Do younger brothers steal more bases than older brothers? Part IV -- Age vs. SB

A few weeks ago, I wrote a series of posts on an academic paper about siblings and stolen bases. That study claimed that when brothers play in the major leagues, the younger brothers are much more likely -- by an odds ratio of 10 -- to attempt steals more often than their older brothers.

Since then, the authors, Frank J. Sulloway and Richard L. Zweigenhaft, were kind enough to write me to clarify the parts of their methodology I didn't fully understand. They also disagreed with me on a few points, and, on one of those, they're absolutely right.

Previously, I had written,

"It's obvious: if the a player gets called up before his brother *even though he's younger*, he's probably a much better player. In addition, speed is a talent more suited to younger players. So when it comes to attempted steals, you'd expect younger brothers called up early to decimate their older brothers in the steals department."

Seems logical, right? It turns out, however, that it's not true.

For every retired (didn't play in 2009) batter in my database for which I have career SB and CS numbers, I calculated his age as of December 31 of the year he was called up. I expected that players called up very young, like 20 or 21, would have a much higher career steal attempt rate than players who were called up older, like 25 or 26.

Not so. Here are career steal rates for various debut ages, weighted by career length, expressed in (SB+CS) per 200 (H+BB):

17 -- 5.1
18 -- 6.9
19 - 11.3
20 - 14.4
21 - 13.6
22 - 14.0
23 - 14.7
24 - 15.5
25 - 13.4
26 - 14.0
27 - 16.5
28 - 10.2
29 - 11.0
30 - 13.5
31 - 10.3
32 - 17.4
33 - 13.0
34 -- 3.9
35 - 10.5
36 -- 6.1
37 -- 7.4
38 -- 5.3
39 -- 8.4
40 -- 0.0
41 - 14.0

It's pretty flat from 20 to 27 ... there is indeed a dropoff at 28, but few players make their debuts at age 28 or later.

Why does this happen? Isn't it true that young players are faster than old players? Perhaps what's happening is that players who arrive in the major leagues earlier also play longer, which means their extra early high-steal years are balanced out by their extra later low-steal years. I'm not sure that's right, but it's a strong possibility. In any case, my assumption was off the mark, applying as it does only to age 28 and up.

I could have figured out that was the case had I looked at Bill James' rookie study from the 1987 Baseball Abstract. Near the end of page 58, Bill gave a similar chart for hits and stolen bases (but on the total number, not the rate). And it looks like SBs decay not much more than hits or games played.

For instance, consider a 22 year old player compared to one who's 25. The 22-year-old, according to Bill, will wind up with 88 percent more base hits than the 25-year-old (623 divided by 331, on Bill's scale). For stolen bases, the corresponding increase is 84 percent (613 to 334). The two numbers are pretty much the same -- which means, since 1987, we've known that career SB rates don't have a lot to do with callup age.

----

Anyway, the "odds ratio of 10" finding in the sibling study was based on individual player-to-player comparisons. So, I decided to test those. Suppose you have two players, but one breaks in to the majors at a younger age than the other. What is the chance that the younger callup attempts steals at a higher rate for his career?

To figure that out, I took the 5,742 batters in the study, and compared each one of them to each of the others. I ignored pairs where both players were called up at the same age, and I ignored pairs with the same attempt rate (usually zero).

The results: younger players "won" the steal competition at a 52.9% rate, with a "W-L" record of 7,387,525 wins and 6,569,412 losses.

Young: 7387525-6569412 .529

However: that includes a lot of "cup of coffee" players. If I limit the comparisons to where both players got at least 500 AB for their careers, then, unexpectedly, the older guys actually win:

Young: 1950250-1965161 .498

The difference between those two lines comprises cases when one or both players had a very short career. When that happened, the young guys kicked butt, relatively speaking:

Young: 5437275-4604251 .541

These numbers are important because they represent exactly what the authors of the sibling study did -- compare players directly. My argument was that I believed the younger player would be the "winner" a lot higher than 52.9% of the time. That's not correct. So that part of my argument is wrong, and I appreciate Frank Sulloway and Richie Zweigenhaft pointing that out to me.

Does that mean I now agree with the study's finding that the odds of a player having a higher attempt rate than his brother are 10 times as large when he's a younger sibling? No, I don't. But it does mean that I need to refine my argument, which I will do in a future post.

