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.

Hypothesis

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.

Conclusion

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.