A rudimentary NFL season simulation

Following a post by Tango a couple of weeks ago on the playoff systems of the various sports, I thought I'd try writing a simulation. This is an update of that work in progress. Actually, I've only started on the NFL, and I haven't even done playoffs yet, just the regular season. But I thought I'd at least share what I've got so far.

In the simulation, each of the 32 teams was assigned a "true talent," from a normal distribution with mean .500 and standard deviation .143. No team was allowed to have talent higher than .900 or lower than .100; if they did, they were moved to .900 or .100. Then, all 32 teams were moved the same amount (arithmetically) in the same direction to get the overall talent to average exactly .500. (I think this method actually reduces the expected SD below .143, but I didn't bother fixing that.)

The 16-game schedule is random, instead of unbalanced (with the restriction that a team can't face any another team more than twice). There are no tie games. There is no home field advantage (although that would be easy to add in). The chance of winning each game is determined by the log5 method. There are no ties in games. Ties in the standings (division or wild card) are broken randomly.

As I said, I stopped there for now; haven't done playoffs yet. That's the next step, along with home field advantage.

Anyway, here are some results. Each result is out of 100,000 seasons. Every result came from a different run of the simulation. Results varied a fair bit per run, but I think everything is reasonably typical.

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I checked for all teams out of 3,200,000 (32 teams, 100,000 seasons) that finished more than 8 games above or below their talent. That's hard to do, obviously. Also, the worse or better you are, the harder it is. It's (relatively) easier for an 8-8 team to go 16-0 than for a 3-13 team to go 11-5. Amplifying that is the fact that there are a lot more 8-8 teams than 3-13 teams. However, offsetting that, a little bit, is the fact that the 3-13 team can also go 12-4 or 13-3 or better.

In any case ... there were 43 cases where a team differed from its talent by 8 games or more. Of those, 26 were teams that outperformed, and 17 were teams that underperformed.

The biggest differential was in season 98,534, where the Broncos a team that had talent of 4.56 wins (out of 16), but went 14-2, for a differential of 9.44 games. That was the only team with a differential of 9 or more. Part of the reason it did so well was that it faced inferior opponents. You'd expect any given team's opponents to average 8.00 games of talent. But in that season, the Broncos' opponents' talent was only 7.45 games. Not a huge difference, but still.

Actually, when it comes to extreme events, a small difference in opponents makes a big difference in probability. Of the 43 teams in the sample, 38 of them had records that went in the direction "aided" by the opposition (in the sense that the underperforming teams played better-than-expected opponents, and vice versa). That's 38-5 in favor.

The worst team in the sample was the season 63,924 Jets, a 3.03 team that went 12-4 (playing 7.11-win opponents). The best team in the sample was a Bucs team that was expected to win 12.04 games, but instead went 4-12 (playing 8.58-win opponents).

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I also took a look at teams that went 0-16.

Those results probably aren't as realistic, because they're heavily dependent on the shape of the tail of the talent distribution ... and we really don't know what that is. Recall that we chose a normal distribution that gets truncated at .100 (1.6 wins). Both those choices -- normal, and truncated -- are arbitrary and probably not close enough to real life. (Also, teams could drop below .100 in talent from the adjustment that sets all league-years to .500.)

In addition, the other shortcuts in the simulation probably skew the results too. The mainstream results are probably right, but the extremes are extremely sensitive to some of the assumptions.

With those caveats: there were 5,663 of those 0-16 teams out of 3.2 million, and their average talent was .181, which is just under 3-13. I suspect the talent of actual flesh-and-blood 0-16 teams is higher than that, but I really don't know.

16-0 should be exactly symmetrical, so I won't show that separately.

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I checked for four-way ties where every team has the same record. That happened 878 times out of 800,000, or about once every century.

There were five seasons out of 100,000 where two divisions had a four-way tie. Actually, that might be a little high ... the test runs had only 1 or 2 such seasons.

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Anyway, before I start on the playoffs, and repeating this for other sports leagues, I'm looking for feedback on what I've got so far. Any suggestions?

And, if you want me to run the sim and check for something in particular, let me know in the comments. It's real easy to add a couple of lines of code to check for something specific.

Being proven wrong is like winning the lottery

Following my last post on being a dick in online message boards, I was going to prepare a list of things that can really piss off people who are trying to have a discussion with you, things that you shouldn't do. Like, for instance, changing the subject when someone brings up key points, or being inappropriately picky in ways that don't affect the main point. That kind of thing.

As I was preparing that list, it occurred to me: these are things that nobody would ever do who really, truly cared about whether they were right or not. They're things that people do when they're trapped by logic, but they're reluctant to admit their position might be wrong.

Why don't people want to admit they were wrong, even when it seems obvious to everyone else? Ego. Nobody likes to be proven wrong. But, if we can get over that pride thing, we should WANT to be proven wrong! It makes things better for us.

Because, it's bad to be wrong. Therefore, if you're wrong, the best thing is to *stop being wrong*. And the way to stop being wrong is to change your mind.

Also, there are lots of side benefits to changing from a wrong view to a correct view. For one thing, you're suddenly more right! And, for another, now being right lets you see things in a whole new way.

If you think that 1+1 equals 3, the world isn't going to make a whole lot of sense to you. You'll think your paycheck doesn't add up, and everyone's giving you the wrong change. You'll think the IRS is ripping you off, and mathematics is just arbitrary, since everyone just seems to be totaling things a different way. You'll be suspicious of everyone, and life is going to be pretty difficult.

But, when you see that 1+1=2, suddenly, everything comes into focus! You'll see the world works logically, after all. You now predict what people will do, and see that everything really does add up. Your life is better -- a lot better.

So, you should be happy and excited at the idea that we might be wrong. The guy you're getting mad at could be the one that changes your life, if it turns out that he's right.

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Another way to look at it: suppose you're a successful major-league pitcher, making a few million dollars a year. You go to the doctor, and he says, hey, there's been something wrong with your elbow since birth.

Should you be insulted and angry that the doctor is insulting your awesome pitching arm? No, you should be very excited -- that's great news! If the doctor is right, and he the problem, maybe you'll be throwing 100 mph instead of 95!

Don't like that analogy? OK, here's another try.

Let's suppose you open a restaurant, and you're very successful, and people like your food. You're very proud of being a great chef. Then, someone tells you, correctly, that one of your appetizers, one that you think is one of your best, is actually pretty awful. Your customers hate it.

Your first reaction might be to get defensive. But, again, you should be thrilled! Now you can fix that dish. Your food, your restaurant, your profit, and your reputation will all be better than before. It's almost the best thing that can happen to you. Being Finding out you're wrong is like winning the lottery!