An NFL field goal "choking" study

In a comment to last week's post on choking in basketball, commenter Jim A. posted a link to this analysis of choking in football. It comes from a 1998 issue of "Chance" magazine, a publication of the American Statistical Association.

The paper comes to the conclusion that field-goal kickers do indeed choke under pressure.

Authors Christopher R. Bilder and Thomas M. Loughlin looked at every place kick (field goal or extra point) in the 1995 NFL season. They ran a (logit) regression to predict the probability of making the field goal, based on a bunch of criteria, like distance, altitude, wind, and so on. They designated as "clutch" all those attempts that, if successful, would have resulted in a change of lead.

I assume that kicks starting or resulting in a tie count as "change of lead" -- if so, then clutch kicks are those where the kicking team is behind by 0 to 3 points.

The authors narrowed their model down by eliminating variables that didn't appear to explain the results much. The final model had only four variables:

-- clutch
-- whether it was an extra point or a field goal
-- distance
-- distance * (dummy variable for wind > 15mph)

It turned out that clutch kicks were significantly less successful than non-clutch kicks, by an odds factor of 0.72. If, in a non-clutch situation, your odds of making a field goal were 5.45:1 (which works out to 84.5%, the overall 2008 NFL average), then, to get your clutch odds, you multiply 5.45 by 0.72. And so your corresponding odds in a clutch situation would be 3.93:1 (80%).

It's a small drop -- less than five percentage points overall -- but statistically significant nonetheless.

----

Now, to ask the usual question (albeit one the paper doesn't ask): could there be something going on other than choking? Some possibilities:

1. All attempts the study consideres "clutch" are, by definition, made by a team that's either tied or behind in the score. Wouldn't that be selection bias, since the "clutch" sample would be disproportionately comprised of teams who are, overall, a bit worse than average? Worse teams would have worse field goal kickers, which might explain the dropoff.

The paper ignores that possibility, explicitly assuming that all FG kickers are alike:

"One difference there is no difference between placekickers is that NFL-caliber placekickers are often thought of as "interchangeable parts" by teams. NFL teams regularly allow their free-agent placekickers, who are demanding more money, to leave for other teams because other placekickers are available."

That makes no sense: free-agent quarterbacks leave for other teams too, but that doesn't mean all are equal. Besides, if all placekickers were the same, those "other teams" wouldn't sign them either.

So I wonder if what's really going on is that the kickers in "clutch" situations are simply not as good as the kickers in other situations. The discrepancy seems pretty large, though, so I wonder if that effect would be enough to explain the five percentage point difference.

2. One of the other factors the authors considered was time left on the clock. It turned out to be significant, originally, but, for some reason, it was left out of the final regression.

But clutch kicks would be more likely to occur with less time on the clock. Behind by 3 points with two seconds remaining, a team would try the field goal. Behind by 5 points with two seconds remaining, the team would try for a touchdown instead.

Why does that matter? Maybe because, if there's lots of time on the clock and the team isn't forced to kick, they might not try it if conditions are unfavorable (into the wind, for instance). But with time running out, they'd have to give it a shot even if conditions were less favorable. So time-constrained kicks would have a lower success rate for reasons other than "choking".

3. The assumption in the regression is that all the coefficients are multiplicative. Perhaps that's not completely correct.

In low-wind conditions, the regression found that every yard closer to the goalposts changes your success odds to 108% of their original. And clutch changes your odds to 72% of the original. So, according to the model, going one yard closer but in a clutch situation should change your odds to 108% of 72%, or 78%.

But what if that's not the case? What if multiplying isn't strictly correct? Suppose that "clutch" makes the holder more likely to fumble the snap, by a fixed amount, and there's also an effect on the kicker that's proportional to the final probability. In that case, multiplying the two effects wouldn't be strictly correct -- only an approximation. And, therefore, the regression would give biased estimates for the coefficients. If the "distance" coefficient is biased too high, but "clutch" kicks happen to be for longer distances, that would explain a higher-than-expected failure rate.

4. The paper included kicks for extra points (PATs), which are made some 99% of the time. And there were lots of PAT attempts in the sample, even more than field goal attempts. At first I thought those could confuse the results. If there were no clutch factor, you'd expect exactly one clutch PAT to be missed. What if, by random chance, there were two instead? That would imply a large odds ratio factor for the PATs, based only on one extra miss, which wouldn't be statistically significant at all.

