Bicycle Helmets IV

(Warning: non-sports post, including speculation on subjects on which I have no expertise.  Read at your own risk.  (I'll try to be back with a sports post soon.)  This is part IV ... here are parts one, two, and three.)

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On Friday, you decide to take the day off work to go golfing.  Your boss objects, because you have an important report to finish for Monday morning.  You tell him you plan to come in tomorrow and finish it, and even Sunday if necessary. Your boss is satisfied with that. 

You decide you want to take the family to Disneyland.  Your wife objects that money is too tight.  You answer, you've decided to keep your car an extra year, and you've already quit your $4-a-day latte habit.  That's more than enough to cover the trip.  Your wife is satisfied.

On your next bike ride, you're not wearing a helmet.  Your friend says, that's risky!  You reply that riding without a helmet is only 40 percent riskier than with a helmet, and that you're compensating by riding less, and not at night.  Your friend is NOT satisfied.  He thinks you're dangerous and irrational.

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Why the difference?  How come, in the first two cases, it's OK to make a trade-off, but in the third it isn't?  How come, when it comes to work and money, it's OK to evaluate based on achieving an objective ... but, when it comes to bicycling risk, it's not?

I've been thinking about it, and I've concluded that it's not really about risk at all.  It's about following a moral code.  Wearing a helmet has kind of established itself as the only right thing to do, kind of an ethical law.  

It seems to me that when you find tradeoffs are frowned upon, it's because of morals.  It's wrong to commit a murder, even if I save a thousand starving Africans to compensate, because murder is immoral.  It's wrong to commit adultery, even if I compensate by treating my wife like a queen afterwards.  It's wrong to cheat on an exam, even if I deliberately score lower on my next exam to make up for it.  

When there are moral issues, the bottom line doesn't matter -- the ends can't justify the means.

In terms of helmets, risk barely figures into it at all.  Suppose I got rid of the helmet, but started reducing my risk by riding only half as much.  But you get so outraged that I can't do that any more.  So, I give in.  I put on a helmet, but resume my normal riding schedule.  My risk actually rises 40 percent ... it drops 30 percent for the helmet, but then rises 100 percent for the extra riding.  But you don't care.  You're satisfied, even though my risk has gone up.

Because: without the helmet, I was breaking a rule.  With the helmet, I'm not.  It's morally OK for me to take on more risk, as long as I do it with a helmet on.

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There are lots of other things that are rationalized as practical issues, but treated with the non-negotiability of moral issues.  

Suppose I refuse to recycle, because I think it's too much hassle.  Instead, I decide to cut down on the packaged goods I buy.  Instead of canned pop, I switch to tap water.  I switch all my utility bills to electronic delivery, and I buy a Prius.  I convincingly show you that doing all these things have done much, much more for the environment than if I just recycled.

My guess is: you're not buying it.  You're going to feel like, when I throw a pile of newspapers in the garbage instead of the blue bin, I'm doing something morally wrong, and I'm using these other things to try to justify my immoral behavior.  

There are others ... "wasting food" is a big one.  Yes, people are starving in Africa.  Is it OK to "waste" $1 worth of food if I send $5 worth to Africa?  No.  It's better to eat the $1 worth of food and send nothing to Africa.  Because it's not about the starvation, it's about the moral principle that you don't waste.

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Another aspect is that when something becomes a moral issue, it moves from a "how much" issue, to a "yes or no" issue.  

It doesn't matter a whole lot *how much* I smoke ... a pack a day won't get me 20 times more disapproval from you than a cigarette a day.  It doesn't matter *how much* I drive without a seat belt ... a trip to the corner store gets me the same lecture from the cop as a five-hour drive.  And it doesn't matter *how much* extra risk there is in riding without a helmet.  Because it's no longer about how much; it's about the fact that I would dare to consider it acceptable at all.  

That's why there's so much outrage about "light" cigarettes.  Even if they *are* less dangerous -- which I believe is true -- they're considered no less immoral.  To some people, talking about "light cigarettes" is a lot like talking about "light rape".

Even worse, the outrage continues when there's almost no danger at all.  There's a new product called "e-cigarettes," which look like cigarettes, and emit smoke-like vapors (which are really just water).  They can be used as a nicotine-delivery system, like gum or a patch, with little to no risk.