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So, in online debates, we should all argue as if God will give us a million dollars if we're proven wrong. That way, when someone disagrees with us, we won't just dismiss him out of hand or twist our logic to try to save our own position. We'll stop and think, "hey, is it possible that this guy has my million dollars?" We'll be less likely to let our ego take over and turn us into dicks.

Okay, maybe that's too much money. Maybe for a shot at a million dollars, we'd listen to idiots way, way too long. Maybe the right amount is, I dunno, a hundred dollars, or something. But you get the idea.

And I should add that I'm not saying that I, personally, know how to suppress my own ego, or even that I succeed in doing it when I try. I'm just saying that I know I *should*.

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I guess my overall point is that any online discussion, even between people who violently disagree with each other, should be a co-operative venture. One of you is wrong, and you're working together to find out who. And, we should keep in mind that most of the benefit goes to the person who was actually wrong in the first place.

When someone you respect, or someone who seems to be expert and knowledgeable, starts disagreeing with you, it's like you've stumbled upon a fistful of lottery tickets. Argue your position, yes, but don't get defensive, and keep an open mind. Sure, it might be that other guy who's wrong. But if you're really, really lucky, it'll be you.

In defense of online rudeness

A couple of weeks ago, the moderator of a certain website I frequent posted a message, reminding us commenters to respect each other. The warning wasn't random, of course; it was prompted by a discussion that got a little less civilized than normal for that site.

This kind of thing plays out all the time on thousands of different sites. But what bugs me about these "please be civil and respect each other" warnings is that they only target one general type of rudeness. I did a Google search for "message board rules etiquette," to get some examples of posted rules. A lot of them include something like this:

"Don't issue personal attacks, use profanity, or post threatening, abusive, harassing, or otherwise offensive language or images. Keep your messages appropriate and courteous at all times. Please disagree with other opinions respectfully."

Now, most of us follow this advice almost all the time. But, sometimes, we don't. When don't we? When we get really frustrated with someone. Why do we get frustrated?

Well, they might be repeatedly misrepresenting something we wrote. They might be ignoring our questions. They might be following the argument back and forth for hours, until they realize they're "losing", and change the subject. They might be obviously disingenuous, denying something they wrote in another post just days before. They might agree with what you say when it suits their argument, but change their mind as soon as it goes against them. They might be trolling for fun. They might be committing any one of a thousand logical fallacies, and refusing to be corrected.

But ... the rules don't prohibit that, do they? The rules say you can get kicked off the forum for calling someone an idiot. But you can't get kicked off for repeatedly (and perhaps deliberately) butchering your logic.

Here's a hypothetical situation I made up:

A: US citizens spend too much on foreign aid. We need to help our own instead. There are thousands out of work. I don't know why you don't see that.

B: I see that, but money spent outside the US can help a lot more people who are desperate. We can save hundreds of lives for almost nothing.

A: I don't believe you.

B: (Goes and searches the internet. Writes several paragraphs of illustration of various public health costs, and how cheap it is to save lives in Africa with cheap drugs or vitamins or something.)

A: Well, maybe, but the multinationals make too much profit when we do that.

B: (Goes and searches the internet) Here are some companies selling drugs at cost, or offering them for free, if we just pay to distribute them!

A: Yeah, whatever. And, regardless, we still spend too much. Charity is nice, but in moderation. We should spend only about half of 1% of our income on foreign aid. That's $1 out of every $200. That's my maximum.

B: Hang on, let me search the internet ... well, as it turns out, we spend only 0.1% of our income on foreign aid! So, we both agree that we could spend a little more, right?

A: I said we should spend half of that! See, we spend too much!

B: No, half of that would be 0.05%. You said 0.5%. Here, let me quote your post: "$1 out of every $200".

A: You're misquoting me. Besides, you can throw numbers at me all you want. They're just numbers. The fact is that we spend too much on foreign aid. We need to help our own instead. I don't know why you don't see that.

B: You're a dick.

What happens next? B gets in trouble for calling A a dick. But A gets off scot-free for BEING a dick. And that's a lot worse.

As far as I'm concerned, it should be A who gets kicked off the site, not B. But that'll never happen. See, B's offense was objective, and easily caught. He used the word "dick". Everyone can understand that, and you can easily make a rule out of it. "Why did B get kicked off?" "He called A a dick." "Oh, OK."

On the other hand, A's offense was subjective. It requires a judgment call from the moderator. And, there's no smoking gun. "Why did A get kicked off?" B would say, "He was a dick." But A's supporters would say, "It's because he didn't agree with B." "It's because the moderator didn't like his politics." "It's because nobody respects B's right to stand up for American workers." "It's because that website doesn't respect dissenting views."

It's hard to describe what A did wrong. The evidence is hard to describe. There's no smoking dick.

And so, the As of the world get away with it, and we just have to put up with them.

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I don't think that that B said anything morally objectionable. A indeed WAS a dick. Sure, it didn't *have* to be said ... but, it was true. At least in the sense that "you're a dick" can ever be said to be true.

And I would argue that B, after investing so much time and effort in moving the argument forward, earned the right to say it.

Sure, you don't want discussions degenerating into name-calling. That's no fun for anyone. But, in the appropriate context, an occasional, controlled outburst is OK.

Strained analogy: think of a discussion as a pot luck, and insults like ketchup. If you show up at a pot luck, you don't just bring a bottle of ketchup. That's rude, and tacky. But, if you bring hamburgers for everyone, and you *also* bring a bottle of ketchup ... that's perfectly OK. In fact, the hamburgers you're providing are actually enhanced by the ketchup you brought.

The rule is, if you want the right to serve ketchup at the pot luck, you have the obligation to serve the meat to go with it. And, if B has just spent the better part of an hour researching foreign aid, and hundreds of characters typing rebuttals to a poster he thought was arguing in good faith ... that's a LOT of meat. You've got to say that B has earned the right to pound the ketchup bottle a little bit.

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This is one of the problems we have with public discussion in general. Whether it's politicians, columnists, academics, or talking heads on TV, the unwritten code is the same. You can butcher logic all you want, and nobody will call you on it. But resort to name-calling, or other "uneducated" forms of language, and you get in trouble.

The public doesn't have the time or patience to judge what you've said. But it does understand *how* you said it!

You probably know what happened to Don Cherry a couple of weeks ago.

