A Foosball Strategy: Passive Goalie Management

Is it better to leave your money with active managers who try to take advantage of market trends, or to invest in a broad index fund which moves with the market?

It turns out that the returns are about equal for both approaches. Why is that true? Consider the intuition: If everybody thinks that the price of an asset will rise in value tomorrow, they’d try to buy a lot of it today. When they do, they bid the price up to to the point that it will rise to.

That’s one of the ways to understand the efficient market hypothesis, which predicts that it’s very difficult for investors to consistently beat the market. Active fund managers over-promise, and the results of their efforts to take advantage of trends is no better than buying into an index fund to invest and forget.

Now let’s apply the idea of passive fund management to foosball.


Say you’re playing a foosball game with one other person, who’s not a novice nor a world champion, and on a standard table with four rows.

This essay presents a central hypothesis: Just as active fund management is no guarantee of above-average investment returns, active goalie management is no guarantee of above-average chances of saving a goal. You should use instead passive goalie management.

Here’s the reasoning.

  1. Foosball is a game with high volatility. Not only is it too hard to have perfect control of the ball, and there are too many random variables. Sometimes your shot is blocked by one of your own rows; sometimes the curve of the table changes the path of the ball; sometimes the ball flies out of the table. All but the most skilled of players have to accept that their shots probably won’t be going to the exact place they want it to go. After all, even experts sometimes score on themselves.
  2. If the side that shoots has difficulty predicting where the ball will go, then the side blocking the shot will only have greater difficulty predicting the same thing. Given how quickly shots can be, it’s very, very hard to move your goalie in the exact position to stop a goal. And given the unpredictability of the ball’s path, you may well be moving your goalie out of place so that a shot gets into your goal. Possibly your quick, careless thrusts nudge the ball into your own goal. It’s just very difficult to successfully block a goal with a goalie by moving it to the right position at the right time.
  3. The goalie row is not like the other rows: You control the row immediately ahead of it. But it’s only a distance of two or three inches. That’s not much at all. If you can’t manage to block and move into the right position with with the first row of defense, it’s unlikely that you have enough time to move the second into the right position. Managing that second row runs into diminishing returns.
  4. The opportunity costs of a second row of defense is high when it means giving up both positions for offense. Your offense line, after all, is your first line of defense. Focus on that instead.
  5. The best reason to believe in passive goalie management is empirical. If your goalie is so important, you would expect those who practice active goalie management to let in very few goals. Yet even those who never let go of the goalie find themselves regularly scored on.

For all these reasons you’re better off with passive goalie management: Just keep your goalie somewhere along the goal. It’s likely to be just as good as rapidly thrusting it around and hoping that you block a shot.

You may not have to keep it at the dead-center of the goal. In fact it may be marginally better if you keep it slightly towards you because your opponent has greater visibility of the ball on his side; he’ll more likely take a shot from a position that he can see better.

Three additional notes:

  1. Passive goalie management does not mean zero goalie management. Sometimes a shot is just slow enough that you can get your goalie in position to block. Then you should block. And sometimes your opponent may have total control over his offense line. At that point you should move your goalie, if only because you don’t leave your gap to be predictable.
  2. You may worry that a very powerful shot knocks your goalie back and so that the ball effectively goes through your goalie. Deal with that concern by tilting your goalie slightly forwards by 35-degrees. When the force of the shot is distributed upwards, the goalie won’t be knocked back.
  3. Passive goalie management simply mimics the characteristics of passive fund management. They face similar conditions, but there’s no rigorous theory and data behind it as there is like the efficient market hypothesis. This essay simply takes cues from portfolio management theory.

The Implication and the Strategy

Passive goalie management does not mean that you should abandon your players in the defense zone. You should keep on hand on defense, pretty much at all times. If you have any chance of blocking a shot, that hand will take you much of the way there; if it can’t be blocked, you’ll have to hope that your goalie is in place to block.

Here’s what passive goalie management looks like in practice: You goalie is tilted slightly forwards and placed somewhere in front of your goal; your left hand takes care of defense; and your right hand toggles between the five-line and the offense.

Here are the tactics of passive goalie management.

  1. Passive goalie management is a high-offense strategy. 2/3rds of your positions, not 1/2, will be focused on offense. When the ball does end up near defense, your one objective is to clear it to your offense lines.
  2. Passive goalie management also speeds up the game. With one fewer position to worry about, you have an easier time covering the whole board. When you stop using one of your defensive lines, you also give up the ability to control the ball for a really good shot. A good passive goalie management player won’t let the ball rest so that the opponent gets jogged around and without the chance to take a clean shot past your goalie.
  3. Again, treat your offense line as your first line of defense. Push as hard as you can on offense so that the ball never makes it to your back rows.
  4. You can further press your speed advantage by making your opponent run. Try out a back-pass (say from your five-line to your defense line) to draw your opponent away from defense. Just don’t back-pass into your own goal.
  5. In general, you should be trying to increase the variance of the ball path. Go crazy and do the unexpected. You have the advantage over speed, so make the ball fly all over the table.