But ... some people want to make them illegal.  Because, for those people, it has never really been about the risk, or the effects of smoking.  The taboo, and moral crusade, is now about the *act* of smoking.  "You shouldn't smoke because it's too dangerous" has morphed into "you shouldn't smoke because smoking is evil, and we'll use danger as a rationalization."  That's the only way that you could argue that taking a cigarette-shaped piece of plastic, and blowing water vapor out of it, is an activity that needs to be banned.  Especially when it has the power to save lives by making it easier to quit.  

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Robin Hanson has written extensively about "signalling." That's when an activity is done not so much for its own sake, but to display something about yourself that would otherwise be invisible.  I think that's what's happening here.  I think it's mostly a desire to identify yourself as belonging to a particular peer group, or social/political group, that thinks helmets are a good idea.  It's saying, "I'm one of us -- the type that's intelligent enough to know that helmets reduce risk, and understand that it's a good idea to wear them."  It's the way you signal to the world that you're a thoughtful, high-status Ken Dryden-type, and not a low-status Don Cherry-type, the type that's too shortsighted to care about his own brain.

For that to work, you have to treat helmet-wearing as obvious and non-negotiable.  If you start arguing open-mindedly about risk numbers, you send the wrong signal.  You show that your position on helmets is iffy, that it's not an obvious moral issue, that maybe you're not as Drydenish as the rest of your group.

It's like ... let's say I'm a famous and well-respected political pundit.  And I say, "You know, the KKK thinks black people are less intelligent than whites.  I'm going to go and study that, and see if they're right."  

My career is over.  Instantly.  And it's over if even, next month, I come back and say, I've looked over all this data, and I've studied it from 100 different angles, and you know what?  It's not true at all.  Those KKK guys have been intellectually dishonest!"

The world would still see me as a potential racist.  Why?  Because I was willing to *consider* the idea that the moral issue was negotiable.  I gave the signal that I care about the bottom line -- whether or not the statement is true -- more than I care about the moral principle that you shouldn't say things like that.

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In a way, these kinds of moral issues take on certain aspects of religion.  We pick a side, embrace its position, and signal our adherence.  We get very uncomfortable when challenged.  We have to be that way -- our signals are judged relative to others.  In a world where the accepted signal is immediate disapproval, an open mind sounds like something the other side would do.  

And considering trade-offs, costs and benefits ... you can't do that at all.  As soon as you let in the possibility that your moral principle could be anything less than absolute -- even in theory -- you're denying the moral imperative.  If you talk about costs and benefits, you're signalling, "I might be willing to give up my ethics for the right price."

Suppose you're a high-ranking public relations person at MADD.  You talk about all the damage drunk driving does, and how the drinking age should be higher, and how there should be more roadside testing, and so forth.  

And then someone asks if it should be illegal to drive after even one drink.  And you say, "no, we don't go that far."

And the response is: "OK, what's the tradeoff?  At one drink, the risk increases maybe Z%.  That's X deaths a year.  That, you say, is OK.  But, you believe that anything over .05%, which results in Y deaths a year, is not OK.  Tell us where your cutoff is, and why.  What number of deaths is a reasonable, albeit tragic, price to pay?"

You have to duck the question, if your goal is to treat drunk driving as a moral principle.  You can't start arguing that it's only bad if it causes more than X deaths.  Because then you're arguing about what X should be, which is not compatible with ethical imperatives.  Moral standards don't depend on numbers.  Moral standards can't admit grey areas.

Ask a Rabbi, "If there were very strong evidence that the bible had been mistranslated, and God actually required pork instead of banning it, would you have a BLT?  How strong would the evidence have to be?"

Ask a career anti-smoking activist, "If they figured out an additive to add to tobacco that would make smoking less unhealthy, would you be less opposed to smoking?"

Ask an anti-drug crusader, "How much would decriminalizing heroin have to reduce the total harm, in order for you to come out in favor of it?"

And, ask a bicycle helmet advocate, "How low would the risk have to be for you to change your mind about helmet laws?"