Could that screw up the overall results? I did a little check, and I don't think it could. I think the near-100% conversion rate for PATs is pretty much ignored by the logistic regression. But I'm not totally certain of that, so I thought I'd mention it here anyway.

5. The authors found that the odds of making a PAT were very much higher than the odds of making a field goal of exactly the same distance -- an odds ratio of 3.52. That means that if the odds of making a PAT are 100:1, the odds of making the same field goal are only 28:1.

What could be causing that difference? It could be a problem with the model, or it could be that there is indeed something different about a PAT attempt.

What could be different about a PAT attempt? Well, perhaps for an FG attempt, both teams are trying harder to avoid taking a penalty. For the defensive team, a penalty on fourth down could give the kicking team enough yards for a first down, which could turn the FG into a TD. For the offensive team, a penalty might move them out of field goal range completely. Those situations don't apply when kicking a PAT.

In clutch situations, the incentives would be different still. Suppose it's a tie game with one second left on the clock, and a 25-yard attempt coming. An offensive 10-yard penalty would hurt a fair bit: it would turn a 90% kick into an 80% kick, say. A defensive penalty wouldn't hurt as much, though: it might only turn the 90% kick into a 95% kick.

Normally, a defensive penalty hurts more than an offensive penalty: it could create a first down, rather than just a more difficult kick. But in late-game situations, an offensive penalty hurts more than a defensive penalty: it lowers the success rate by more than a defensive penalty raises it.

Therefore, in a clutch situation, could it be that FGs are intrinsically more difficult, just because the offense has to play more conservatively, but the defense can play more aggressively?

A Pythagorean formula to predict overtime winners

There's a study in the latest JQAS where we learn something concrete about teams' probabilities of winning overtime games. It's called "Predicting Overtime with the Pythagorean Formula," by Jason W. Rosenfeld, Jake I. Fisher, Daniel Adler, and Carl Morris.

The "usual" pythagorean formula looks like

winning percentage = RS^a / (RS^a + RA^a)

where RS = runs scored (or points scored, or goals scored), RA = runs allowed, and "a" is an exponent that makes the equation work for the particular sport.

The original formula for baseball used an exponent of 2; it was later found that 1.83 was better, and there's a version called "PythagenPat" that varies the exponent according to league-average runs scoring.

Anyway, the authors start by taking a bunch of real-life games in three of the four major sports, and finding the best-fit exponent. They come up with:

NBA: 14.05
MLB: 1.94
NFL: 2.59

Those are the best exponents for full games. Now, what about overtime?

From the title of the paper, you'd think that the authors would do the same thing, but for overtime games: look at overtime runs scored and allowed, and find the best fit exponent.

But that's not actually what they have in mind. Their actual question is something like: suppose a baseball team scores 5 runs per game and allows 4 runs per game in general. Using the usual exponent of 2, that team should have a winning percentage of .610. But: what should that team's winning percentage be if we limit the sample to extra-inning games?

That is: forget how many runs that team *actually* scored in extra innings. Assume only its *expectation* in extra innings, that it will, on average, continue to score 5 runs to its opponents' 4 (after adjusting for the effects of walk-offs). What percentage of tie games do you now expect it to win in extra innings?

To figure that out, the authors use a database of actual tie games, and try to find the exponent on "regular" RS and RA that match the team's actual extra-inning record. But, for extra-inning games, you can't assume the opposing teams average out to .500. So the authors made an assumption: that you can adjust the team's RS/RA ratio by dividing it by its opposition's.

So, again, suppose our team outscores its opponents 5 to 4, but now it's in the 10th inning against a team that also outscores its opponents, 4.75 to 4.25. Our team has a RS/RA ratio of 1.25. The other team has an RS/RA ratio of only 1.18. Dividing the two numbers gives 1.06. And, so, for this particular game, our team will go into the database with a ratio of 1.06 -- as if it scores 4.24 runs for every 4.00 runs it gives up.

Having made that adjustment for each of the overtime games in the database -- 1,012 NBA, 269 NFL, and 1,775 MLB -- the authors computed what pythagorean exponent gave the best predictions. Here's what they found:

NBA: 9.22 overtime
MLB: 0.94 overtime
NFL: 1.18 overtime

So, if our baseball team scores 5 and allows 4, for a .610 winning percentage overall. What would its winning percentage be in extra-inning games? To get the result, just rerun the pythag formula with an exponent of 0.94. The answer: .552. Seems quite reasonable.