Over the summer, in separate incidents, three former NHL players took their own lives. They had all been "enforcers," players kept on the team for their willingness to start fights with opposing players. Speculation ensued that there was somehow a link between being an enforcer and having mental health issues. Three other former enforcers, Stu Grimson, Chris Nilan, and Jim Thomson, apparently made comments that expressed support for that hypothesis.

Don Cherry went on TV and accused Grimson, Nilan and Thomson of hypocrisy. Those guys, themselves, once chose to make a very good living with their fists, Cherry said, knowing that they'd be out of professional sports if they didn't. Now, they're trying to deny the same choice to today's players, since, with their careers long over, banning fighting would not longer cost them anything. And this, Cherry argued, was on the basis of a flimsy hypothesis with no solid evidence behind it. Hypocrites!

Seems like a legitimate argument, right? I mean, you can certainly disagree with it, but it's not that unreasonable a point to make, in the context of a controversial issue that's already attracted a lot of discussion.

But Cherry got himself in trouble. Why? Because he didn't use educated language. He didn't say it formally, the way I described it. He used less fancy words. One word, in particular: "pukes." Cherry called Grimson, Nilan, and Thomson "a bunch of pukes."

Without the word "pukes," it's just another Don Cherry TV segment. But with the word "pukes," suddenly there's outrage. There were news stories, outraged columnists, and even newspaper editorials, all of them prominently featuring the word "pukes."

In the midst of all this, Grimson threatened to sue Cherry if he didn't apologize. That was more than an idle threat: Grimson is a lawyer, and his statement threatening "further recourse" was issued by his own law firm. Cherry apologized a few days later. Grimson issued a new statement that said, OK, he wouldn't sue, but maybe the CBC should fire Cherry anyway.

Cherry got a raw deal: not just because of the content, which wasn't really any more controversial than his usual, but because of the attention he got by breaking the taboo against name-calling. "If you call somebody a name," goes the unwritten, unspoken rule, "it signals that you're uneducated and boorish, so, accordingly, we will oppose your argument exceedingly vigorously."

The media and public would do better to take some now-famous advice from MGL: "If you guys can’t separate tone from substance, that is your problem not mine. Stop being such whiners about tone.”

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P.S. Kind of off topic, but while I'm here ...

I don't agree with Cherry's logic that Grimson is a "puke" for speculating on the link between fighting and mental health. I think that's a perfectly reasonable thing for a former goon to wonder about.

But, I do have a problem with Stu Grimson's conduct afterwards.

I mean ... What kind of guy spends his career beating people up, then complains about a "lack of decency" because someone has the temerity to criticize his views about it? What kind of guy threatens to sue someone just because he's been called a childish name? What kind of guy speaks out on a position of public importance, and then when someone disagrees, tries to get him fired? What kind of guy would leverage his advantage -- knowing he's a lawyer and can cause all kinds of problems for Don Cherry at no cost to himself -- to extort an apology with credible threats of a lawsuit?

Maybe Don Cherry was right about Grimson, after all.

How much does "Moneyball" help a team?

How much is sabermetrics worth to a team?

That's probably a hard question to answer. Every team uses statistics to some extent. Even before sabermetrics, teams were looking at player statistics to decide who to play and who not to play. They may not have had any fancy formulas, but they had a pretty good idea of how to weight the relative contributions of players. Nobody ever released a 30-HR guy because he was only hitting .240, and nobody ever released a .330 hitter because he had no power. Intuitive evaluations weren't perfect, of course, but they were pretty reasonable most of the time.

Where sabermetrics helps, I think, is not in evaluating actual performance, but in helping figure out *future* performance. How to extrapolate minor-league performance in to major league performance ... how to take luck out of a player's batting or pitching line ... figuring how different kinds of players age ... that sort of thing.

Suppose you took a team management right out of the early 1970s, and gave them a team today without letting them learn anything discovered after 1977. How much would that team underperform compared to the rest of MLB? I don't have an answer to the question, but I'd be interested in hearing yours.

Anyway, here's a narrower question. How much can a more sabermetric approach *today* benefit a team, compared to, say, the typical team's sabermetric approach? For instance, how much did Billy Beane really mean to the A's?

A couple of weeks ago, Tango did a study to figure out which teams did better or worse than expected, given their payroll. The A's were the team that outperformed the most over the last decade -- about 7 games per season, it looks like. That's a lot, but there's probably a whole bunch of luck there, since we're cherry-picking them as the best of the lot. Also, it's possible that much of their outperformance came in the early years, when, as many critics of "Moneyball" hype have pointed out, they had three underpriced ace starters.

So, we'd have to regress that 7 games to the mean a fair bit. If you made me make an arbitrary guess, I'd be willing to bet that less than half of that seven game advantage came from sabermetrics. (But, I have no real basis for that guess without studying it.)

Anyway, with the Cubs signing Theo Epstein, we now have a market estimate for what sabermetrics might be worth today. Epstein's new agreement is for about $4 million per season. He still had one year to go on his contract with the Red Sox, for which they will receive some sort of compensation from the Cubs. Let's say that compensation will be worth $1 million. So Epstein's value is around $5 million. I don't know how much an average replacement level GM makes, by comparison. To be conservative, let's say it's $500,000, although it's probably more than that. That means that Epstein's excess value is $4.5 million, exactly what it costs in free agent players to gain one extra win.

It looks like that's what Epstein is worth: one win per season.

Is that a lot? Frankly, I don't know. It's a competitive market for players these days, with lots of money on the line, and there's lots of random luck in who makes it and who doesn't. In that light, it could be that one win per season is an exceptional, genius-level performance.

If that's the case, doesn't it mean that the "Moneyball" approach is overrated? I mean, one win a year. At that rate, it would take decades, even centuries, to have good statistical evidence that the sabermetric approach works.

Of course, you have to remember that that's compared to other teams ... and, nowadays, those other teams are doing a fair amount of statistical work themselves. Maybe it's three or four games over a team that won't look at anything new at all, that never heard of Voros McCracken and winds up overpaying pitchers with lucky BABIPs. And, maybe Epstein took less pay than he was worth in order to become a Cub. Maybe it's a win and a quarter, or a win and a half.

Still ... to me, one game doesn't seem that unreasonable. The point might not be that an you can win pennants just by embracing sabermetrics. The point might be that, with every team in a sabermetric arms race against every other team, you certainly can *lose* pennants if you persist in living in the 70s.

But, again ... one game. Doesn't that mean that if a team does well, and someone credits "Moneyball," they're probably just blowing smoke?


UPDATES:

1. In the comments, Bill Waite suggests that sabermetrically-savvy managers might have a significant impact, too. He says that just rejigging the lineup is worth almost half a game a season, and says that the difference between best and worst could be as much as eight games.