You won't get an answer from any of them.  Even admitting there's a cost/benefit issue is forbidden, much less actually trying to quantify one.  The best you'll get, sometimes, is something absurdly low, one that runs no chance of happening.  "I'd repeal helmet laws if it was only one extra death per decade."  

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Usually, abiding by these moral principles require you to conduct your personal life a certain way -- in other words, to pay a cost, to make a sacrifice.  You have to wear a helmet.  You have to recycle.  You have to go to church.  You have to pay a little more for fair-trade coffee.  

And most of those things are public -- which, they'd have to be, if the main purpose is to signal.  Everyone can see you're wearing a helmet.  Everyone in church sees you're there.  Everyone notices your recycling bins, and your reusable cloth shopping bags.  

But the interesting thing about the signalling is ... the sacrifice is only a small part of the signal.  The most important part of the signal is to *not admit you're sacrificing*.  You have to pretend that it's no trouble at all, and you couldn't imagine doing anything different.  

You're active in your church, and very well-regarded by your fellow worshippers.  You go to church every Sunday, and you think everybody should, and you often lament at how attendance is on the decline.  

But, then, one day, you admit, "You know, I really hate going to church.  Most of it is boring, and it cuts into my golf time.  And I have to get up early, which I don't like, and I have to dress up.  But, I guess, that's the kind of sacrifice you have to make, because God wants it."

You look a little bit less devoted now, don't you?  

In a way, you'd think it should be the reverse.  If you go to church every Sunday even though you don't like it, shouldn't that show that you're sacrificing *more* to the cause, and so you're *more* devoted?  But it doesn't.  

Because, you're not going to church to signal that you go to church.  You're going to church to signal that you're the type of person who *likes* going to church, the type of person who goes to church willingly and enthusiastically.  Signalling is "a method of conveying information ... by performing an action which is more likely or less costly if the information is true than if it is not true".  By going to church, you're implicitly saying, "Look, I must be devout.  Would an immoral atheist be doing this week after week?"  You're saying, "look at how I can do this *without* sacrificing."

It's the outgroup that has to sacrifice -- the group that you're trying to signal you're not one of.  The guy next door, who's not religious.  You tell him he should go to church.  He says, "I hate it -- it's boring, and it cuts into my golf time, and I have to get up early and dress up."  And you reply, "It's for God.  You should make the sacrifice and do it anyway."

You're signalling two things here: first, that you abide by the moral principle of going to Church enough that you think other people should do it too, and, second, that you'll still be superior to your neighbor even if he makes the sacrifice you want him to, because, even though he does what he should, he doesn't really *want* to.  

So, I doubt you'll ever hear Al Gore, or David Suzuki, say, "you know, I really hate recycling.  Those cans are dirty, and they stink, and it's such a pain in the butt.  It would be great if we found a way to just throw these things in the garbage while still saving the planet."  

That won't look good.  See, you're supposed to WANT to recycle.  You're supposed to LIKE recycling.  If you're environmentally enlightened, the pleasure you get from walking to the bin, and taking it out every week, are worth it, for the glow you get for doing the right thing.  It's only a pain in the butt to the people who don't like doing it, the enemies of the planet.  

To an environmentalist, not liking recycling is like not liking dogs and babies.  It's not something you look good admitting.

What led me to start thinking about this is that I didn't understand why hardly any of the helmet advocates, in any of the other helmet posts, ever mentioned how they find helmets uncomfortable, or inconvenient, or unwieldy, or that they wish they didn't have to wear one.  It struck me as strange.  Helmets *are* uncomfortable and inconvenient, which is why we choose not to wear them when we drive, or walk, or even when we're making repairs up on our roof (when they would actually make sense!).  

But, I think this is the reason.  If you admit that you dislike helmets, but you wear them anyway because of the risk, you're detracting from the signal that you're an enlightened, educated, sensible, safety advocate.  You're mostly just signalling that you don't want to hurt your head.

More luck in outcomes doesn't imply less skilled players

A couple of weeks ago, Michael Mauboussin posted about how there's so much luck in the NHL's shortened season. (Mauboussin is the author of "The Success Equation: Untangling Skill and Luck in Business, Sports, and Investing".) 

