Game Theory and Football: How Irrationality Affects Play Calling

June 15, 2011 by 24 Comments

Coaches and coordinators in professional football get paid a lot of money to call the right plays – not just the best plays for particular situations, but also unpredictable plays that will catch the other team off guard. It’s a perfect setup for game theory analysis!

As in other game theory situations, the best play depends in part on what your opponent does. Your running play is much more likely to succeed against a pass-prevent defense, but would be in trouble against a run-stuffing formation. If the defense can guess what you’re going to call, they can adjust accordingly and have an advantage. Even on 3rd down and long – a common passing situation – there’s value in calling a percent of running plays, because the defense is less likely to be geared toward stopping that. But as you do it more, the chance of catching the defense off guard gets smaller. There’s some optimal balance where the expected success of a surprising run is equal to the expected success of a more sensible (but anticipated) pass.

The goal is to stay unpredictable and exploit patterns where your opponent is using a sub-optimal combination. If a team notices that passing plays are working better, they’ll be more likely to call them. As the defense notices, they’ll shift away from their run-defense and focus more on defending passes. In theory, the two teams reach an equilibrium.

In practice, it doesn’t quite work that perfectly – human beings are making the decisions, and humans are both vulnerable to cognitive biases and notoriously bad at mimicking true unpredictability. Brian Burke, a fellow fan of combining sports with statistics, was poring over the play-calling data for second downs and noticed something odd:

There’s a strange spike in percent of running plays called at 2nd and 10! Tactically, 2nd and 10 isn’t all that different from 2nd and 9 or 11, so it’s strange to see such a difference. Why would they call so many more running plays in that particular situation?

The key is to realize that there are two ways a team tends to find itself facing a 2nd and 10 situation – runs that happen to go nowhere or any incomplete pass. Of those, incomplete passes are far more common. So in cases of 2nd and 10, it’s most often because the team just failed a passing play. That suggests two reasons coaches might be irrationally switching to running plays, even at the cost of sacrificing unpredictability:

(1) The hasty generalization bias (also called the small sample bias) and the recency effect are cognitive biases in which people overgeneralize from a small amount of data, especially recent data. Failed passes are very common (about 40% fail), so there’s no good reason for a coach to treat any single failed pass as evidence that they’d be better off switching to a running play. But the urge to overreact to the failed pass that just happened is strong, thanks to these two biases.

(2) People are terrible at generating unpredictability — when asked to make up a “seemingly-random” sequence of coin flips, we tend to use far more alternation between Heads and Tails than would actually occur in a real sequence of coin flips. So even if coaches weren’t overreacting to a failed pass, and they were simply trying to be unpredictable, they would still tend to switch to a running play after a passing play more often than random chance would dictate.

Indeed, when Brian separated the data by previous play, the alternation trend is clear — passes are more likely after runs, and runs are more likely after passes:

(My favorite team, the Baltimore Ravens, was pretty bad about this under the previous regime, Coach Billick)

Brian concludes:

Coaches and coordinators are apparently not immune to the small sample fallacy. In addition to the inability to simulate true randomness, I think this helps explain the tendency to alternate. I also think this why the tendency is so easy to spot on the 2nd and 10 situation. It’s the situation that nearly always follows a failure. The impulse to try the alternative, even knowing that a single recent bad outcome is not necessarily representative of overall performance, is very strong.

So recency bias may be playing a role. More recent outcomes loom disproportionately large in our minds than past outcomes. When coaches are weighing how successful various play types have been, they might be subconsciously over-weighting the most recent information—the last play. But regardless of the reasons, coaches are predictable, at least to some degree.

Coaches are letting irrational biases influence their play calling, pulling them away from the optimal mix. The result, according to Pro Football Reference stats, is less success on those plays. I wonder how well a computer could call plays using a Statistical Prediction Rule…

Filed under Game Theory, Psychology

Asking for reassurance: a Bayesian interpretation

June 9, 2011 by 25 Comments

Bayesianism gives us a prescription for how we should update our beliefs about the world as we encounter new evidence. Roughly speaking, when you encounter new evidence (E), you should increase your confidence in a hypothesis H only if that evidence would’ve been more likely to occur in a world where H was true than in a world in which H was false — that is, if P(E|H) > P(E|not-H).

