Sunday, November 15, 2009

Why Goalie Equipment Was Not Responsible for the Scoring Drop

I'm interrupting a series of posts on win thresholds to continue a discussion we had in one of the comment threads about goalie equipment. A lot of people make a big deal about the size of goalie equipment in the NHL, and the NHL is currently working on yet another attempt to "fix" this problem. Many see large goalie pads as the main reason for the low scoring rate, and feel that if more restrictions were put on equipment then the league would become significantly more high-scoring. I've seen some fans go so far as to argue that the main difference between the 1980s scoring environment and the scoring environment today is that goalies wear much larger equipment.

I think those claims are completely unfounded. The reasons for the rapid improvement in goalie numbers over the last two decades have been improved goalie technique and better defensive play. Goalie equipment size has been a minor factor.

The main proof for this is the way that the goalie crop turned over in the late '80s and early '90s. The old guys were phased out of the game, a new wave took over, and there was a rapid increase in the league-average save percentage. All of this happened before goalies started increasing the size of their equipment.

Patrick Roy is generally credited with popularizing the butterfly style. Roy played his first NHL game on February 23, 1985. At that time goalies spent most of their time on their feet, they relied on their limbs rather than their body to make saves, and they made skate saves and stacked the pads and hugged the post with their arms and did all the other traditional things goalies had been doing for years. Let's look at what happened to that group of netminders.

There were 66 goalies who played a game in that same 1984-85 season, including Roy. Their average age was 25.7 years old. Just 25 of them (38%, a little over one-third) were still in the NHL in the 1989-90 season, a mere five years later. Only 8 of those 25 were still in the NHL a decade later in the 1994-95 season. Only 2 of of those 8 performed at a high level compared to league average in the 1990s, Roy and John Vanbiesbrouck. Roy was the only one of them that won a Vezina Trophy in the 1990s, and he won his last award in 1992.

Let's fast forward a decade to that shortened 1994-95 season, and do the same analysis for that group of goalies. Remember, this is still before the equipment got huge. Here's a picture of Patrick Roy in action against the Quebec Nordiques during the 1993-94 season, for example. He has hardly any thigh-rise on his pads and his pants, chest protector and jersey all fit fairly snugly.

In 1994-95, 68 goalies played in the NHL, with an average age of 26.3. Jump ahead 5 years to 1999-00, as we did for the prior group, and we find that 44 of them are still in the league (65%, or about two-thirds). Not only that, but a dozen of them were still playing 11 years later when the league came back from the lockout for the 2005-06 season. Six out of the 9 Vezinas awarded from 2000-2009 went to goalies who were active in 1994-95, and that group included many of the top goalies of the 2000s.

Having established that the goalies from 1994-95 had much more longevity than the goalies from 1984-85, let's look at the average save percentages for those two seasons. I'll also throw in the average for 2003-04, the season with both the lowest average goals per game and the highest average save percentage of the so-called Dead Puck Era.

1984-85: .874
1994-95: .901
2003-04: .911

Power plays per game were at about the same level for all three seasons, 7.9 per game in 1984-85, 8.6 in 1994-95, and 8.3 in 2003-04. Some of the increase in save percentage would have been from defensive play, but most of it was because the goalies were better. League-wide defensive play also improved from 1994-95 to 2003-04, yet the league average save percentage only went up by .010, despite goalie equipment getting much larger. It is obvious that the more significant change happened between 1985 and 1995, not between 1995 and 2004.

We can also get a sense of the changing dynamic from 1985 to 1995 by comparing the save percentages of the goalies who were active in both periods. I chose to look at three year averages to avoid small sample sizes, including the year before and the year after for each goalie (i.e. 1984-86 and 1994-1996). There were 8 goalies in the group, but I dropped Roy since he only played 1 game in 1984-85 and therefore would really only have one season count. Roy played the modern technique anyway so his progress isn't really meaningful to what we want to track, which is how the older goalies adapted their games to a changing league.

1984-86: .886
1994-96: .900

There is a substantial improvement in the numbers. It is important to note, though, that this improvement was mostly being driven by the younger goalies in the group. The goalies who saw their numbers jump the most were Ken Wregget (.871 to .900), Tom Barrasso (.886 to .898), and especially John Vanbiesbrouck (.882 to .915), all of whom were 21 years old or younger in 1984-85. Not only were these goalies young and still not at their prime in the mid-'80s, but they already used some modern techniques or were able to adapt to the changing game.