Food for thought. It would be interesting to consider how to try to look for this in the historical record (if indeed that is possible), since we know that some managers are indeed more numbers-oriented than others.

2. Matt Swartz e-mailed me about a study where he found a positive correlation between sabermetric management and team performance. It's here.

Capital Gains and Warren Buffett: Part II

This is a continuation of the previous post about why capital gains taxes should be lower than regular taxes, and perhaps even zero.

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3. More Double Taxation

One year, the New York Yankees draft Mickey, a player with star potential.

The team signs him to a five-year contract at $2 million a year. They figure that's a bargain. Mickey is good enough that he's expected to produce $15 million a year in revenue, so the Yankees figure, reasonably, that they're making $65 million on the deal.

The day after the draft, along comes the IRS. "Hey," they say to the Yankees. "You just signed a deal that's worth $65 million in profit. We want the corporate tax on that, $22 million. Pay up!"

The Yankees say, "Wait a second! Mickey hasn't played a single game for us yet, so we haven't made any profit! How can you be asking for the tax already?"

The IRS says, "We don't want to wait. We want the money now. But, don't worry, we know we're collecting the money in advance, so we're discounting the amount owed by the current interest rate."

The Yankees protest. "That's still not fair," they say. "You shouldn't tax us until we actually make the money. After all, Mickey just signed a contract for $10 million. You're not taxing *him* on that $10 million right away ... you're going to tax him only when he gets his paychecks. You're not going to his house and demanding $4 million from him right this second, are you?"

The government agent replies, "I don't know why you have a problem with this. I already told you we're adjusting for the time value of money. And we know you *have* enough cash to pay us now, because you're the Yankees. So why not?"

"What if Mickey doesn't perform and we don't make the expected profit?" the Yankees ask.

"No problem," replies the IRS. "We'll give you a partial refund. But, of course, if Mickey starts playing like Albert Pujols, and you clean up, we'll ask for more."

"Hmmm," the Yankees owner says. "I guess it doesn't really matter to the long-term bottom line. But it still seems like it's not right."

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Is it unfair? Yeah, I think it is ... if the Yankees haven't made any profit yet, they shouldn't pay any tax on that profit.

Still, the present value of the tax paid is the same, whether the Yankees pay it in a lump sum, or whether they pay it on a year-by-year basis. So if paying in advance is unfair, it's unfair only from a timing standpoint. Either way, the Yankees pay the right amount of tax. It's just that one way, the IRS is in an ungodly hurry, that they have no business being in. But it's the same amount of money. You might even imagine a situation where the Yankees would *choose* to pay in advance.

So this is just slightly unfair. What would make it *really* unfair is if the IRS made the Yankees pay BOTH WAYS. First, if they made them pay $22 million on their projected $65 million profit, and then they also made them pay regular corporate tax on the annual $13 million profit. That would be pure double taxation, right?

It has to be one or the other. Either they pay the tax on the projected profit in advance, or they pay the tax as the profit comes in. If you make the Yankees pay both, you really are making them pay exactly twice as much tax. Instead of 35% tax, they'd be paying 70%.

Now, if you don't stop to think about it at all, it might not seem unfair that way. When they sign the contract, the accountants say, "Congratulations, Mr. Cashman, that deal you just made with Mickey is worth $65 million." And, at the end of the next five years, the accountants say, "Congratulations, Mr. Cashman, you made $13 million more this year because of Mickey." It may be tempting to add all those up to get $130 million in profit. But you can't do that. The $65 million is THE SAME MONEY as the five $13 millions.

Tax the profit in advance, or tax it when it comes in. Choose only one. If you do both, it's grossly unfair.

With me so far?

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Now I'm going to argue that when you have a capital gain on a stock, this is almost exactly what happens: the profit gets taxed twice: once in advance, and once when it comes in.

You buy a stock in a drug company, Acme, for $1 a share. Acme is just barely breaking even. After you buy the stock, Acme discovers a new drug that prevents heart attacks. It's going to be a blockbuster. In fact, it's so good that it's going to produce annual earnings and dividends of $2 a share, indefinitely. But, first, the FDA has to approve the drug. It's so good, with no side effects, that FDA approval is assured, but it will still take two years.

Wall Street immediately calculates that $2 a share, indefinitely, starting in two years, makes the stock worth $31. Shareholders celebrate. You sell your share of Acme for $31, incurring a $30 capital gain. Should you pay tax on that capital gain?

Look what's happened. Acme hasn't actually made any profit yet. The $30 increase in the stock price represents *future earnings*, just like the $65 million contract with Mickey is future earnings. So if you tax the $30 increase -- which is what capital gains tax does -- and then you later tax the corporate profits -- which of course you will do -- that's exactly analogous to what happens if you tax the Yankees twice.

To make things fair, the IRS should pick one: either tax the capital gain right now, or tax the corporate profits later. One or the other.

Otherwise, the IRS is getting a lot more than the corporate tax on the profits. Because, the fact that I sold my share does not change the future tax bill of the corporation, or the new shareholder, at all. Whether I sell the share or not, the corporation will still pay the normal taxes on the profits. But, by me selling the share, I trigger an *extra* tax, a capital gains tax, on the value of the future profits. That's two taxes on the same money.

The only thing that makes this example different from the Yankees example is that the two taxes are paid by two separate people, instead of one. That kind of hides the unfairness. The original buyer pays the full, future corporate tax, which seems OK because he just made a big gain on his stock. And the new buyer pays the full, future corporate tax, which seems fair because he's the owner at the time the profit was made.

But, still, they're both paying tax on the *same money*. [See footnote 1.]

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As I said, it should be one or the other. Since it's hard to discount the corporate tax by capital gains tax that's already been paid, the easiest solution is to just eliminate the capital gains tax. That way, the profit is only be taxed once, when the corporation earns it.

That may seem unfair, because, after all, when you earned your $30 capital gain on your $1 investment, that's a lot of money. Why shouldn't you pay tax on it?

One answer is: you already did, kind of.

When you sold the share at $31, that was the market price. That market price is based on after-tax profits. We said the corporation pays a $2 dividend. That means it will make $3 in profits and pay $1 in corporate tax, leaving a $2 dividend. The buyer of your share gets the $2 dividend, and pays 15% tax on it, leaving $1.70 in his pocket.

That $1.70 in his pocket, year after year, is why the new buyer was willing to pay $31 for your share. That means he's looking for an after-tax return of 5.48% on his money, which is what he's getting: $1.70 divided by $31.