I think this is indisputably correct. What I’ve been less sure about is whether Bayesianism tends to lead to conclusions that we wouldn’t have arrived at anyway just through common sense. I mean, isn’t this how we react to evidence intuitively? Does knowing about Bayes’ rule actually improve our reasoning in everyday life?

As of yesterday, I can say: yes, it does.

I was complaining to a friend about people who ask questions like, “Do you think I’m pretty?” or “Do you really like me?” My argument was that I understood the impulse to seek reassurance if you’re feeling insecure, but I didn’t think it was useful to actually ask such a question, since the person’s just going to tell you “yes” no matter what, and you’re not going to get any new information from it. (And you’re going to make yourself look bad by asking.)

My friend made the valid point that even if everyone always responds “Yes,” some people are better at lying than others, so if the person’s reply sounds unconvincing, that’s a telltale sign that that they don’t genuinely like you/ think you’re pretty. “Okay, that’s true,” I replied. “But if they reply ‘yes’ and it sounds convincing, then you haven’t learned any new information, because you have no way of knowing whether he’s telling the truth or whether he’s just a good liar.”

But then I thought about Bayes’ rule and realized I was wrong — even a convincing-sounding “yes” gives you some new information. In this case, H = “He thinks I’m pretty” and E = “He gave a convincing-sounding ‘yes’ to my question.” And I think it’s safe to assume that it’s easier to sound convincing if you believe what you’re saying than if you don’t, which means that P(E | H) > P(E | not-H). So a proper Bayesian reasoner encountering E should increase her credence in H.

(Of course, there’s always the risk, as with Heisenberg’s Uncertainty Principle, that the process of measuring something will actually change it. So if you ask “Do you like me?” enough, the true answer might shift from “yes” to “no”…)

Filed under Psychology, Rationality

Why Imagined Indulgence Helps Us Diet

June 8, 2011 by 11 Comments

What makes decadent waffles so damn satisfying in the morning? Is it the optimal balance of crispy and soft textures? The fat in the whipped cream? The sugar content? It turns out that there’s a factor beyond the actual food: your frame of mind. A team of researchers at Yale just performed a clever study and found that you feel fuller and more sated if you believe you just ate something indulgent.

As with most psychology experiments, the study involved lying to people. Subjects were given a milkshake on two separate occasions but were told that one contained a whopping 620 calories and the other had a more sensible 140 calories. In reality, both shakes were the same – right in the middle at 380 calories.

Before and after each test, the researchers monitored the subjects’ ghrelin levels as a measure of how satisfied they were. Ghrelin – the hormone which triggers hunger – increases and spikes before meals, then drops off after people eat. If the calorie content were all that mattered, there would be no difference in reactions to the two shakes. But there was:

Results: The mindset of indulgence produced a dramatically steeper decline in ghrelin after consuming the shake, whereas the mindset of sensibility produced a relatively flat ghrelin response. Participants’ satiety was consistent with what they believed they were consuming rather than the actual nutritional value of what they consumed.

What should we make of the finding (besides a continued fascination with the placebo effect)? For one thing, it reinforces the notion that our stomachs are very crude sense organs which aren’t precise or accurate at judging how much food they need.

For anyone trying to achieve (or maintain) a healthy weight, the dynamic makes it tougher to diet. The conscious decision to eat ‘sensible’ food motivates our bodies to demand more calories. What a frustrating situation!

Patrick at Discoblog toys with a creative solution:

It definitely suggests some new approaches to dieting, like berating yourself for eating celery sticks in an effort to make them seem more luxurious and satisfying. But it’s not clear if lying to yourself is as effective as having other people lie to you. And believing that you are constantly eating poorly might have other psychological side effects, one supposes.