The authors do a similar calculation for teams that are .750 overall (which isn't that realistic for baseball, but never mind). The results:

NBA: a .750 team is .673 in overtime
NFL: a .750 team is .616 in overtime
MLB: a .750 team is .630 in extra-innings

------

This is good stuff and new knowledge -- an empirical result that we didn't have before. Because of that, I'm even willing to forgive the authors' not including the NHL. Actually, for hockey, you don't need empirical data to figure it out -- at least if you assume the playoff sudden-death format, where they play indefinitely until one team scores. In that case, the exponent must be very close to 1.00.

Why? Imagine that team A scores 4 goals a game, and team B scores 3. If you mix those 7 goals up in random order, and pick the first one to be the overtime winner, the probability is obviously 4/(4+3) that team A wins, and 3/(4+3) that team B wins. In other words, the pythagorean formula with an exponent of exactly 1.

It might actually be a little less -- better teams have more empty-net goals, which really should be eliminated from the overtime calculation. Also, better teams might have slightly better power plays, and, because there are fewer penalties in overtime, that might reduce their chances a bit. Still, an exponent of 1.00 is probably close.

------

The study gives us a pretty good empirical answer to the question it asks. But, to be picky, we could argue that there's not necessarily a reason that Pythagoras should work, theoretically. That's because, in MLB and the NFL, the overtime game is scored differently from the regular game.

Take football first. In an NFL overtime (ignoring this year's rule change), the first team to score wins, and it doesn't matter whether it's a field goal or a touchdown. So it's no longer a game of *points* -- it's a game of *scoring plays*. To properly predict who wins, you want to know about the teams' probabilities of scoring, unweighted by points. For instance, suppose team Q scores 28 points a game, and team R scores 20 points a game. But Q does it with four touchdowns, and R does it with two TDs and two field goals. In that case, you'd expect the two teams to have exactly equal chances of winning in overtime, since they score the *same number of times per game*. There would be no real reason to expect a pythgorean formula to work that's based on points -- you'd want a pythagorean formula that's based on scoring plays.

(Except for one complication: you'd need to somehow estimate how many extra field goals the touchdown team would score if they never went for a touchdown while in field-goal range. That is: sometimes a team will be at their opponent's 20 yard line, but they'll go for the TD instead, and, as a result, they'll sometimes lose the ball without getting any score at all. So a TD might really be the equivalent of (say) 1.2 field goals in terms of scoring plays, because, maybe for every TD scored, there's 0.2 potential FGs that they lost by failing a TD drive other times. If the ratio were 2.33, of course, then points would work perfectly, since 2.33 equals 7 divided by 3. But I suspect that it's not nearly that high.)

A similar argument applies to baseball. In the NFL, an overtime "big inning" (TD) is worth exactly the same as a "one-run inning" (FG). That's not quite the case in MLB -- it's still better to score four runs in the top of the 10th than to score just one run. But, not *much* better. In extra innings, what matters more is *your chance of scoring* in an inning, and not the average number of runs (which matters more in a full game).

Having said that, I should say that I'm not sure it matters very much at all. I'm sure that, in baseball, big-inning and small-inning teams have different pythagorean exponents too, but we don't worry about that too much. So why should we really worry about it here?

------

Finally, two questions I don't know the answers to.

First, the authors write,

"One might expect the relative alphas [overtime exponent divided by regular exponent] in these three sports to equate roughly to the square root of the relative lengths of overtime, compared to a full-length game. If so, that would suggest hat the NBA overtime alpha would be 5, not the NBA's estimated 9.22."

Is there a reason the square root argument should be true? I mean, yeah, when you talk about standard deviations, you use the square root of sample size, but, here, we're talking about the value of an exponent. So is there a mathematical argument for why it should be true anyway?

Second: on page 13 of the study, the paragraph before the section break, the authors give an calculation that, if you eliminate the NFL overtime coin flip, a .750 team's probability of winning the overtime would rise from .6116 to .6160. I don't understand the calculation, and the change in winning percentage seems low. Can anyone explain?

Do foul shooters choke in the last minute of close games?

Searching Google Scholar for studies about "choking," I came across an interesting one, a short, simple analysis of free-throw shooting in NBA games.