Now, suppose there were no corporate tax or dividend tax. Then, instead of $1.70 a year, the new owner of the share would receive the full $3 profit. For the same yield of 5.48% after tax, he'd now be willing to pay $54.74. So, if there were no taxes, the shares would have been worth $54.74 instead of $31, and you would have made a capital gain of $53.74 instead of $30.

So the corporate tax actually did cost you money! It cost you almost exactly the same rate as the overall taxes on the profits -- in this case, about 45% -- because you received only $31 instead of $54.74. That is, in order to take over *your* obligation to pay all that future tax to the government, the new buyer demanded a discount of $23.74 to compensate him for taking over your obligation.

It may look like you're not paying any tax on your capital gain, but, you are, in a hidden kind of way.

Look at it this way. Suppose that while you owned Acme, the government decided to double the corporate tax on drug companies, forever into the future. What would happen? Well, because of the new tax, Acme would only be able to pay $1 in dividends, instead of $2. That means the new owner would receive only 85 cents a year.

But the new owner still wants his 5.48% after-tax yield. So, he's not going to pay $31 for the stock any more. He's only going to be willing to pay $15.50. So that's what you'll have to sell it to him for.

See? The extra corporate tax comes right out of your pocket, even if you're not the one writing the check. [See footnote 2.]

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Here's another way to look at it: when you sell the company, you sell it for $54.74, its full value if there were no taxes, but you promise the buyer to pay all the taxes into the future. Instead of paying every year, though, you hand the buyer a cheque for $23.74, and say, "here, invest this and it'll pay your tax bill every year." The buyer says, "OK, that's a deal."

Instead of you actually physically paying the $23.74, you just take it off the price of the share, which is why you wind up with $31. It doesn't look like you paid any tax, but you actually paid all of the corporation's tax into the future!

And, again, that's WITHOUT a separate capital gains tax. With a full capital gains tax, you'd be paying double.

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Here's a simpler case.

You grow apples. There's a 50% income tax on the apples you grow. There's also a 50% capital gains tax.

You take two apple seeds, plant them, nurture them, fertilize them, and grow them into two healthy trees. The apples start growing. You harvest them and send half the apples as your income tax. The government, therefore, gets one tree's worth of apples a year -- half the harvest of the two trees.

Now, you sell the two trees to your neighbor. Since you grew them from nothing, your capital gain is the entire two trees. So, at a 50% capital gains tax, you owe the government one tree. But you're out of trees, so you have to buy one tree back from your neighbor, which you now give to the government.

What's happened? The government used to get one tree's worth of apples a year. Now it gets 1.5 trees' worth! First, the tree that you just paid it in capital gains tax, which now belongs 100% to the government. Second, half the apples from the other tree the neighbor now owns.

So, effectively, the government is now taxing the apples not at 50%, but at 75%.

But it's hidden between the two of you. You pay the first 50%, and your neighbor pays 50% of what's left.

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It may seem counterintuitive that Warren Buffett should get away with almost no tax on his capital gains. You have to look hard to see that even if the capital gains tax rate is zero, Warren Buffett, and the rest of us, are still, in a hidden way, paying the normal rate.

It may not be obvious, but I think it's true.


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Footnote 1: This argument applies when the profit goes on indefinitely. If not, the double taxation isn't quite as bad. Suppose the patent on the drug runs out in 20 years. At that point, the stock will tank and the new buyer will have a capital loss, exactly offsetting the capital gain the old buyer had 20 years before.

However, the government will have earned interest on that capital gains tax for 20 years, before refunding it without interest. After 20 years, because of forgone interest, the refund might be worth, say, only 1/4 the original amount. So it's not double taxation, but only "1.75-ble" taxation.


Footnote 2: Actually, it's not quite that simple. We assumed the new buyer's demand for 5.48% after-tax was fixed. Really, it's in comparison to other investments of equal risk. And those other investments also have tax burdens associated with them. The reason the new buyer demands 5.48% is because that's what he could get, after tax, from a bond of similar risk.

But if there were no corporate taxes, the rate of return on bonds would also be higher. Therefore, the new buyer might be demanding, and receving, a higher rate. That shows that the overall investment tax rate affects the buyer, too.

So it's not really as clear-cut as saying the original owner, the one who gets the capital gain, pays all the tax. It's a complicated thing to figure out what proportion of the corporate tax is actually "paid" by the original owner, and what proportion is "paid" by the second owner. All we know is that the proportions add up to 100%, and the total tax paid is the corporate tax plus the dividend tax.

I might be wrong here ... economists, please correct me.

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Capital Gains and Warren Buffett: Part I

Recently, Warren Buffett noted that the rate of tax he pays on investment income (around 17%) is much less than the rate his employees pay on their earned income (around 36%). In a previous post, I argued that the comparison is meaningless, at least in the case of dividends.

Some commenters, here and at Tango's blog, criticized me for not dealing with capital gains, which they say is where most of Buffett's income arises.

Capital gains come from many different sources, which bring up different issues of fairness. So, I'll have several things to say instead of just one. My conclusion will be that there's an argument to be made for taxing capital gains at a very, very low rate, perhaps even zero.

I will argue that position is true even if you believe that tax rates on the rich are too low. I believe that even if you think the rich should be taxed, at, say, 60%, or 70%, or 80%, you should STILL favor a system where their "regular" income is taxed at a higher rate and capital gains are taxed at a lower rate.

Here goes.


1. Double taxation inside a corporation

If you buy a stock, and then sell it at a higher price, your profit is a capital gain. But, in many cases, the corporation has already been taxed on the profit that forms some or all of the gain. To tax it again at the full rate is unfair double taxation.

Suppose you buy a share of a company at $100. This year, they earn $10 in profits. They pay $3 corporate tax on the profit, and keep the other $7.

So, a year later, and all things being equal, the company is worth $107 a share. You sell your share for a $7 capital gain.

But, the piece of the company you owned actually earned $10 in profits, not $7. At a 30% tax rate, you already paid $3 in corporate tax on the profit. To tax you another 30% on the remaining $7 would be unfair. That would mean you'd only keep $4.90, and your effective tax rate would be 51%.

The concept of "horizontal equity" says that people who have the same income should pay the same amount of tax, regardless of where the income came from. If the top tax rate on employment income is, say, 40%, then the effective tax on income earned through a corporation, when you combine all the taxes, should also be 40%.

As I described in more detail in the previous post, a personal capital gains tax rate of around 15% gives the result we're looking for: you keep 85% of 70% of corporate earnings, which works out to a tax rate of 40.5%.

This is exactly the same argument as in the other post, just for capital gains instead of dividends. I realize that if you didn't like that argument, you probably won't like this one either.