Let's look at the older group of goalies, which includes Andy Moog, Grant Fuhr, Don Beaupre, and Kelly Hrudey. These goalies did not change their styles as much over the same period:

1984-86: .889
1994-96: .896

Despite seeing their save percentage numbers rise as a result of better defensive play in front of them, this group of four lost a ton of ground to the rest of the league during this period. They went from +.015 compared to league average in the mid-'80s to .002 below league average in the mid-'90s.

Let's compare that to the 1995 group. We want to look at the goalies who were still playing a decade later, so I picked out the 12 that played in the post-lockout NHL. I decided to compare their 1994-96 results to their numbers from 2002-04, since we want to look at seasons with no equipment restrictions.

1994-96: .907
2002-04: .911

That's just a slight increase. To be fair, we should remove Dominik Hasek, who is older than the rest of the group and is skewing the numbers with a mostly age-related decline from .926 to .914. Without the Dominator the group goes from .904 to .911, an increase of +.007. In a more defensive league with larger equipment, the increase in numbers is exactly the same as the increase we saw from the standup goalies from 1985-1995. In both cases, the league improved defensively over the period. Larger equipment would have had some small effect, but certainly not the game-changing impact that some would have you believe.

Finally, recent years have also showed us that there is not much of a relationship between equipment size and goalie play. After the lockout in 2005 there were new restrictions placed on goalie leg pads (reduced from 12" to 11") as well as glove and blocker sizes. Yet today the average save percentage in all game situations is back up to the same levels as it was in the early 2000s, despite the removal of most of the clutching and grabbing.

Just to recap, the league average save percentage went up by .037 from 1985 to 2004. Most of that improvement (.027) was already made by 1995, which was before the league-wide increase in goalie equipment size. The rest of the improvement coincided with an increasingly defensive league. When we look at the standup goalies who played in both 1985 and 1995, and compare their performance to goalies who played in both 1995 and 2006, we find that both groups increased their numbers by a similar amount even though only the latter group benefitted from huge equipment.

If I had to estimate and rank the factors that led to the change in league save percentage between 1985 and today, I would rank them in this order:

1. Improved goaltending technique (~.015-.020)
2. Improved defensive play (~.010-.015)
3. Goalie equipment size (~.005-.010)

The post-lockout crackdown on goalie equipment was still probably a good idea, but the continued focus on equipment size is in my view excessive and not something that will yield significant rewards. If the league wants to increase scoring, there are better alternatives to pursue.

45 comments:

Triumph said...

i know it's not particularly germane to the excellent article, but what alternatives would you suggest?

also nice to see tom awad and gabriel desjardins to confirm something which i always thought - namely that new jersey's scorekeeper undercounts shots on goal relative to the league average.

Vic Ferrari said...

Triumph

I suspect that the opposite is true. The New Jersey scorer is overly generous with shots, but just by a touch, not material really.

The blocked shots and missed shots drop off even more on New Jersey ice.

When a team wants to play a low tempo game, the opponent is more likely to oblige in your barn than in front of their own fans.

Though I've neve checked, the teams that are trying to draw more fans to home games should see a higher tempo game (more total shots directed at net) on home ice. The opposite for teams that are more conservative and/or know that they are going to sell out anyways (MIN, MTL, VAN, N.J, etc).

Someone could track shots over a few games for New Jersey. Maybe pick home games against SE division opponents. Count the shots, blocked shots, and missed shots.

Do the same for the next four road games against the same clubs ... you'll see.

Vic Ferrari said...

CG:

I don't know how this relates, but Ron Smith has been counting scoring chances for most years since 1981 or so, when he was Roger Neilson's scoring chance tracker. He says that the scoring chance totals per game have been very consistent over the years. He is certain that the drop in scoring is simply due to the goalies being a hell of a lot better.

NHL shooters don't score on 1 of every 4 or 5 scoring chances any more, they score on 1 of every 6 or 7 now.

And don't forget the new sticks as well, the release off a composite stick is awesome. Harder shot too, especially on a snap. I shoot like a girl with a wooden stick, but I'm a threat from further out with a composite.

If they want more scoring chances they'll need to make life even harder on the defenders with strictly enforced rules. And if they want more goals they need to make the nets bigger. IMO it's not going to improve on it's own, the opposite in fact. Every new generation of goalies is a better level of athlete than the last.

Triumph said...

vic:

forgive me as i am suffering from a massive hangover, but am i misunderstanding this article?

http://www.puckprospectus.com/article.php?articleid=351

i do not understand how this jives with what you're saying here, though of course i did see you're doing your own investigation of this. i also do not understand your theory, as it seems rather far-fetched.

Vic Ferrari said...

Far-fetched?

Each to their own, I suppose. I thought I was pointing out the obvious there. As I say, check the games, I'd be stunned if I was wrong.