It's called "Choking and Excelling at the Free Throw Line," by Darrell A. Worthy, Arthur B. Markman, and W. Todd Maddox. (.pdf)

The authors looked at all free throws in the last minute of games in the three seasons from 2002-03 to 2004-05. They broke their sample down by score differential, and compared the success percentage to the players' career percentages.

They found that for most of the scores, the shooters converted fewer than expected. Here's the data as I read it off the graph (but see the PDF for yourself). The score differential is from the perspective of the shooting team, and the "%" column is actually percentage points.

-5 points: -3%
-4 points: -1%
-3 points: -1%
-2 points: -5% (significant at 5%)
-1 points: -7% (significant at 1%)
+0 points: +2%
+1 points: -5% (significant at 5%)
+2 points: +0%
+3 points: -1% ("also signficant")
+4 points: +1%
+5 points: -1%

The authors conclude that choking occurs, especially when down by 1 point.

It may not be obvious at first glance from the chart, but there's a tendency to "choke" all the way down: there are 8 negatives and only 3 positives (and the negatives are generally more extreme than the positives). Do players actually shoot worse in the last minute of close games?

----

I couldn't think of any statistical reason the results might be misleading ... but in an e-mail to me, Guy came up with a good one.

Suppose that career shooting percentage is not always a good indicator of a player's percentage that game. Maybe it varies throughout a career, somehow -- higher at peak age and lower elsewhere, or, even, increasing throughout a career. (It doesn't matter to the argument *how* it varies, just that it does.)

You might expect that the differences would just cancel out. However, the overestimated shooters would be appear in each category more than the underestimated shooters. Why? Because they would miss the first shot more often, and take a second shot *within the same score category*.

As an example, suppose two players have 75% career percentages, but, on this day, A is a 100% shooter and B is a 50% shooter. Suppose they each go to the line twice with the game tied. On their first shot, A makes two and B makes one. So far, their percentage is 75%, as expected. Perfect.

But, only B gets to take a second shot with the game still tied. He does that once, the one time in two he missed the first shot. And he makes it half the time.

So, on average, you have these guys taking five shots, and making 3.5 of them. That's 70 percent -- 5 percentage points less than the career average would suggest.

Now, the numbers I used here are not very realistic -- nobody's a 100% shooter, and hardly anyone is a 50% shooter. What if I change it to 80% and 70%?

Then, following the same logic, and if my arithmetic is correct, those two players combined would make 74.8% of their shots instead of 75%. It's still something, but not nearly enough to explain the results. Still, I really like Guy's explanation.

----

So, there you go: it does look like, for those three seasons, players shot worse in the last minute than expected. Can anyone think of an explanation, other than "choking" and luck, for why that might be the case? Has anyone done this kind of analysis for other seasons to confirm these results?


UPDATE: Maybe it's just fatigue! See comments.

Does a "year of the pitcher" mean more 20-game winners?

"Pitchers Rule," declares the cover of the July 5, 2010 issue of Sports Illustrated. The accompanying story quotes some statistics about how pitching in MLB is very much improved this year.

"The 1968 season will always be the Year of the Pitcher ... Bob Gibson boasted a 1.12 ERA for the Cardinals ... Danny McLain won 31 games for the world champion Tigers ...

"[In 2010] there's an across-the-board dip in offensive statistics: through Sunday an average of 8.9 runs per game had been scored, down from the average of 9.3 through the same date last season. ... Home runs are in similar decline ...

"At week's end 15 hurlers ... were on pace for 20-win seasons; in the last six seasons there have been 12 20-game winners combined."

Ignore the obvious problem that there will always be more pitchers "on pace" for a goal than actually reaching it (for instance, there are lots of players "on pace" for a 162-home run season after one game). There's another thing there that didn't make sense to me: the idea that when pitching is up and batting is down, there will be more 20-game-winners than otherwise.

It makes sense for ERA, but not for wins. No matter how good or bad a league's hitting is, there is always the same number of wins to go around -- one per game played, or, in total, 162 times half the number of teams in baseball. Why should those wins be concentrated among fewer pitchers (which is what happens when you have lots of 20-game winners), just because the hitters are worse?

One explanation: perhaps hitters are worse because there are a bunch of great new pitchers and those are your extra 20-game winners. But that's not what's happening this year, is it? Even veteran pitchers are seeing their stats improve this year, aren't they?

