### 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 defenseMLB: 102.4 offense, 103.7 defenseNBA: 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?

Labels: basketball, distribution of talent, hockey, NBA, NHL

## 17 Comments:

I don't know for sure, but soccer seems like a likely candidate...

I punched in the numbers for this NFL season real quick. Barring typos, teams averaged 364 points for (over the course of the whole season) with a SD of 74.25 while their opponents averaged the same 364 but with a SD of 58.79.

DSMok1: off to work soon, but I'll see if I can find some numbers later.

Alex: excellent, thanks!

Forgot to also mention ... goaltending and (other) defensive skills aren't necessarily independent, so the "square and subtract" technique might not be accurate if they're very closely connected.

I think an important factor for explaining greater offensive variation in the NBA is foul shooting. Teams vary on offense (SD of about .5 points last season), but have virtually no ability to impact opponent FT%.

Right, Guy ... I hadn't thought of that. Good call.

Here's the NFL data for 2012, 2011, 2010, and 2002:

Means

2012.....364

2011.....355

2010.....353

2002.....347

Std. Dev. Offense

2012.....74

2011.....88

2010.....64

2002.....62

Std. Dev. Defense

2012.....59

2011.....61

2010.....59

2002.....56

Coefficient of Vstiation

(Std. Dev. divided by Mean) Offense

2012.....20.4%

2011.....24.7%

2010.....18.2%

2002.....17.8%

Coefficient of Vstiation

(Std. Dev. divided by Mean) Defense

2012.....16.1%

2011.....17.2%

2010.....16.7%

2002.....16.1%

A couple of comments: Overall scoring levels have not changed a whole lot since 2002; the average offense/defense is about 1 point per game higher now than then.

The standard deviation of offense is always higher than that of defense. But, interestingly, it looks like the effect is much more pronounced in 2011 and 2012 than in 2010 and 2002 (I didn't take the time to look at 2003 - 2009; data on ESPN goes back only to 2002).

And there is much more variation over time in offense than in defense. The coefficient of variatiopn of points allowed (the stadrad deviation divided by the mean) is essentially constant at aroung 16% to 17%, while the coefficient of variation of points scored is now considerably larger than in 2002--or 2010.

I have no particular explanation for that.

Thanks, Doc! Yeah, the difference in 2002/2010 is pretty small. But, even in the 16 years of the NHL I looked at, there were seasons where offense had a wider spread than defense. So, could just be random variation ...

One thing that will make the NFL weird, compared to other sports, is that teams can score while pplaying defense (and thus also give up points while playing offense). So teams with really good defenses will also looke better offensively (thus possibly increasing the s.d. both of points scored and points allowed?). I'm not quite sure how much difference this makes, but it is, at least conceptually, possible to split defenseive scores out.

I must not have anything much to do. I now have NFL data for the 16-game-season period (beginning in 1978, but excluding the strike year of 1982). Over that period, the coefficient of variation in points scored has tended to rise fairly steadily, and is now about 23% higher than it was in the late 1970s (up from a little less than 18% to almost 22%). Meanwhile, the coefficient of variation in points allowed has decreased some (but not in any statistically significant way) and is now about 8% lower than it was in the late 1970s (down from a little under 18% to a little over 16%). So over the last 35 (or so) years, the variation in team points scored has increased significantly, while the variation in team points allowed has decreased, but insignificantly.

Also, and perhaps coincidentlly, the major increase in the variation of points scored has come since 1993, and, since 1995, scoring has almost continuously increased, from about 300 points per team per season to about 365 per team per season...

Another thing that occurred to me is that the transition from offense to defense (and vice versa) is cleare in some sports than in others. For example, in baseball, a team cannot score unless it is on offense. And "going on offense" is clearly defined. In football, teams now routinely entirely change who is playing when they transition. But the transition in (for example) basketball is much less clear. Outstanding defensive teams may score moe "off the transition," and thus a part of their offense is a direct consequence of their defense. (I don't know enough about hockey or soccer to say anything sensible.)

Doc:

I think the main factor that explains your results is that passing has become a much more important part of the game over the past 20 years. And the success of a team's passing game likely relies more on the skills of a single player (QB) than it's running game. The increased passing also accounts for the rise in scoring.

Premier League soccer, 2011-12:

Goals scored, SD 15.73. Goals allowed, SD 14.22.

Have to do these manually. I'll do more eventually.

Clearly, I'm not as motivated as Doc. :)

Or you still have a day job.:)

A little more in-depth look at scoring in the NL from 1992 to 2012. The variation is runs allowed is larger than the variation in runs scored.

http://isolatedpower.blogspot.com/2013/02/variations-n-runs-scored-and-runs.html

late to the party but I'm really enjoying this site and, as I have Premier league numbers for the last 12 seasons in a very workable format I thought I'd add to the discussion

Goals scored SD = 14.22, goals allowed SD = 12.87

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