The ideal passive goalie management play resembles a blitz, with shots at all times with the offensive lines, catching rebounds until the ball ends up in your opponent’s goal.

How should strategy be adjusted when two passive goalie management players play against each other? That calls for further analysis, perhaps in a different framework.


People will score on your all the time if you don’t actively manage your goalie. But they’ll also score on you all the time if you do manage your goalie, because a) the ball is unpredictable, b) you may end up moving the goalie out of a position to block, and c) it’s not as if you cover additional area when you move around. Just focus on this high-offense strategy so that your opponent doesn’t often have a chance to shoot into an easy gap from up close.

Ignoring your goalie and going on high offense will unsettle your opponent. To really unsettle your opponent, make sure to talk about the theory behind your strategy during the game. He’ll be totally nettled. For bonus results, start talking about the efficient market hypothesis while holding the ball before you serve. And for best results, start an on-the-spot discussion of kurtosis, fourth moments, and transition probabilities and how they may affect a foosball game.

The Kindness of W.H. Auden


The NYRB writes about the personal life of Auden. He was an extraordinarily kind person. These are some excerpts from the piece.

“W.H. Auden had a secret life that his closest friends knew little or nothing about. Everything about it was generous and honorable. He kept it secret because he would have been ashamed to have been praised for it.

I learned about it mostly by chance, so it may have been far more extensive than I or anyone ever knew. Once at a party I met a woman who belonged to the same Episcopal church that Auden attended in the 1950s, St. Mark’s in-the-Bowery in New York. She told me that Auden heard that an old woman in the congregation was suffering night terrors, so he took a blanket and slept in the hallway outside her apartment until she felt safe again.

Someone else recalled that Auden had once been told that a friend needed a medical operation that he couldn’t afford. Auden invited the friend to dinner, never mentioned the operation, but as the friend was leaving said, “I want you to have this,” and handed him a large notebook containing the manuscript of The Age of Anxiety. The University of Texas bought the notebook and the friend had the operation.

At literary gatherings he made a practice of slipping away from “the gaunt and great, the famed for conversation” (as he called them in a poem) to find the least important person in the room.

When he felt obliged to stand on principle on some literary or moral issue, he did so without calling attention to himself, and he was impatient with writers like Robert Lowell whose political protests seemed to him more egocentric than effective.

He was disgusted by his early fame because he saw the mixed motives behind his image of public virtue, the gratification he felt in being idolized and admired. He felt degraded when asked to pronounce on political and moral issues about which, he reminded himself, artists had no special insight. Far from imagining that artists were superior to anyone else, he had seen in himself that artists have their own special temptations toward power and cruelty and their own special skills at masking their impulses from themselves.

He had no literal belief in miracles or deities and thought that all religious statements about God must be false in a literal sense but might be true in metaphoric ones.”

Collateralized debt obligations and credit default swaps

Find this piece with prettier formatting published here.

The CDO, the CDS, and the Subprime Mortgage Crisis

How these two financial instruments helped cause the financial crisis

What exactly are collateralized debt obligations (CDOs) and credit default swaps (CDSs)? This post draws from The Big Short by Michael Lewis and a study on CDOs by A.K. Barnett-Hart to summarize how these two financial instruments are structured and why they’re in part responsible for the financial crisis.

They have a well-deserved reputation for being very technical, but at their core they are simple concepts. A CDO is just a fancy bond, while a CDS is basically an insurance policy. Bear with me and I’ll try to explain them in the clearest terms I can. This is not so much about the actions of individual banks or hedge funds; instead, it’s about how these two instruments are structured.

First we get into the CDO, then the CDS, then how they relate to each other, and finally their role in the subprime mortgage crisis.

Mortgage-backed Securities

CDOs are made up of sections of mortgage bonds, or mortgage-backed securities (MBS). So to understand the CDO you have to first understand the mortgage bond. What is a mortgage bond?

If you’re buying a house you’re probably taking out a mortgage. That means that you’re getting a loan from a bank or a lending agency and then making a payment back every month with some interest.

Interest rates on mortgages are fairly high. A 30-year U.S. Treasury Bond may yield about 3 to 6%, while a homeowner pays between 5 to 10% on her monthly mortgage payment.  Mortgages offer much higher returns, and so investors are more attracted to them.