So, maybe it's just a mistake, and SI didn't realize what they were saying. But, just to be safe, I checked. For every season since 1982 (except 1994), I counted how many pitchers won 20 games, and calculated the league ERA. (Actually, I mean the *MLB* ERA, not the "league" ERA. But that sounds awkward. Is there a better way to say it?)

Then, I ran a regression. And, to my surprise, the correlation was significant (p=.04). The higher the ERA, the fewer 20-game winners. For every 0.37 increase in overall ERA, there was one fewer 20-game winner that season.

Leaving out 1995 made the result a bit less significant (p=.06) but kept the effect size about the same (+0.42 ERA gives one less 20-game winner).

So what's going on?

Here's one possibility: managers are failing to adjust for the higher offense, and are going to the bullpen too soon. In a low-scoring league, a pitcher having a bad day might give up four runs in the first five innings, but stay in the game. In a higher-scoring league, he might give up five runs, and be lifted. The manager doesn't quite adjust enough for the fact that the two performances are equivalent. As a result, some of the wins that would go to the starter wind up going to the bullpen instead.

There's a better alternative, one that doesn't have to assume managers are irrational. It could be pitch counts. Suppose a starter stays in for 100 pitches. In a high-offense league, a starter's 100 pitchers lead to five runs in four innings. In a lower-offense league, the 100 pitches yield five runs in five innings. The low-offense starter gets the win; the high-offense starter doesn't.

In any case, I don't know which of the two explanations is right. It could be a combination of both. Or can anyone think of other explanations?

Poor play can be caused by bad luck

Why hasn't England won a World Cup since 1966? Who knows? The sample size is too small to draw any real conclusions. It could just be luck. In an excellent column in Thursday's Ottawa Citizen, Dan Gardner explains:

"Unfortunately, this habit of dismissing luck as a factor is not limited to sports. It's human nature. We fabricate explanatory stories automatically and effortlessly, but luck is routinely excluded from those stories because we have no intuitive feel for randomness. We often struggle merely to see luck.

"Consider England's 40 years of disappointment at the World Cup. The very fact that it has lasted four decades is often the foundation of claims that it reflects national character or whatever, but in those 40 years there have only been 10 World Cups and England has only been a serious contender in -- I'll pick a fairly arbitrary number -- six or seven. And what disasters befell England in those six or seven events? One year it was Diego Maradona's "hand of God" goal. Several times, England was ousted by penalty kicks, which are only a little more dependent on skill than coin tosses: The keeper guesses left, the ball goes right, and another chapter in the history of English misery is written."

Gardner goes on to talk about luck in other sports, and also in world events. (I also enjoyed his book about risk, which came out a couple of years ago.)

One thing I wish had been emphasized more is what you might think of as "micro luck." Gardner mostly talks about "macro luck," the big events that were obvious and obviously out of their control -- Maradona's hand of God, the goal against the Germans the referee didn't see, and so on. But most of the luck affecting sports is the smaller things, the outcomes that don't look like they involve luck at all because they appear to be entirely within the player's control. The pass that goes right to the teammate so he has an extra split-second to shoot, or the challenge that manages to get the ball from the other team at midfield.

A perfect pass is seen as a sign of skill -- which it is. But not every pass, even by the best player, will be perfect. If there were a way to make the same player attempt the same pass a thousand times or so, you'd probably see a normal distribution of where the pass would go. Some of the time the pass would be perfect; some of the time the pass would be a little off; and, rarely, the pass would be mis-hit and be completely off, perhaps a giveaway to the other team.

The difference between a good passer and a weak passer is not that the good passer is *always* good and the weak passer is *always* weak -- it's that the good passer has a tighter distribution of where the passes go, so that his passes are more often closer to the target.

Previously, I used basketball free throws as an example. An NBA player has shot thousands and thousands of foul shots in his life. All of them came in exactly the same circumstances -- same distance from the hoop, same height, same regulation size basketball, no opposing player to worry about. What happens? Even in those perfectly-controlled conditions, they can only hit 80% or so. Why? It's just a limitation of the human body. If you're even the slightest bit off in trajectory or velocity, the shot won't go. It's just a limitation of human physiology that we can't control our arms and legs precisely enough to hit the target 100% of the time. We're just not built for that level of precision.