I agree, it probably doesn’t work as well to lie to yourself (and nobody will be able to convince me that celery sticks are fatty treats). But we can draw a useful tactic that doesn’t require deception. Instead of applying the study’s findings when we eat light food, keep it in mind when eating dessert. Next time you want a rich slice of cheesecake, look up how many calories it has! According to the study, focusing on the fact that the slice has 50% of your recommended calories will make you feel more satisfied eating less of it.

What I’d like to see is a study that’s honest about the number of calories but emphasizes different ingredients to foster that ‘indulgent’ mindset. Would our bodies react differently to drinking a “300-calorie fruit milkshake” compared to the same one described as a “300-calorie shake with bananas, heavy cream, vanilla extract, and pure cane juice”?

If that works, we can help our friends and families by focusing attention on the fattiest, sweetest, and tastiest part of a dish. Next time Julia is willing to make those delicious-looking blintzes again, sign me up. I can eat one as she tells me about the heavy cream that went into the homemade ricotta.

[UPDATE] I’m looking a little deeper into what exactly was being measured – the abstract and researchers said “Participants’ satiety was consistent with what they believed they were consuming rather than the actual nutritional value of what they consumed.” but news sources report this as well:

The study also didn’t find that the larger drop in ghrelin in those who drank the indulgent shakes was accompanied by a larger drop in hunger levels, a finding that the researchers couldn’t fully explain. “We may not have used a reliable measure of hunger,” says Crum. “My sense is that hunger levels should have changed.”

I had assumed that the participants’ satiety was the same as their remaining hunger – but those two quotes seem at odds at first glance.

Filed under Health, Psychology

Kindles not Replacing Textbooks Yet

May 17, 2011 by 7 Comments

Are e-readers ready to replace textbooks? The lower costs would be welcome, that’s for sure. But is the technology good enough to serve the same purpose as a physical book? Researchers gave students Kindles with their books loaded to see how they’d be used. Turns out, not much:

By the end of the school year, nearly two-thirds of the students had abandoned the Kindle or were using it only infrequently. Of those who continued to use it regularly, the researchers write, “some attempted to augment e-readers with paper or computers, others became less diligent about completing their reading tasks, and still others switched to a different and usually less desirable reading technique.”

Now, I haven’t read the study so I don’t know if the Kindles made learning difficult or were merely unfamiliar and unpopular. After all, students have spent years developing study habits with physical books. Either way, they didn’t cut it. The article points out that the User Interface in Meatspace has incredible advantages:

Because we’ve come to take printed books for granted, we tend to overlook their enormous flexibility as reading instruments. It’s easy to flip through the pages of a physical book, forward and backward. It’s easy to jump quickly between widely separated sections, marking your place with your thumb or a stray bit of paper or even a hair plucked from your head (yes, I believe I’ve done that). You can write anywhere and in any form on any page of a book, using pen or pencil or highlighter or the tip of a burnt match (ditto). You can dog-ear pages or fold them in half or rip them out. You can keep many different books open simultaneously, dipping in and out of them to gather related information.

That’s all true. I’ve toyed with the idea of buying a Kindle, but I’m an avid highlighter and found that feature extremely clunky – definitely a deal-breaker for me. Yes, the technology will probably improve with time. I’m told iPads are better at it, though I haven’t been impressed.

Of course, that’s not an insurmountable challenge. Once e-readers can handle my style of reading and highlighting, I’m sold. Just thinking about that incredible amounts of searchable information at my fingertips… *Drool*

The researchers raise one advantage that won’t be easy to overcome: the physical books have an edge at creating a better cognitive map of the information. The constant unconscious cues we get by holding the book – how thick the sections are, how many pages are left, which side of the page a passage is on – all help us remember the content. Julia’s post on Memory Champions comes to mind – we remember things much better if we tap into our spacial memory as well.

I don’t know if visual cues are as powerful as kinesthetic cues, but I’m sure we can tweak the programs to give better constant feedback about our place in the book. It might not fully compensate for the shift to digital, but it’ll help.

The study focused on whether e-readers could replace textbooks in classroom settings, which might be where they’re at the biggest disadvantage. Textbooks are dense with information students are expected to be able to recall unaided. Outside the classroom, we’re rarely unable (or forbidden!) to look something up. As more information gets indexed, we need to hold less of it in our immediate memories.