Most of the comments to the post didn't quite get it.  In particular, one commenter wrote, disbelievingly, 

"Did you watch the Rangers/Bruins game last night?  Luck?"

That, I think, is a pretty common response -- and not unreasonable.  NHL hockey players are among the best in the world.  hey've practiced thousands of hours, and any serious weakness in their game is instantly exploited by their opponents. How can we say that hockey is mostly luck?

Well, we don't. We're not actually arguing that hockey has more luck than skill. We're arguing something different: that the *outcome* represents luck more than skill. Or, more specifically, we're saying that the standings are more the product of *differences in luck between teams* than *differences in skill between teams*.

Which is what Mauboussin replied to the commenter:

"Here's the point: the article doesn't say that hockey players are not skillful (they are). It says that the skills of the players on opposing teams offset one another, leaving more to luck." 

The misunderstanding, it seems, stems from some readers not realizing we're talking about relative skill ... rather, they think we're talking about actual levels of player talent. We're not. If you found a peewee hockey league where the relative distribution of talent was the same as in the NHL, the luck/skill analysis would be exactly the same. The NHL season would be 60% luck, and the peewee season would also be 60% luck. The statement says nothing about how skilled the players are in a real-world sense, and it says nothing about how much skill is actually required to play the game.

Maybe we should making that more explicit. Instead of, "The standings are 60% luck," or "Hockey is 60% luck," we can say, "The standings are determined 60% by which teams are luckier than their opponents, and 40% by which teams are more talented than their opponents."

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Another part of the problem, perhaps, is that, in real life, we're not all that used to luck being a big factor. We rarely observe such small differences in skill as exist in most sports. In the NBA, even the worst team has a 10% chance to beat the best team. But I'm pretty sure that, at work, if you pick five random employees, and play them against the five best basketball players on staff, they'd win, like, zero percent of the time.  

In my recreational ball hockey league, my team is pretty bad. When we play the best team in the league, we *know* we're going to lose. No 10 percent, no 5 percent chance. We're going to get beat. Probably 19-3, or something. Maybe, if we're lucky, it'll be 13-5, or 14-7, or some such.  

In the real world, differences in talent are large. In professional sports, they're small.  

As Mauboussin says, in a related interview,

"This leads to one of the points that I think is most counter to intuition. As skill increases, it tends to become more uniform across the population. Provided that the contribution of luck remains stable, you get a case where increases in skill lead to luck being a bigger contributor to outcomes. That’s the paradox of skill."

We're not used to that. In our personal worlds, people are very different.  In school, the SAT-taking senior that's good at math is going to outscore the one who isn't, at least 99 percent of the time. The best programmer at work will finish faster than the worst programmer at work, 99.9 percent of the time.  And so on.  

In real life, when we see one person perform better than another, we can be fairly sure that person is actually better at the task.  

We can't do that as readily in professional sports. There, skill is much more uniform. We're not used to that, the idea that you can't tell the better team just by watching. We're not used to luck being such a big factor.

Gut reactions about foul shooting and luck

This is just something I've been thinking about lately.  I'm not sure what my point is, or even if I have a point, but I'm finding it interesting.

For the past few seasons, Dirk Nowitzki has been one of the best free throw shooters in the NBA, with success rates ranging around 90 percent.  Now, let me give you six scenarios.

1.  One game, Nowitzki has a bad night and goes 3 for 6.  And, the Mavericks play roughly as expected but lose by a point.  Would you say Dirk was unlucky?  Would you say the team was unlucky?  

2.  In an alternate universe, the NBA decides that free throws are boring for fans to watch.  So, before the season starts, every player shoots a few hundred free throws.  The scorekeepers have the results.  Any time there's a foul, they go to the sheets, take the player's next shots off the list, and adjust the score accordingly.

Nowitzki still shot 90 percent overall.  But this game, they were at the part of his sheet where had three misses in six shots.  The Mavs lose.

Again, how unlucky was Nowitzki?  How unlucky was the team?  More, or less than the previous scenario?

3.  Same situation, but, this time, instead of progressing on the sheet in the order in which Nowitzki took his 800 preseason shots, the scorekeepers choose randomly.  There's a big urn labled "Nowitzki 90%," with 720 white balls and 80 black balls.  Whenever Nowitzki gets fouled, they reach into the urn.  

