis -- only on a percentage basis. 

If the poor had lost the same amount as the rich, or close to it, I might buy the argument. But it wasn't even close. From the chart, it looks like the poorest lost about $25,000 in net worth, dropping from $30,000 to $2,000. But the richest lost a million dollars in value, literally, from $4 million down to $3 million. 

That is, the top quintile lost thirty times as much as the bottom quintile percent.

So, for the authors to defend their hypothesis, it's not enough that they show that the poor cut spending per dollar more than the rich do. They have to show that the poor cut spending per dollar *more than 30 times as much* as the rich do.

I doubt that's the case. A back-of-the-envelope guess shows that it's pretty much impossible. Let's guess at the average income of the bottom quintile -- $50,000, maybe?  And, suppose they spent all of it before the crash. 

After the crash, they get scared, and spend less. How much less?  Let's say, $5,000 less?  They still have to pay the mortgage, and taxes, and food, and clothing. 

Now, the top quintile. Let's suppose they spent all their income before the crash, and, to be generous to the authors, assume they again spent all their income after the crash. 

But, what about their wealth?  Do we really think they won't spend *any* less of their stash now that it's $3 million instead of $4 million?  

Most people accumulate wealth because they eventually want to spend it -- otherwise, what's the point?  Let's suppose they plan on spending half of it before they die, and leaving the other half to charity or heirs. After the crisis, they have $500,000 less to spend over their lifetime. If they've got 30 years left, simple arithmetic says they have to spend an average of $16,000 less per year. (And that doesn't even consider that their income from that wealth will drop proportionately.)

Now, you could argue that they won't cut their spending by $16,000 a year *immediately*. But, why not?  Maybe they're saving for retirement, so the cut in spending comes later. But, some of the richest quintile is *already* retired, so their spending cuts would be immediate, and larger than $16K.

And, look at it the other way. If you're worth $3 million, and the market booms, and suddenly you're worth $4 million ... are you really not going to spend MORE?  I would. And if it works one way, it should work the other way.

(Sure, your personal spending might not change if you're so rich that you have everything you want either way -- like a Bill Gates, or Warren Buffett. But the top quintile isn't even close. I can assure you, personally, that I'd be spending more with $4 million to my name than with $3 million.)

It's undeniable logic that when your net worth drops, your lifetime future spending (or donating) has to drop by exactly the same amount. The idea that richer peoples' spending drops by zero ... that seems to contradict both arithmetic and human nature.

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Coincidentally, I found an answer to the "how much more do the rich spend?" question in a recent book review by Larry Summers, a prominent economist who was Secretary of the Treasury during the Clinton administration. Summers writes,

"The determinants of levels of consumer spending have been much studied by macroeconomists. The general conclusion of the research is that an increase of $1 in wealth leads to an additional $.05 in spending [per year]."

That would mean the top quintile, dropping $1 million in wealth, would spend $50,000 less next year. (More than I would have guessed.)

The above two sentences by themselves don't differentiate between richer and poorer. But the context is clearly about the rich, in a discussion about how the wealthy don't actually get that much wealthier because they tend to blow a lot of the money they've already got. 

Near the end of the article, Sufi and Mian confirm themselves that academic economists disagree with them:

"Former Federal Reserve Chairman Ben Bernanke described why academics doubt the importance of distribution issues ... suggesting that differences in spending propensities because of wealth would have to be "implausibly large" to explain the decline in spending during the 1930s."

"We disagree."

But there's nothing in their data that provides a basis for their disagreement. 

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It occurred to me that there's evidence out there that we could check on our own. Specifically, sales of "rich people" goods. If the wealthy didn't cut spending during the crash, sales wouldn't have dropped -- or at least, not as much as for "normal people" goods. 

Looking at cars ... as a baseline, let's take Ford, the automaker least affected by the 2007 crisis. Here are total US Ford sales for 2006 to 2010, (and year-over-year percentage change):

2006 2,901,090
2007 2,507,366 (-14%)
2008 1,988,376 (-21%)
2009 1,620,888 (-18%)
2010 1,935,462 (+20%)

Compare those percentage changes to some of the luxury brands. I've added Honda, too, as a second "middle-class brand" reference point.

Bentley:       +3% -33% -49%  +5%
BMW:           +7% -15% -21% +12%
Mercedes:      +2% -21% -17%  +6%
Cadillac:      -5% -25% -33% +35%
Jaguar:       -24%  +2% -25% +12%
Lexus:         +2% -21% -17%  +6%
---------------------------------
Ford:         -14% -21% -18% +20% 
Honda:         +5%  -6% -19% + 5%

It does seem like luxury cars were hit almost exactly the same way as Ford and Honda, doesn't it?  

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Among the large, publicly-traded US home builders, one of them, Toll Brothers, specializes in luxury homes. According to their annual report (.pdf, see first page), their average home sold for $639,000 last year.

If rich people didn't cut spending during the crisis, you'd expect that Toll Brothers' sales wouldn't have declined, or, at least, declined less than those of the builders of "middle-class" houses. 