I’m curious to see a study of how spacial memory aids learning processes vs. learning facts. I suspect it helps most with facts – the exact things that searchable libraries make easiest to handle. While our education system requires the memorization of facts, physical textbooks will have an edge. If we ever change to a model that prizes process-based learning and allow students to tap into external fact-mines, that edge will go away.

(Via Andrew Sullivan)

Filed under Education, Psychology

“Is there an answer?” Searching for the meaning of life in The Hitchhiker’s Guide to the Galaxy.

May 9, 2011 by 1 Comment

(posted at 3 Quarks Daily)

The Austrian philosopher Ludwig Wittgenstein gets credit for pointing out that many classic philosophical conundrums are unsolvable not because they are so profound, but because they are incoherent. Instead of trying to solve such questions, he argued, we should try to dissolvethem, by demonstrating how they misuse words and investigating the confusion that motivated the question in the first place.

But with all due respect to Wittgenstein, my favorite example of the “dissolving questions” strategy comes from Douglas Adams’ The Hitchhiker’s Guide to the Galaxy, which contains a cheeky and unforgettable dissolution of which I’m sure Wittgenstein himself would have been proud:  A race of hyper-intelligent, pan-dimensional beings builds a supercomputer named Deep Thought, so that they can ask it the question that has preoccupied philosophers for millions of years: “What is the answer to life, the universe, and everything?”

After seven and a half million years of computation, Deep Thought finally announces the answer: Forty-two. In response to the programmers’ howls of disappointment and confusion, Deep Thought rather patiently points out that the reason his answer doesn’t make any sense is because their original question didn’t make any sense either. As I’ve written before, questions like this one, or the very similar “What is the meaning of life?” question, seem to be committing a basic category error: life isn’t the kind of thing to which the word “meaning” or “answer” applies.

But in this article I want to take my analysis a little further than that.

Read the rest, at 3 Quarks Daily.

Filed under Fiction, Philosophy, Psychology

RS#34: Why do people listen to celebrities’ opinions?

May 8, 2011 by Leave a comment

Episode #34 of the Rationally Speaking podcast is all about celebrities giving their opinion on topics they don’t know much about: why do they get invited to opine on those topics at all, and why are people influenced by them? Even people who are experts in a technical field often give misleading viewpoints when they’re offered a platform to talk about fields other than their own. Massimo and I talk about some examples, describe some relevant psychological studies on influence, and still somehow manage to work in our standard bickering about philosophy.

http://www.rationallyspeakingpodcast.org/show/rs34-celebrities-and-the-damage-they-can-do.html

Filed under Psychology, Rationality

How Smiles Might Beat Poker Faces

April 29, 2011 by 70 Comments

Is putting on a poker face the most effective strategy in cards? People talk about spotting players’ ‘tells’, involuntary behavior that gave away their confidence level. To prevent people from picking up on your tells, you were supposed to work on a poker face – a blank look that gives nothing away.

But instead of shutting down and sending no signals, can we send misleading signals?

Well, via NCBI ROFL, a recent study wants to suggest that a blank face isn’t the best – a trustworthy face is:

Participants made risky choices in a simplified poker task while being presented opponents whose faces differentially correlated with subjective impressions of trust… [P]eople took significantly longer and made more mistakes against emotionally positive opponents… According to these results, the best “poker face” for bluffing may not be a neutral face, but rather a face that contains emotional correlates of trustworthiness. Moreover, it suggests that rapid impressions of an opponent play an important role in competitive games, especially when people have little or no experience with an opponent.

[Quick note: As I read through the procedure, I wasn’t sure that I agreed with their assessment of ‘mistake’ in this simplified version of poker. I’ll look into it, but it’s still interesting to note that people folded more against trustworthy-looking faces]

It’s a natural habit to develop – a if a person looks confident and trustworthy, we’re more likely to believe them if they say they have an advantage (by, say, betting). They provide an image which I think lays it out well:


We have access to the information in grey – our own cards, our opponent’s bet, and our opponent’s facial expression. We’re trying to make a decision based on how our cards compare to theirs – which is unknown. Their style is also unknown, which is a problem because it’s a hidden factor influencing their bet.