I noticed that Tom and Gabe posted that as a reply to my simple check of scorers ("study" is far too big a word). There are some huge gaps in reasoning though. frankly, most people will not take the time to understand either, and will choose to believe the article that best fits their preconceived notions. And that's fine.

BrianW said...

CG,

Perhaps you're presenting a false dichotomy? I'm not sure you should separate equipment from technique. My assumption has long been that technique changed largely because of the bigger equipment.

Being that the modern style is so heavily predicated on simply blocking the net, it seems natural to me that a butterfly goaltender would get more milage out of bigger pads. If so, then stand-up goalies may have fallen behind the pack simply because their tachnique made less use of the new technology, and not because that technique was inferior in any absolute sense.

Triumph said...

vic,

as i suspected, i misunderstood what you were saying. i thought you were saying that the home scorer was responsible for the disparities - as though teams would brief the home scorer on how to register shots and thought that overcounting of shots on goal had any effect at all on attendance. that sounds really tinfoil hat and like something one might read in the TSN comments section.

i hadn't considered what you are saying, which makes a kind of intuitive sense.

The Contrarian Goaltender said...

If the objective is to increase scoring, I agree with Vic that the only ways to do it are to restrict defensive players more to increase the number of scoring chances per game, or to increase the nets to increase the number of goals per scoring chance. Which one is preferable depends on whether you like to see more action or just more goals. I'm OK with hockey as is right now, but then again I'm a goalie so I don't view a save as a boring or undesirable event.

The Contrarian Goaltender said...

BrianW:

You need to review the timeline and update your assumptions. The major revolutions in goalie equipment that favour blocking butterfly goalies (larger equipment and box pads designed to rotate and seal to the ice) hit in the mid to late '90s. That was after the new wave of goalies had pretty much taken over, and after the league had already become significantly more low-scoring. Up until that point, goalie equipment was just getting lighter and more flexible, which is an advantage to all goalies regardless of style.

Equipment changed because of technique, not the other way around. A lot of people mistook one for the other because it all happened over a relatively short time frame, but the evidence is really clear on this one. Just look what happened between 1985 and 1995.

The Contrarian Goaltender said...

I haven't got too much into the scorer bias debate, and the reason I haven't is that I think simply comparing home shots to road shots is just too simplistic and that the topic requires a deeper analysis.

I've thought that ever since I saw a shot count breakdown that said New Jersey, Minnesota and Dallas were 3 of the 4 teams with the most biased home scorers in this decade. It doesn't surprise me at all that good defensive teams who play a low-event style and rely on line matching allow relatively fewer shots against at home. In fact, it strikes me as absurd to assume that discrepancy is entirely because of the guy counting shots. A better place to start would seem to be the guy behind the bench, and if there's anything left over after that then maybe we can focus in on the official scorer.

Some teams have much better records at home than on the road, and other teams have similar records at home vs. on the road. It is very likely that teams will have different underlying numbers as well that reflect different strategies or styles of play depending on the venue.

If we're going to be able to find an answer, I definitely think we need to be looking at shot attempts rather than just shots, like Vic has done. I expect some teams just naturally perform better on the road, and I also assume that some teams are under orders to play a more exciting game at home. I looked at the Buffalo Sabres' post-lockout home and road scoring splits and shot attempt splits, for example, and it sure looks to me like somebody upstairs has been telling that team to entertain the paying customers.

Justin Bourne said...

The NHL can't take away goalie technique or improved defensive play, and wants to see more scoring. So gear is the only thing they can control, right? I mean, logically, it's harder to make saves with less gear, and if it isn't, then great - I'd rather watch athletic mobile goaltending than strong positional play from a sumo-wrestler.
Then again, I skipped to the bottom and read a few sentences (not because it wasn't well written, I just have stuff to do and it's long), then decided my point was worth making. Now I'm that guy leaving a comment on something that was already addressed. I apologize in advance.

Oh, and totally random: I'd never seen your site until today, and was going to write my blog today about how Brodeur playing well this year justifies his career for me. Previously, I thought he was on the best team in a defensive era.

Steve said...

Goalies shouldn't be allowed to wear any extra equipment a skater can't wear. Then good athletes won't want to be goalies, and we'll just get slow, dumb guys who don't care too much about taking one off the head.

Fundamentally though, the game is a defensive game and that's what needs to change. I say get rid of the bonus point, give no point for an overtime/shootout loss. Force teams to play to win, instead of playing not to lose.

Anonymous said...

What would a .889 save percentage in 1985 (very high for back then) be in today's numbers, assuming that the goalie in question did learn modern technique and not stagnate like Grant Fuhr, Kelly Hrudey, Andy Moog, or Allan Bester?