Nope.  Here's the 2006-2009 percentage drop in sales for all the homebuilders Value Line covers:

82% Beazer 
76% D.R. Horton
74% Hovnanian
84% KB Home
81% Lennar
81% M.D.C.
72% Meritage
56% NVR
71% Pulte
73% Ryland
70% Std. Pacific
71% Toll Brothers

Toll Brothers fits right in.

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Here are some luxury-goods makers' revenue changes from 2006 to 2009:

-27% Sotheby's
+ 2% Tiffany
-27% Zale
-29% Movado
+71% Coach
-49% Brunswick
-17% Harley-Davidson
-75% Winnebago

All are down more than the overall 8%, except Coach and Tiffany. The simple average is still more than -8%. The weighted average is probably a little smaller than that, because Winnebago, Sotheby's, and Movado have lower sales than the other companies. 

Also, I'm not sure Coach should count ... it had been growing wildly throughout the decade, and continued to do so until recently. Also, its growth did slow significantly during the crisis. From 2002 to 2013, Coach's revenues grew by an average 13% annually -- but from 2008 to 2009, sales rose only 2%.

In any case, even if you include Coach, the results are in line with the 8%. If you don't include Coach, then, wow, those companies' sales did much, much worse than -8%.

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Sufi and Mian also seem to think their hypothesis is somehow related to the issue of income inequality:

"[This] shows how important distributional issues should be in macroeconomics. As the recent craze over French economist Thomas Piketty's new book, 'Capital in the Twenty-First Century,' shows, both economists and lay people are beginning to understand that wealth inequality is crucial for understanding the broader economy."

But, inequality doesn't impact their argument at all. What their hypothesis says is that shocks to poorer people are more likely to cause recessions. In that case, what prevents recessions is not equality, but wealth. 

In fact, by their argument, inequality is almost completely uninformative as a predictor. If we were all equal and poorer, the recession would be severe. If we were all equal and richer, there would be no recession at all. It's *wealth* that matters for their theory, not inequality.

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So, in summary: the authors are writing to refute conventional thinking on recessions. But, they don't really tell us why they think the established science is wrong. Their key premise seems to be contradicted by arithmetic and actual sales figures. And, the data they choose to show us doesn't actually bear on the disagreement. 

Do I have this wrong?  Am I missing something?  Any economists out there want to correct me?

Disputing Hakes/Sauer, part III

(This may not be of general interest ... it's mostly a technical addendum to part I and part II, which is where the meat of the argument is.   You should read those first, if you haven't already.)

To recap again: the Hakes/Sauer study ran a regression to predict the log of player salary from last season's "eye" (BB/PA), "bat" (batting average), and "power" (TB/H).  I argued that one of the problems with the regression is that they were using a geometric model for an arithmetic relationship.

Specifically: when it comes to salaries, research has shown that every expected walk is worth the same -- about $150,000, for a free agent.  But the Hakes/Sauer model had every walk increasing salary by a certain *percentage*.  That would make good players' walks appear to be worth more than mediocre players' walks, at the margin.

I just wanted to show evidence that that's happening.  In my own regression, where I used "next year salary value of offense" instead of just salary, I got these coefficients, which I reported last post:

       eye  bat power
---------------------
2001   4.06 5.52 1.43
2002   5.82 3.53 1.20
2003   5.97 4.76 1.46
2004   8.48 4.76 1.46
2005   6.92 2.58 1.08
2006   7.61 5.98 0.82

Now, I'll give you the same chart, but with the sample divided into "full time" (400+ PA) and "part time" (130-399) players.

This is full time:

       eye  bat power
---------------------
2001   7.49 8.94 1.98
2002   4.90 3.28 1.39
2003   5.10 9.97 1.21
2004   6.04 5.68 1.29
2005   4.43 5.26 1.26
2006   4.77 9.90 1.63

And this is part time:

       eye  bat power
---------------------
2001   0.41 1.87 0.88
2002   6.89 3.84 1.10
2003   7.19 1.03 1.61
2004  11.58 4.63 1.07
2005  10.48 1.50 1.03
2006  10.33 3.60 0.77

There's a huge difference in coefficients for the two groups.   

The return on "eye" is consistently higher for part-time players than for full-time players, as I suspected.  It's the reverse, though, for batting average.  

How come?  Isn't the logic the same?  

Maybe the difference is this: when one part-time player has a higher batting average than another part-time player, it's probably just luck, and there's not much relationship to next year's value.  But when one part-time player has a higher *walk rate* than another part-time player, that's more likely to be real, and that comes out in next year's stats.  

Walk talent does vary more among players than batting average talent ... the SD of batting average, among players with 4000+ career AB, is about 21 points.  For walk average, it's about 30 points.  Furthermore, the season SD due to luck is about 50% higher for batting average (since hits happen more often than walks).  

So, overall, the "signal to noise ratio" is more than twice as high for walks as for hits.

I think that's what's going on, why the walk numbers show one effect and the batting average numbers show another.

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Oh, and, in case it's not obvious: the entire "Moneyball" effect for walks comes from the part-time players.  There's no effect at all for the full-time players.   What drove the Hakes/Sauer result, I think, is that, in 2004 and 2005, part-time players with walks just happened to have good numbers the following year.