Since we can only work with the information we have, we go backward: given the face we see, what is their style/attitude? Given their style and bet, what cards do they have? Of course, the random static computerized faces weren’t ‘inadvertently’ giving cues, but we’ve unconsciously learned to treat facial cues are a vital part of figuring out how the bet correlates to cards.

So is a trustworthy smile better than a blank poker face? As the authors point out, the study holds for first impressions, “when people have little or no experience with an opponent.” I would love to see a study of how long the effect holds up. After repeated interaction with the trustworthy-looking computer opponent, do people adapt and re-calibrate the assumed face-to-attitude correlation? I expect there to be some difference even over time – the unconscious connection is tough to shake. But its impact would diminish.

Perhaps we can smile and look trustworthy whenever we want opponents to fold? Sending misleading information is a powerful tool in game-theory. But I suspect decent card players would adapt quickly. Unless you’re damn confident that you know how to exploit their assumptions, you’ll be giving them an edge. Poker faces give up the chance to send intentional false information, but it also cuts out the unintentional cues we’re not even aware of.

I can’t pass up this perfect opportunity to quote Harry Potter and the Methods of Rationality after Harry’s attempt to bluff Snape:

Professor Quirrell had remarked over their lunch that Harry really needed to conceal his state of mind better than putting on a blank face when someone discussed a dangerous topic, and had explained about one-level deceptions, two-level deceptions, and so on. So either Severus was in fact modeling Harry as a one-level player, which made Severus himself two-level, and Harry’s three-level move had been successful; or Severus was a four-level player and wanted Harry to think the deception had been successful. Harry, smiling, had asked Professor Quirrell what level he played at, and Professor Quirrell, also smiling, had responded, One level higher than you.

Against true amateurs in a little house game, I’ll try some one-level deceptions. But when I’m in a new place with good players, I tend to play it safe and focus my energy on staying blank rather than on sending false signals.

Filed under Game Theory, Psychology

Beware of the Granfalloon

April 27, 2011 by 34 Comments

In this week’s video I discuss my new favorite word — “Granfalloon” — and how identifying yourself with a particular group can distort your thinking.

Filed under Fallacies, Psychology, Video

Going with Your Gut: Subtle Cues Spread Obesity

April 26, 2011 by 3 Comments

Obesity is, apparently, transmissible. Studies already found evidence that it spreads through communities and social networks. If you have a friend who becomes obese in a time period, you’re 57% more likely to follow suit. But it’s not just shared regional foods or common experiences. Merely interacting with overweight people impacts us — and not the way most people expect when asked.

A new study found that simply seeing pictures of overweight people motivates us to eat more. Jonah Lehrer describes the situation:

A majority of people insist that the picture of [an overweight person] would reduce their consumption of cookies. (31 percent believed that [seeing it] would inspire them to abstain entirely from the sweet treat.) This is how we like to think ourselves: independent minded creatures, able to learn from the unflattering photographs of others.

Alas, our responsible self-image is entirely divorced from reality. The Colorado researchers demonstrated that, in several situations, the exact opposite occurred: When people were exposed to pictures of someone who was overweight, they ended up consuming far more calories.

It’s a neat study. The researchers asked people to take a quick survey which had a random picture of an overweight person, a person of normal weight, or a lamp. Afterward, the subjects were invited to take candy from a bowl. The ones whose surveys had the picture of the overweight person took 30% more. In a similar study, the subjects were asked to do a cookie taste test (what an offer!). Those first exposed to pictures of overweight people ate twice as many cookies.

The first takeaway lesson is that if you’re asked to participate in a psychology study, there’s almost always a trick – they’re probably testing something completely different than what they claim. (On a side note, if there’s one other “subject” with you; don’t trust him. He’s almost certainly working for the researchers. Cynical and paranoid enough for you? …*cough* But back to the study at hand.)