This game, they happen to pull three white balls and three black, and the Mavericks lose by a point.  Again: how much luck would you say determined the outcome?

4.  In another alternate universe, all free throws are saved up and taken at the *end* of the season, before the playoffs.  Nowitzki winds up shooting 90 percent, as usual.  But, when it comes time for the shots that are going to apply to *this* game, they tell Dirk, "you need to sink four to tie, five to win."  To everyone's surprise, Nowitzki sinks only three, and the Mavericks lose.  

Does that make a difference?

5.  This time, Nowitzki is not told the score, or what game his end-of-season free throws are going to apply to.  But the session is televised, and the announcers know.  They tell the viewers.  There is tension in the booth.  Nowitzki steps up and hits 3 of 6 again.  

If Nowitzki didn't know the situation, does that make it feel more unlucky?  

6.  Finally ... almost the same thing, but, this time, Nowitzki starts by just taking the shots, without anyone knowing which game they apply to.  It's only afterwards that they determine the game, by randomly spinning a big wheel.  They get to the part where Nowitzki's next six shots happen to be 3 makes and 3 misses.  The NBA spins the wheel, and it comes up that particular game, and they add Nowitzki's 3-for-6, and the Mavericks lose by 1.

This one is the most unlucky so far, right?  

And what if Nowitzki had taken the 800 foul shots *before* the season, but the wheel was still spun after?  To me, that scenario seems the most like bad luck.

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As I said, I don't have a specific point here.  I just find it interesting how my gut reaches different conclusions about each situation, even though my brain thinks they're really almost the same.  

NHL teams vary more in defense than offense

In the NHL, the spread of goals allowed is wider than the spread of goals scored.  For instance, in 2010-11, the standard deviation of team goals was 22.0, but, for team goals allowed, it was 25.9.  That is: there's more variation in defense than offense.

It's not the same in other sports.  In baseball, since 1971, offense and defense have been almost equal -- a 102.4 run SD for runs scored, and 103.7 for runs allowed.  For the NBA, it goes the other way -- offenses vary more than defenses.  In 1978-79, the SD of team points per 100 possessions was 3.26, but only 2.64 for opposition points.  In 2006-07, it was 3.78 to 2.64.  (Those were the only two years I checked).


(In the links above, you have to do your own SD calculations.  I wish the Sports-Reference sites listed SDs along with averages, to save time for geeks like me.)

Averaging out those two NBA seasons, and the NHL from 1995-96 to 2011-12, and switching to a nicer font, and making it bold to catch your eye in case you're just skimming:

NHL:  24.8 offense,  28.7 defense
MLB: 102.4 offense, 103.7 defense
NBA:   3.5 offense,   2.6 defense

Big differences.

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It might seem like offense and defense should be equal, since one team's offense is the other team's defense.  But that's not necessarily true.  Often, it's easier to influence your score than your opponent's score.  Like in golf.  Players' scores vary quite a bit; Tiger Woods averages low, other guys average high.  But *opponents'* scores would be almost the same for every golfer.

That, of course, is because there's actually no defense in golf -- you don't have any control over your opponents' scores, so there's no intrinsic variation in how well Tiger Woods scores against different opponents.  That's an extreme case ... but it's easy to imagine "partial" cases.  Imagine if MLB decided to use pitching machines instead of actual humans.  Now, you can no longer keep your opponent off the scoreboard with good pitching.  You only get fielding, which gives a much narrower range.  Gold Gloves will still help, but the difference between the team allowing the most and fewest runs will be much narrower. 

For the other way around, imagine MLB using a batting machine for the designated hitter.  Now, your team's hitting skill matters only 8/9 as much as it used to, and it's a bit harder to influence your own scoring, relative to the opponents'.

So, the balance between offense and defense depends on the structure of the game.  In fact, I think the near-equal balance in baseball is in large part just coincidence.

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Another factor is how much one or a few exceptional players can influence the results.  The more players you average out, the lower the SD.  It's like how the distribution of heights among individuals is more extreme than the distribution of average heights among groups of individuals.  It's easy to find someone who's 6-foot-4 ... but it's nearly impossible to find a neighborhood, or even a street, where the average is 6-foot-4.