In soccer, whether a particular player successfully makes a particular pass is about how good the player is, but it's also about whether he was lucky on the attempt. We can't control the movements of our bodies perfectly. With practice, we can be more and more consistent, but not perfect. Even 95% isn't good enough. Suppose that it takes 12 consecutive passes to move the ball from down the field to the opponent's penalty area. The probability of winning twelve consecutive 95% bets is 54%. Almost half the time, our attack will fail, and it'll be because a 95% pass, an almost sure thing, failed. It doesn't look like luck -- it looks like a gross error on the part of a certain midfielder. But that error is still luck if 95% is typical for players of that caliber.

Furthermore, what if, on a given day, the team only completes 92% of passes instead of 95%, just by random chance? Now the probability of getting the ball down the field is only 37%. That's only about 2/3 as many scoring chances as before.

If that happens to a team, and it loses the game, the narrative will be about how ineffective it was -- they couldn't get an attack together, and their passing wasn't crisp. And that's absolutely legitimate. The team did play poorly, and a lot of passes did indeed go bad.

The point is that poor play, too, can be caused by simple bad luck.

FDA: non-filtered cigarettes aren't any more dangerous than ultra-lights

(Warning: non-sports post)

Last month, the USA banned the use of words such as "mild" or "light" to describe cigarettes. The government claims that "light" cigarettes are no safer than regular ("full flavored") cigarettes. There are lots of reports about this on the web, such as this one from the CBC:

The U.S. Food and Drug Administration says cigarette packs no longer can feature names such as "light," "mild," "medium" or "low," which many smokers wrongly think are less harmful than "full-flavour" cigarettes.

To which I say: I don't believe the "wrongly" part. The idea that light cigarettes aren't less harmful than regular cigarettes just doesn't make sense to me.

First, consider this: if light cigarettes aren't less harmful than regular cigarettes, that implies that regular cigarettes can't be *more* harmful than light cigarettes. It's simple logic and simple mathematics. If A is not less then B, then B is not greater than A. Right?

I just can't believe that if you take a "light" cigarette, and take the filter off of it, the resulting cigarette is no more harmful than with the filter on it. Do you believe that? If you do believe it, then, if you're a smoker of light cigarettes, why not switch to the stronger, unfiltered ones? The government itself says the stronger ones aren't any worse! Apparently, you can take a light cigarette, rip off the filter, and add as much tar and other carcinogens as you want -- but still, the original light cigarette is not less dangerous than the modified one!

If it had been the cigarette companies saying that, instead of the government, the s**t would have hit the fan, wouldn't it? Imagine an ad for unfiltered cigarettes that said, "Hey, these have more tar and carcinogens than normal. But switch to these, since they're still no worse for you than normal filtered cigarettes."

Can you believe that the government, and the anti-smoking groups, would let any tobacco company get away with that? Not a chance. It would take about five seconds before lawyers started looking for people who believed the tobacco companies and decided to smoke non-light cigarettes, and then got cancer. The lawsuits would fly.

Seriously, I don't think anyone really believes that the stronger cigarettes aren't worse for you. What I think is happening is that there's a moral panic with regard to smoking, a panic that makes everyone scared to tell the truth because it's politically incorrect. In today's anti-smoking climate, the goal isn't to describe the issues impartially -- the goal is to denounce the evil. The object is to never say anything that sounds like you're condoning the moral evil. So, you can say "light cigarettes aren't better" but you can't say "regular cigarettes aren't worse" -- even though those two statements *mean exactly the same thing*. The words "aren't worse," when applied to the evil of smoking -- any kind of smoking -- sound like you're condoning the activity, and that's not allowed. Every sentence you utter has to appear to support the position that smoking is wrong and bad and evil.

Now, the anti-smokers do have some reasonable arguments about why light cigarettes aren't as "less unsafe" as they may appear. They argue that in order to get their nicotine, smokers have to puff harder on "light" cigarettes, which negates their "lightness". They say that smokers block some of the airholes in the filters of light cigarettes, and so get a stronger dose of carcinogens than stated on the label, which are measured by smoking machines in labs. And so it all evens out in the end.

It does sound like there's some truth to that ... if you don't think about it too much. If you do think about it a bit, you realize that it doesn't work for other things, does it? For instance, restaurants in New York City now have to post calorie counts for all their menu items. The idea is that customers will be scared off by high calorie counts and eat less.