But for various reasons, it’s hard to invest in individual mortgages. They’re easier to invest when thousands of individual mortgages are bundled together to form a mortgage bond. The mortgage bonds were packaged by agencies like Fannie Mae and Freddie Mac, who bundled the mortgages from banks like Wells Fargo or lending agencies like the New Century Financial Corporation.

A mortgage bond isn’t like a corporate bond or a government bond. Instead, it’s a claim on payments from its thousands of mortgages. But just as a corporate bond can default, a mortgage bond can fail too: When enough individual mortgages failed, the entire bond won’t be able to generate its promised returns.

What happens when thousands of bonds get pooled together? Then the law of large numbers kicks in: Maybe a few mortgages will fail, but it’s unlikely that all of them will fail. The failure of a few are unlikely to sink the whole bond. So they’re pooled together to reduce the idiosyncratic risk of letting any single failure get in the way.

Continue reading

The Up Side of Down, by Megan McArdle

The book’s lesson is that we can’t engineer away failure and indeed that we shouldn’t. Instead, we ought to embrace it intelligently, because failure is the only way that we really learn.

I wrote about some of the main stories for the Shopify blog.

There are lots of good quotes. Here are a few:

There is a famous story of a rich old man being interviewed by a young striver, who asks him for the secret of his success. “Good judgment,” says the magnate.
His eager young follower dutifully scribbles this down, then looks at him expectantly. “And how do you get good judgment?”
“Experience!” says our terse tycoon.
“And how do you get experience?”
“Bad judgment!”

When people try to explain why the Mona Lisa is the most famous painting in the world, they talk about her mysterious smile, the gauzy technique, the background. And yet Watts points out that they are not really explaining the painting’s appeal; they are just describing the painting.

In Deep Survival, a stunning book about how people survive in extreme terrain, Laurence Gonzales about a phenomenon known in orienteering as “bending the map.” It’s summed up with a pithy quote from Edward Cornell: “Whenever you start looking at your map and saying something like, ‘Well, that lake could have dried up’ or, ‘That boulder could have moved,’ a red light should go on.”

Groups are capable of much more stupid behavior than individuals are. They frequently fall prey to what I’ve taken to calling “groupidity”: doing something stupid because other people around you seem to think it’s safe.

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Days of Fire, by Peter Baker

Peter Baker is a reporter at the Times. He’s somehow managed to write a book with scenes of every important moment of the Bush presidency as if he were part of the deliberations himself. We get a view of how Cheney in the White House reacted on the day of 9/11; the internal deliberations of invading Iraq; the frustration over Katrina; the crisis precipitated by Ashcroft’s refusal to authorize metadata surveillance; the nominations of Roberts and Alito; planning the surge; the dynamics of how Bush, Cheney, Rice, Rumsfeld, Powell worked together; and a lot more. It was enthralling.

Baker takes pains to stress how Bush was not subservient to Cheney. The beginning and of the book are dedicated to exploring that relationship, and Bush’s growing independence from his vice president is a central theme throughout the book.

I never read books about politics, but this is a good one. Every page was filled with reporting, and there isn’t really a great deal of analysis. You’ll learn so much beyond the headlines you saw not too long ago.

My single favorite paragraph is this, about the post-invasion planning for Iraq:

A twenty-four-year-old who worked at a real estate firm had never been to the Middle East was assigned to rebuild the stock exchange. An army officer busied himself rewriting Iraq’s traffic laws by cutting and pasting from Maryland’s code. A twenty-one-year old who had yet to finish college and whose most significant job had been ice-cream truck driver was among those charged with purging the Interior Ministry of militia members.


Times feature on upstate orchestras

Today the Times published a reported piece on the state of orchestras in Buffalo, Rochester, and Albany. It features a beautiful shot of Kodak Hall at the Eastman School of Music, part of the University of Rochester.



Though orchestras everywhere are struggling, the ones in these three cities are experimenting with techniques to draw new audiences, some of which are quite innovative. The story ends with a quote from the director of the Albany Symphony: “When I moved here from Los Angeles, I was very sad in the fall,” Mr. Miller said of Albany. “All the leaves died and fell off the trees, and I associated fall with death. And then finally my wife had to explain to me that it’s not about death. People love fall because it’s the first step to rebirth.”’

The most striking sentence in the story is this one, four paragraphs in:  “(This year’s festival starts on Monday; article, Page 17.)” It’s not hyperlinked.

That sentence is obviously meant for print. It’s amazing that it was not only unamended but also failed to link to the proper article. I’m a fan of both orchestras and news sources, but it’s grim to see one institution that has been struggling in the digital age is covered as a story of hope and rebirth by another institution that has seen arguably greater wrenching changes in the digital age. When the latter is so obviously stuck in the past, doesn’t it feel like conditions are bleak for both institutions?