Taken together, this research begins to explain how obesity moves through a social network. It turns out that the habits and hungers of others shape our own, that we unconsciously regress to the dietary norms around us. Because we’re not particularly good at noticing when we’re sated and full – the stomach is a crude sensory organ – we rely on all sorts of external cues to tell us how much to eat. Many of these cues from other people, which is why our eating habits are so contagious.

It’s not shocking when we look at it like that: we look to others for signs of how to act. A picture of a stranger influences us – and even if the subject explicitly stated a goal to maintain healthy weight.

The point that our stomachs are crude sensory organs hit home for me. Those “external cues” influence our perception even about something as intimate as the amount of food we want to eat! “Going with your gut” to make the decision is an easy strategy but doesn’t lead to great results. If we want more control over our weight, a more objective and deliberate strategy based on measures like calories, glycemic index, and metabolic rates would probably work better.

Filed under Psychology

Sense of Meaning in Dreams: NOT too Hard for Science

April 19, 2011 by 3 Comments

What questions seem implausible for scientists to answer? Are they really out of reach? In an intriguing new feature at Scientific American, Charles Q. Choi solicited questions that science would have trouble investigating. It’s called ‘Too Hard for Science?‘ It’s a great concept:

The idea here is to interview scientists about pet ideas they would love to explore that seem impossible to investigate in real life. Perhaps they involve machines beyond the realm of possibility, such as particle accelerators as big as the sun; perhaps they would be completely unethical, such as lethal experiments involving people; perhaps they would be too expensive, or require centuries to run, or could never find volunteers to participate, or are in some way unprovable.

This feature aims to look at the seemingly impossible dreams, the most intractable problems in science. However, the question mark at the end of “Too Hard For Science?” suggests that nothing might be impossible. Perhaps these very interviews could spur brainstorms that actually make these ideas a reality.

I’m looking forward to reading these. Foucault’s Pendulum would have been a good one back in the day, but the 1850’s came and went. What other challenges can we overcome with a new perspective?

One example is “In dreams, could we discover where the mysterious feeling of revelation comes from?” That’s the question which led Choi to start the feature in the first place.

At first blush, it might seem outside the realm of science to ask what gives us meaning. But that’s not the question. We’re asking what gives the feeling of meaning while we dream. What if we’re not reacting to a metaphysical “meaningful” property but can find a physical cause for the sensation? Can it be plausibly tested?

That’s what Robert Stickgold, director of the Center for Sleep and Cognition at Harvard Medical School brainstormed about. He notes that during REM sleep the brain shuts down the release of serotonin – something that only happens during sleep and while using LSD, “when people seem to have these totally uninteresting experiences they describe as profoundly meaningful called ‘acid insights.'”

This sense of meaning may be a physical phenomenon “just like hunger or thirst, save that it’s the excitement we feel upon a great insight, that ‘Aha!’ feeling,” Stickgold says. “Who knows why, for instance, fireworks often seem to trigger it — maybe there’s something about the geometric patterns that evokes this sense of awesomeness, the feeling that we can almost understand something amazing but not quite that drives us to seek a better understanding of things. It’s like what you feel during a religious experience — you sense the oneness of mankind.”

During dreams, the brain might be associating disjointed experiences together to create potentially valuable combinations of thoughts. “It could be the brain is making you focus your attention on material that was only weakly associated before and investing this association with this feeling of profundity to help it mine these connections for something not immediately obvious but potentially important,” Stickgold says. “It makes sense that the sensation would be a positive and reinforcing one.”

Sure there are some obstacles, but now there’s something we can test! Let’s separate people into three groups: one that gets serotonin-boosting drugs, one that gets serotonin-blocking drugs, and a third that gets placebos. Show them each the same poem, piece of music, painting or somesuch and see how ‘meaningful’ they rate it.

It’s important distinguish between what scientists can do and what science can do. Science is the most powerful tool we have to learn about the world, but sometimes we mere mortals have limitations. The more ways we figure out to use science while accommodating those limitations, the more we can learn.

Filed under Philosophy of science, Psychology

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