Agent Orange said...

Good article. One thing I would be interested to see would be what eras you consider the following to be (if we can seperate them)

1) goalies getting better (ex 89-93)
2) defenses getting better (ex 94-97)
3) equip getting bigger (ex 98-2003)

The reason I bring this up is because sv% is a capped stat. As we increase it gets harder to increase by the same fraction. By that I mean you have to double SA to halve sv%.

Because the equipment size increase came last it has less of an impact on sv% but does more to do it.

Because we don't have any eras where just large equipment was in the league we can't confirm this.

TCO348 said...
This comment has been removed by the author.
Anonymous said...

Interesting research. If the butterfly & larger equipment seals off the lower half of the net, then to score in the top half means that players would have to get closer to the net than previously. It's much harder to get a long high shot at the net than a long low shot, as it will be blocked/hit skaters. I think it's harder to get close to the net for a shot than it was during the wide-open (pre mid 90's?) years.

TCO348 said...

The shooters are starting to adapt to the butterfly. I see way more goals top shelf than I did 10 yrs ago or even 5 yrs ago. Guys just don't shoot for the low corners much anymore and especially from in close. When a goalie drops into the butterfly and the shooter is in close to the net there is absolutely nothing to shoot at 1 foot high or below. You need to lift it to score. Usually in that situation your best chance is to roof it - not as easy as shooting it low - but the shooters are better and better at it all the time.

TCO348 said...

Good point anonymous. When I was a young player we were taught to shoot low. The logic was that the goalie can move his arms and especially his glove, faster than he can move his feet. Before the butterfly that made sense. Goalies would wait for the shooter to shoot and if it was a low shot to either side of the net the goalie would kick out his leg on that side. With the butterfly that just doesn't apply anymore. Even before you release your shot that goalie is dropping down into the butterfly, essentially kicking out both legs at the same time, and since he doesn't need to determine which side the shot is going to he can do it before the shot is even released, making it impossible to blow it past him. The low corners are taken away first because the goalie just covers them both on all shots. Its the high corner shots on which he still needs to pick up the puck before he sticks out his glove or blocker.

The Contrarian Goaltender said...

Shooters are definitely responding to the goalies' improvement. That's likely one of the reasons why we did not see much of an improvement in save percentages between 1995 and 2004. In addition to the near universal usage of composite sticks, shooters realized their scoring rates were dropping so they started taking more high shots and looking for more high-percentage scoring plays.

On the topic of low shots, no doubt the save efficiency has radically improved from the skate save days to today where goalies drop as soon as the shooter commits to shoot. I was watching old footage from 1974 the other day and Gilles Gilbert made a kick save with his right skate on a shot low to his blocker side and the rebound somehow went in front of him and into the opposite corner on his left side. It looked like just about the most inefficient save movement possible for that type of shot.

I am always surprised by how often today's announcers yell out, "Great pad save!" when somebody shoots low from in close and the goalie takes away the bottom of the net. To me that's a routine play. If I get beat by any shot along the ice, I'll almost always consider it a bad goal. Sometimes you have little chance because of a rebound, deflection or cross-crease pass, or if a guy just perfectly catches the five-hole while you're moving across, but otherwise it's pretty much assumed nowadays that if it's low it should be stopped.

TCO348 said...

Don't get me started on what announcers yell out. I think most of them either never played or they think that the audience can't tell a significant play from an insignificant play so they over-dramatize at every opportunity. Agreed though - saves on low shots are almost all routine nowadays.

Anonymous said...

Just for laughs you guys should watch a Rangers feed and listen to Sam Rosen and his "great save by Lundqvist" routine. It's top quality comedy.

Butterfly Aliyah said...

CG, do you think 7uongo would be more consistent with larger pads?

nightfly said...

Sorry to come in late... but I think another reason shooters were so often told to shoot low is that it's harder to freeze a low shot. Low shots create more rebound chances, and those are always dangerous.

Since goalie technique has advanced, keepers are much better at controlling where those rebounds go, and as an adaptation, shooters are trying to pick corners, especially against keepers who cheat a little and drop too soon. Fewer rebounds that way, but a better chance that the initial shot will go in.

Anonymous said...

We have to look at not only the size of the equipment, but also the weight. The pads before the 90's was not only smaller, but also heavier. They were twice as heavy, plus they were mostly made of leather and a cotton/ foam batting. These materials are very absorbant and the pads would get much heavier than the new generation pads as the games wore on due to sweat and water from the ice. The newer equipment has made a difference in better goaltending performances.