If that works for food, why shouldn't it work for smoking? Why is it that it's presumed that smokers won't end their smoke break until they reach a certain nicotine dose, but not that eaters won't end their meal until they've been satisfied by a certain calorie dose? It seems to me that either the food premise or the nicotine premise must be wrong.

Even if you accept the premise that smokers measure by nicotine, that still isn't enough to justify the conclusion. Suppose it's true that smokers automatically compensate for low nicotine levels by smoking harder. All things being equal, wouldn't that make high-nicotine cigarettes safer? You might only have to smoke half a cigarette to get your nicotine fix (and nicotine itself isn't that dangerous, which is why the nicotine patch is such an improvement over smoking).

But remember the scandal when it was revealed that cigarette companies artificially boosted their cigarettes' nicotine content? By this argument, you'd think that they'd be hailed as heroes -- you could get your fix with less smoking! But, no: they were denounced. The higher nicotine levels were taken as evidence that the cigarette companies were trying to get their clients dangerously hooked.

That argument implies that higher nicotine levels are bad for smokers. Doesn't that imply that lower nicotine levels are *less* bad for smokers? Again, if A is worse than B, then B must be less bad than A.

Again, if no cigarette is any "less unsafe" than any other cigarette, then how can you criticize the cigarette companies for changing their products' recipes? Again, it seems like it's possible to make a cigarette A that's more dangerous than cigarette B, but, by some miracle that supersedes Aristotelian logic, cigarette B somehow escapes being less dangerous than cigarette A.

Besides, even if smokers do smoke light cigarettes harder, to try to maximize their nicotine, that still doesn't make them all equal. This government document (.pdf) lists tar and nicotine levels for several hundred brands and types of cigarettes. They all have different ratios. Take, for instance, the third and fourth cigarettes on the list. One is "full-flavored" (regular) with 15 tar and 0.9 nicotine. The other is "light" with 9 tar and 0.7 nicotine.

Do the arithmetic. With the regular cigarette of that brand, you can smoke one cigarette and get a 0.9 dose of nicotine with 15 tar. With the light, you can smoke 1.29 of those cigarettes, and get the same 0.9 nicotine dose with only 11.57 tar. Doesn't it seem obvious that the light cigarette gives you less tar for the same nicotine hit? Isn't less tar going to be less harmful than more tar? So isn't the light cigarette in this case indeed going to be less harmful than the regular cigarette?

It's not just tar. According to this article (and many others), there are some 4,000 compounds in cigarette smoke, many of which are harmful or carcinogenic. That is: the health risks of smoking come from the chemicals inhaled. But if cigarette A, with X micrograms of carcinogens, is no "less bad" than cigarette B, with 2X micrograms of carcinogens ... then doesn't it follow that smoking one pack of A isn't any "less bad" than smoking two packs of A? Your body only knows the dose of carcinogens -- it doesn't care how many cigarettes it took to get that way. (Otherwise, we could cure cancer by giving everyone a single two-ton cigarette to smoke over their lifetime. One cigarette won't kill you!)

In a just world, the government would lay out the exact risks from different levels of tar, nicotine, and other carcinogens, brand by brand, and let smokers choose what level of risk they're willing to tolerate. But there's a moral panic out there. Anti-smoking groups seem to believe that it's OK withhold risk information from smokers, and even lie to them, in order to avoid acknowledging that there are less risky (but still dangerous) alternatives that some smokers might prefer.

And it's all because "less harmful" sounds like it's off-message. It's like saying "rape is less harmful than murder" -- it's true, but unpalatable. It doesn't come down hard enough on rape for our taste. If you choose not to think about it, your brain might register only the words "rape" and "not" and "bad" and come to the wrong conclusion. But your discomfort, your hysterical reaction, and your failure to think about it do not make the original statement any less true.

You know what it's like? It's exactly like when some religions don't want to teach teenagers about condoms. They're happy to tell stories about how condoms don't reduce the risk of disease entirely (which is technically true), but they won't actually discuss just how much they *do* reduce the risk (a lot). They refuse to acknowledge that oral sex is safer than penetrative sex. They claim to care about preventing harm, but, when you look at their actions instead of their words, what they *really* care about is preventing sex.

Smoking is the new sex. The only politically correct policy is to promote abstinence, even if you have to lie shamelessly about the risks.