Imagine changing baseball so that you only have one batter instead of nine.  (If the one batter gets a hit, a pinch runner comes in, so the same guy can bat again.)  In that case, team offense would have a much wider range than team defense.  The team with Barry Bonds would score, say, 12 runs per game, while the team with Albert Pujols would wind up with only 7 or 8.  That's a much larger range than real life.  On the other hand, the range of defense would be narrower, since you can't have Pedro Martinez pitching every at-bat, and not every ball can be hit to Ozzie Smith.

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So, here's an idea.  When you look at a sport, search for the tasks at which there's wide variation in player talent, and where those tasks can be concentrated the most on certain players.  If those tasks tend to impact scoring -- like in "one player bats" baseball -- the offense will have the wider spread.  But if those tasks tend to impact more on *preventing* scoring, it's defense that will vary more.

In the NBA, where do you find that kind of task?  Shooting is the most obvious -- there's wide variation in skill, and you can easily arrange to give your best players the ball more often.  So, you'd expect wider team variation in offense than defense.  Of course, the guy who shadows Kobe gets "concentration" on the defensive side, because he gets the most important job most often.  But, intuitively, there's probably less variation in ability to defend good shooters than there is in ability to shoot against good defenders.  (Of course, I say that knowing the result in advance, so that may just be benefit of hindsight.  But I still think it's right.)

What about baseball?  You don't have a lot of concentration on offense; the better hitters, at the top of the lineup, bat a bit more often ... but that's about it.  On defense, your best pitchers get a few more innings.  It seems kind of even.  And, hitting and pitching seem about equal in importance (again with the benefit of hindsight).  So you get roughly an even spread.

What about hockey?  Where do you find a wide varation in talent, concentrated in just a few players? 

Goalie. 

You've got five guys who work together on offense, but *six* guys who work together on defense -- and the sixth one has the most important position, and he's almost always the same guy, getting maybe 80 percent of the ice time.  So I think that's why, in the NHL, defense has a wider spread than offense -- because of the goaltender.

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The numbers support that, kind of.

A while ago, I ran some estimates for the talent distribution of number-one goaltenders.  I got that the SD of talent, in terms of shooting percentage, was around .008.  With around 1700 shots per season, that's 13.6 goals.

It turns out, that's almost exactly makes up the difference between the spreads of offense and defense!  The SD of goals allowed 28.7.  The SD of goaltending talent was 13.6.  If you subtract the square of 13.6 from the square of 28.7, you get ... the square of 25.3. 

That 25.3 is very close to the SD of goals scored, which was 24.8.  You could credibly argue that if every team had the same caliber goalie, the spread in team offense would be the same as the spread in team defense.

13.6 -- SD of goals allowed attributed to starting goalie
25.2 -- SD of goals allowed attributed to the other players
24.8 -- SD of goals scored

But, as I said, there's nothing that special about a 50/50 split, so this isn't really a proof of anything.  In fact ... well, I'd have thought that if you adjusted for goaltending, you would find that offense had a slightly *higher* spread than defense, not an equal one ... for roughly the same reasons as in the NBA.  The difference in hockey should be lower: your superstar can't control the play in hockey as much as in the NBA, and Wayne Gretzky got only half the playing time that Michael Jordan did.  But you should get a *slight* effect.

But we didn't control for everything.  Even without the starting goalie, the "defense" SD still includes the effects of the backup goalie.  Still another factor is that I used overall save percentage for goalie talent, without adjusting for power-play shots.  That factor probably overstated the goalie SD a little bit.

The biggest factor we didn't control for is that teams vary a lot less in power play opportunities than they do in *opposition* power-play opportunities (that is, some teams take a lot of penalties).  Maybe that makes up the difference.  Maybe my gut feeling is still correct, that Phil Espositos are generally more important than Harry Howells.

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I didn't look at football at all, so this allows the theory to make a prediction.  Obviously, the QB is the most concentrated talent position on the field, and it affects offense the most.  So, after adjusting for possessions and field position, the SD of points scored in the NFL should be significantly higher than the SD of points allowed.  Anyone got that data?

And are there other sports than hockey where defense varies more than offense?