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Want a real-life example? Suppose you owned one share of Chevron.

Over the 16 years from 1995 to 2010 (.pdf), Chevron made a total profit for you of about $123. It had around a 40% corporate tax rate (I'm not sure why so high -- other companies seem to be around 30%). That means it paid around $50 in taxes, leaving $73 in after-tax earnings. It paid around $27 in dividends over that stretch, leaving $45 inside the company.

In that time, the stock went from around $25 to around $100, a $75 capital gain. More than half of that capital gain -- $45 -- is from the profit on which the corporation has already paid tax for you.

To fully tax you again on that $45 profit is not particularly fair.

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What about the rest of the capital gain, the remaining $30 out of the $75? That probably shouldn't be taxed much either, since probably a lot of that is just inflation. Which brings us to number two.


2. Inflation

The idea behind income tax is that when you become wealthier, you give some of it to the government to provide public services. But when the nominal value of your assets goes up only because of inflation, you're not wealthier, are you?

In 1980, you bought a house for $100,000. Today, you sell it for $300,000. Are you really $200,000 wealthier? Of course not. That's just inflation increasing the price of your house. In non-monetary terms, you might have paid 200,000 loaves of bread for it in 1980 (at 50 cents a loaf). In 2011, you sell it again for 200,000 loaves of bread (at $1.50 a loaf). Really, you've broken even.

This is pretty obvious, and I think almost everyone understands this already. That's why, in both Canada and the US, they offer tax relief for capital gains on houses you live in. In Canada, you pay absolutely zero capital gains tax when you sell your primary residence. In the USA, I once read, your first $400,000 in gains is tax-free if you buy another house with it. (Is that still true?)

If the government didn't do that, there would be riots in the streets. You wouldn't be able to move! If you're living in a $500,000 house with $200,000 worth of taxes due when you sell it, you'd have to downsize substantially. That would obviously be unfair. In most cases, the profit you made on the house is artificial, just an artifact of inflation.

The same is true for, say, stocks and mutual funds. Suppose you bought a share twenty years ago for $10. It never paid dividends. Today, you sell it at $20, but because of inflation, the $20 buys only what $10 bought then.

You really haven't made a profit. Yes, you got more dollar bills now then you paid in the past, but in terms of actual wealth -- the number of loaves of bread it would buy -- you just barely got your investment back.

That's part of the reason why the capital gains tax rate is lower than the regular tax rate: to compensate for the fact that a significant portion of a capital gain isn't really an increase in wealth.

Perhaps the best policy would be that when you sell an asset, you adjust for inflation when figuring your gain, and then you pay tax on that adjusted gain. The problem with that is that it's complicated and involves lots of arithmetic. I'd support implementing it anyway.

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Now, you might be saying, that's fine if your capital gain just keeps pace with inflation. But Warren Buffett is famous for his investing prowess, where he makes capital gains that far outstrip inflation!

To which my response is: OK, but first, can we agree that he shouldn't have to pay tax on the inflation portion of his gain? (And if we agree on that, then at least we agree on at least one reason that Buffett's capital gains rate should be less than his employment income rate, right?)

But, yes, that still leaves the non-inflation portion of Buffett's gain, which is probably still substantial. That'll be in Part II.

Would MLB salaries drop if all players were free agents? Part II

In my previous post, I said I had another argument for why free agent salaries would drop if all players were free agents. Here it is.

Right now, some players are free agents. Their value seems to be about $4.5 million per win.

Now, suppose that, instead of *more* players being free agents, *fewer* players become free agents. In the extreme case, suppose that only one player is a free agent, with a value of 1 WAR. What happens?

It seems like his price will be bid up. But why? It can't be not scarcity in and of itself. Because, even in the real world, when there are lots of free agents, there is still be a time when there's only one left, and HIS price still seems to be $4.5 million per win. There's something else going on. Here's what I think it is.

In in a world with few free agents, wins must be distributed without regard to where they can make the most money. They go to whichever teams made the best draft choices or trades. That's inefficient, financially, for the league as a whole.

The Yankees value wins highly, and would like to buy more, but they can't. The Pirates don't value them much, and would like to sell some to the Yankees. But MLB rules forbid that. So the Yankees are stuck with many fewer wins than they want, and the Pirates are stuck with many more.

So what happens when this one and only free agent goes on the market? Clearly, the Yankees and Red Sox are desperate for wins, with which they can make a lot of money. They'll easily outbid the Royals and Pirates.

But why will the price wind up higher than $4.5 million? Because $4.5 million is the price that results when teams have the ability to fill a lot more of their needs. The Yankees may have been blessed with only 80 wins from their farm system, but they've been able to sign free agents to bring themselves up to 95. And $4.5 million is the value of that 95th win. The wins before that, they valued much higher (or they wouldn't have bought them).

But, in this case, the Yankees are truly stuck at 80. That 81st win they're thinking of buying must be worth more to them than the 95th win (which is worth $4.5 million). And so, they'll be willing pay a lot more for it.

The same logic applies to the Red Sox, and the Phillies, and other teams, and so the price of the single free agent gets bid up well beyond $4.5 million.

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That argument shows that fewer free agents means higher costs. That means that more free agents means lower costs, which is what we were trying to prove.

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Another thing we can conclude is that the more free agents there are, the less competitive balance. Why? Because the fewer the number of free agents, the more wins are distributed haphazardly among teams. Since teams aren't allowed to sell those wins, small-market teams wind up with wins they otherwise wouldn't have bought. That means more competitive balance.

If all players were free agents, it's possible that some teams would not find it profitable to buy ANY wins, and would stay with replacement-value, minimum-salary players. Obviously, that means competitive balance suffers.

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At the risk of my usual overkill, here's another way to look at it:

Suppose that there is a fixed supply of BMWs. In a free market, only rich people would own them, because they're of little use to poor people (who can't drive them much because they can't afford much gas or maintenance). There might be 100,000 rich people in the city who might fancy a nice BMW, but only 10,000 actual cars. So the BMWs go to the people who bid the most for them, and maybe the auction price is $50,000 each.

Now, suppose MLB calls half of the cars "draft choices", airdrops them randomly on households, and prohibits selling them for what they're worth. The poor people are happy to have them, since they're free, but they don't get much benefit from them. On the other hand, the rich families who got them are thrilled: some of them were about to go out and spend $50,000 on one, and now here's one for nothing!

But now, that leaves only 5,000 cars left for auction. And there might still be 99,000 rich people who are interested. Obviously, with fewer cars available on the market, but not many fewer buyers, the price goes up, maybe to $100,000.

Also, "competitive balance" increases. It used to be that the rich owned 100% of the BMWs. Now the rich only own maybe 60% of the BMWs.

And, none of this would happen if the poor people were allowed to sell their cars to the rich people. In that case, the cars would still go for $50,000, same as before, and "competitive balance" wouldn't change. If Bud Selig changed the rules so that the poor could sell to the rich, both the poor and rich would benefit: the poor people would have more money, and the rich people would get their cars cheaper.

Who wouldn't benefit? The BMW fans rooting for poor people. These fans don't care how much money their poor friend has: all they live for is the day that their poor friend drives a BMW to the World Series! Before, when their poor friend had to keep his car, they had some hope. Now that their poor friend will almost always sell his airdropped car, they have little to no hope.

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Another thing we can conclude is that it must be true, right now, that there do exist poor teams who have BMWs they'd like to sell but can't. In previous posts, I assumed this didn't happen, to keep things nicely theoretical. I assumed that even the Royals can earn a little bit more by buying a win or two, at the going rate of $4.5 million.

But now we have evidence that's not true, that there are some teams who want to sell wins but can't.

Why do I say we have evidence? Because the previous post showed that, today, if all players were free agents, the price would come down. This proves that there must be at least some BMWs being held by poor households. Otherwise, it wouldn't matter if you airdropped all the BMWs, or none of them: either way, they'd go to the same rich people at the same price. The fact that free-agent restrictions are increasing prices proves that MLB could make more money redistributing wins to the rich teams.

But, that makes an additional assumption: that the fans only care about wins, and not about the fairness of a sport that organizes itself so the Yankees will always be great, and the Royals will always be bad. As I once wrote, I think that even though wins seem to drive revenues today, the fans might get sick of it in the future, and MLB might be better off sacrificing some short-term revenues in favor of keeping the fans interested in the long-term.

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In summary, I think these arguments lead to a few real conclusions about the current state of MLB:

1. More free agents would mean lower salaries for those free agents;
2. MLB could make more money by allowing small-market teams to sell players to big-market teams;
3. A marginal win is worth an equal $4.5 million not to all teams, but only to the middle-class and rich teams;
4. The "arbs" and "slaves" do, in fact, contribute to competitive balance.

Would MLB salaries drop if all players were free agents?

If every player became a free agent, would player salaries drop? Here's an argument that suggests that, yes, they *must* drop. I'm not sure if it's right, but I can't find a flaw ... maybe you guys can.

Assumptions: all teams are rational, and all teams know the expected value of the future performance of every player.

Here goes.

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Suppose that right now, at equilibrium, a marginal win in the major leagues is worth about $X million.

That means that the last win every team buys (in free agency) must give them $X million in extra revenues. If it gave less, they wouldn't have signed the guy. If it resulted in more than a $X million increase, the team could probably increase profits by signing even more free agents.

OK, now the hypothetical: what if EVERY player were a free agent? That is, what if there were no "arbs" or "slaves", so that every player cost the same price per WAR?

I don't know the exact breakdown of free agents vs. arbs vs. slaves. But, for the sake of argument, let's suppose that, right now, free agents contribute 1/2 the overall WAR, arbs contribute 1/4, and slaves contribute the other 1/4.

Also, let's assume that arbs make half of what free agents do, and that slaves make $0. Then, the average WAR costs major league teams exactly $0.625X -- that is, 5/8 of what a free agent WAR costs.

The fraction 5/8 works out to 62.5%. That's not too far from the fraction of revenues that go to player salaries. So, if every player were a free agent at $4.5 million per WAR, the 62.5% would go to 100%, and it would turn out that ALL of MLB's revenues would go to payroll.

That can't happen, can it? If payroll is higher than revenue for the league, it must be the case that payroll is higher than revenue for at least one team. For that team, it would be better to cut payroll. The only way it wouldn't be better to cut payroll would be if that team would lose even MORE money with EVERY possible payroll cut.

But ... minimum payroll is only about $13 million. It's hard to imagine that even a small-market team wouldn't get $13 million in revenue, even with a replacement level team expected to go 60-102. (And, in any case, the team could fold, and avoid losing money that way.)

So, no team would ever spend more on payroll than it got in revenues. Therefore, payroll can't be more than 100% of revenues. Therefore, at least one of the assumptions in our model must be false. The most likely candidate is the assumption that wins would still cost $4.5 million.

So it must be the case that the cost per free-agent WAR would drop, from $4.5 million to something lower, to allow the league to still turn a profit.

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Does that argument work? I think it does. But I have another one if that one doesn't.

Why Warren Buffett is wrong about tax rates

Note: non-sports post. Lots of numbers, though!

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As you've probably heard by now, Warren Buffett thinks the rich should pay more taxes. Much of his argument is based on the fact that wealthy people pay a lower percentage of their income to the government. Buffett writes,

"Last year my federal tax bill — the income tax I paid, as well as payroll taxes paid by me and on my behalf — was $6,938,744. That sounds like a lot of money. But what I paid was only 17.4 percent of my taxable income — and that’s actually a lower percentage than was paid by any of the other 20 people in our office. Their tax burdens ranged from 33 percent to 41 percent and averaged 36 percent."

But, like a lot of numbers that get thrown around, this "percent of taxable income" is misleading. Yes, the number 17.4 is lower than the number 36. But if you look more closely, Buffett is actually paying at a comparable rate to that of his employees.

The issue that confuses things is that Buffett earns most of his income through corporate dividends (some of it also comes from capital gains, but I'll ignore those for now). Dividends are paid out of after-tax profits of corporations. That means, effectively, that the corporation has already paid most of Buffett's tax.

Suppose Buffett's employee earns $50,000, and pays $18,000 in taxes, which is 36 percent. As for Buffett himself, suppose he owns shares of McDonald's. Let's say he owns 7,609 of those shares, which correspond to the same $50,000 in McDonald's pre-tax profits. (My figures are approximate, all rounded from this Value Line summary.)

So, what happens? Well, McDonald's gets taxed at about a 30% rate. So that leaves only $35,000 in after-tax profits. Then, the company pays Buffett a dividend. It doesn't pay the entire $35,000, because it keeps some to reinvest. It pays Buffett only about half of that, maybe $17,000. Then, Buffett pays an additional 15% tax on that $17,000.

So: on his $50,000 in profits, Buffett pays $15,000 through the corporation, and then an extra $2,550 in dividend tax. That's a total of $17,550 out of $50,000, which is ... about 35%, approximately the same as his employee.

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Actually, that's not quite right. It actually understates Buffett's tax rate.

As we saw, McDonald's makes $50,000, pays $15,000 in taxes, sends $17,000 to Warren Buffett, and reinvests the remaining $18,000. But our calculation assumed that the $18,000 part is still Buffett's, but is fully tax paid. It's not. Eventually, Buffett will claim that $18,000 personally, either through another dividend, or through a capital gain when he sells his stock. At that point, he'll pay another 15%.

So, really, the bottom line is: Of every dollar Buffett earns through McDonald's, he gets to keep 85% of 70% of it. That's 59.5%. So his effective tax rate is 40.5%.

You can argue that 40.5% is too high, or you can argue that 40.5% is too low. But you CANNOT argue that Buffett's tax rate is only 17%. That simply isn't true in any real sense. It's true only in a misleading technical sense, in that McDonald's pays some of Buffett's tax for him. The fact that the corporation makes the payment doesn't mean that it doesn't actually come out of Buffett's pocket.

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This is actually a standard explanation of why taxes on dividends are lower than taxes on "work" income. In fact, it's actually the stated rationale. Canada has a complicated method of calculating taxes on dividends, a method that actually takes into account how much corporate tax was already paid. The explicit idea is that the overall tax rate should be the same, no matter if you earned the income through a direct investment, through an investment in a corporation, or through employment. It doesn't always work out perfectly, according to my accountant (who tells me it's a little higher through a corporation), but it's close.

It's well-enough known to economists and accountants and people who work in corporate finance that, like other bloggers who have written about this, I'm surprised Warren Buffett didn't know it.

Now, it could be that he knows it, but doesn't believe that the corporate taxes should "count". A lot of people somehow believe that corporations should count as separate "people," and so it's fair for both McDonald's and Buffett to pay taxes separately, where the total adds up to more than if Buffett made the money directly.

But that really doesn't make sense. The fact is that if Buffett owns McDonald's, and McDonald's earns $50,000 from his investment, that $50,000 *belongs to Buffett*, even if, right now, it's classified as corporate earnings. Corporations, and their earnings, are the property of their owner, and Buffett is that owner. The fact that the first $15,000 of taxes appears on the corporate tax return instead of Buffett's absoutely does not change the fact that Buffett is paying that tax.

If you still don't agree with that, if you think that Buffett really isn't paying that 30%, then you might like these two options I'm about to show you. Those could reduce personal taxes substantially, while still providing the same amount of money to the government!

Here's number 1. As of tomorrow, ever person in the country has to start up a corporation, of which he/she is the sole shareholder and CEO. Also, all employers now have to pay any salary to the corporation.

So, what happens is this: your corporation now pays 30% of its income -- your salary -- in corporate tax. It then pays you the rest as a dividend. Like Warren Buffett, you now pay only 15% in taxes. Indeed, you might pay zero in taxes -- according to this Wikipedia page, low-income Americans pay 0% tax on dividends!

That means that Warren Buffett's employees will now definitely have a lower tax rate than he does -- or at worst, the same rate -- because they are taxed exactly the same way!

Would you support that new law? You probably wouldn't. You'd see that that was just a sneaky way of taxing people the same rate as always, but making it look like they're not paying much tax. That's exactly what I'm arguing in the case of McDonald's.

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Here's number 2. Right now, people take home a lot less than their salary, because of payroll deductions for income tax. Someone making $50,000 might actually take home only $35,000.

So here's what we do. We eliminate payroll deductions and personal income tax completely. Instead, we implement a corporate payroll tax, which works out to exactly the same as the income tax used to. So, now, your employer still gives you $35,000 to take home, but pays an extra corporate tax of $15,000. You pay zero percent tax on the $35,000.

Perfect, right? Now the income tax on "work" is zero percent. Warren Buffett is still paying 17.4% on his investments. Situation resolved!

I bet you think that's ridiculous. You probably should. Whether you pay the tax, or your employer pays the tax, it's the same thing: you do $50,000 of work, and the government gets 30% of it.

Well, it's the same thing for McDonald's profits. Whether McDonald's pays the tax, or Warren Buffett does, or they both do, the fact remains: McDonald's makes $50,000 of profit, and the government gets 40.5% of it. How much of that 40.5% comes from a cheque from Buffett, and how much comes from a cheque from McDonald's, doesn't matter.

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OK, here's one more suggestion that's less ridiculous.

Change the law a bit, so that when McDonald's pays a dividend to an American taxpayer, they don't pay tax on that part of their profit. That sounds kind of fair, right? If McDonald's doesn't get to keep it, they don't pay tax on it. Just like they can deduct interest that they pay to a bondholder, they can deduct interest that they pay to a shareholder.

Then, when the shareholder receives the dividends, tax them at the normal rate, as if they were "work" income.

Sounds reasonable, right? Well, it works out to almost same amount of tax collected. Actually, if Buffett's personal tax rate is around 33%, you can leave out the "almost" -- it's exactly identical.

McDonald's makes $50K. They send Warren Buffett $21,428.57. Buffett pays about 33% of that in taxes, or $6,978, leaving him $14,450. After paying Buffett, McDonald's has $28,571.43 left. They pay the government 30% of that, or $8,571.43. That leaves them $20,000 to reinvest.

That's EXACTLY what's already happening, in today's system where Buffett *appears* to be only paying 15%:

-- McDonald's makes $50,000
-- Buffett keeps $14,450 after taxes
-- McDonald's keeps $20,000 after taxes
-- The government gets $15,550.

One way you look at it, it looks like Warren Buffett pays only 15% in taxes. Another way, it looks like he pays 40.5% in taxes. A third way, it looks like he pays 33% in taxes. But the results, all three ways, are exactly the same!

No matter how you figure it, the bottom line is the same. Buffett gets 28.9% of the profit, McDonald's keeps 40% of the profit, and the government gets 31.1% of the profit. The difference is how you do the accounting. If you're a government that wants to make it look like the rich have it too good, you levy the entire 31.1% on the corporation, so that it looks like Buffett pays zero. If you're a government that wants to make it look like corporations aren't taxed enough, you levy the entire 31.1% on Buffett, so that it looks like McDonald's pays zero.

In a vacuum, Warren Buffett's supposed 17% tax rate doesn't mean anything. It's an artifact of how you do the accounting. To really see what's happening, you have to look at the end result. And that end result, in this example, is that the government winds up with 31.1% of the money that would otherwise have been Buffett's.

You may think that's too low. You might think that's too high. That's fine. But either way, the "17%" figure is not relevant, even if Warren Buffett thinks it is.