Anonymous said...

lol. what a joke pick up a copy of goalies world and read some useful information.Patrick roy never played on a good team like broduer.lol

Alec Berg said...

To increase scoring just play 4 on 4 or give incentives for scoring goals like an extra point if you score 5 or more goals.

Anonymous said...

Here:

http://sierra-rayne.blogspot.com/2012/03/nhl-hockey-in-1980s-unique-era-of.html

And to disagree, utterly and completely, with the one soul's comment, the goalies purportedly better athleticism has nothing to do with the the NHL's current era of mediocrity. Poorer talent in the league does. You know we're in trouble when that gal from Grantland writes about the Kings' fearsome line of Kopitar, Brown and Williams, or 25, 22, and 22 goals respectively. She might instead try 58, 57, and 47 (Dionne, Simmer and Taylor), or 64, 50 and 38 (Bossy, Trottier and Gillies) or 71 and 70 (Gretzky and Kurri).

And the defense isn't any better, which is explained by Craig Ramsay sitting at no. 22 on the all-time +/- list. And I'd take Luce, Ramsay and Gare over Kopitar, Brown and Williams in the heartbeat.

And for the OP, humans aren't mentions and the genetics doesn't have to be equal over generations. See the current crop of woefully inferior NBA centers compared to times past. Worked the same in the NHL, when from the late 70s through the 80s there was simply a better crop of hockey players. There is no Gretzky, there is no Dionne, there is no Bossy, there is no Perreault, etc. For how bad the young folk today are in their estimation of the game's relative talent, I was speaking to some young folk, Kings fans, and they were all excited over Doughty. Meh. Give me Reijo Ruotsalainen. Or Paul Coffey, Ray Borque, or Phil Housley.

Oh, and by the way, you horribly underrate Rogie Vachon. Before the Dionne, Simmers, Taylor era, Rogie saved that team from being simply abysmal.

And for one more:

http://www.youtube.com/watch?v=sXcJShJcnk0

Note what Gil says about making his mates better. Few and far between are the players today who can do that.

Anonymous said...

Here:

http://sierra-rayne.blogspot.com/2012/03/nhl-hockey-in-1980s-unique-era-of.html

And to disagree, utterly and completely, with the one soul's comment, the goalies purportedly better athleticism has nothing to do with the the NHL's current era of mediocrity. Poorer talent in the league does. You know we're in trouble when that gal from Grantland writes about the Kings' fearsome line of Kopitar, Brown and Williams, or 25, 22, and 22 goals respectively. She might instead try 58, 57, and 47 (Dionne, Simmer and Taylor), or 64, 50 and 38 (Bossy, Trottier and Gillies) or 71 and 70 (Gretzky and Kurri).

And the defense isn't any better, which is explained by Craig Ramsay sitting at no. 22 on the all-time +/- list. And I'd take Luce, Ramsay and Gare over Kopitar, Brown and Williams in the heartbeat.

And for the OP, humans aren't mentions and the genetics doesn't have to be equal over generations. See the current crop of woefully inferior NBA centers compared to times past. Worked the same in the NHL, when from the late 70s through the 80s there was simply a better crop of hockey players. There is no Gretzky, there is no Dionne, there is no Bossy, there is no Perreault, etc. For how bad the young folk today are in their estimation of the game's relative talent, I was speaking to some young folk, Kings fans, and they were all excited over Doughty. Meh. Give me Reijo Ruotsalainen. Or Paul Coffey, Ray Borque, or Phil Housley.

Oh, and by the way, you horribly underrate Rogie Vachon. Before the Dionne, Simmers, Taylor era, Rogie saved that team from being simply abysmal.

And for one more:

http://www.youtube.com/watch?v=sXcJShJcnk0

Note what Gil says about making his mates better. Few and far between are the players today who can do that.

Host PPH said...

It is quite important to highlight it. because people should understand a little bit more about goalie equipment.

hemcoined said...

The low corners are taken away first because the goalie just covers them both on all shots.

regards
Loading Arm

Unknown said...

IT IS THE EQUIPTMENT AND HERE IS WHY: I play goalie since 1995 and do today in 2014. It is not the goalie equipment size that is the reason for less scoring. It is how the equipment of goalies functions. LEG PADS PRIMARILY... They function so that goalies can play the butterfly position far more effectively than in the 90's. The guy who wrote this is DUMB and doesn't play goalie or at least did not in 90's and TODAY w/new EQUIPTEMNT. That is why you see less scoring. That is the ONLY reason. LOOK AT GOALIE NUMBERS FROM THE 90's compared to TODAY. If you are a goalie today and have a GAA above 3 you are not going to be a starter. SIMPLY PUT. Example: CURTIS JOSEPH, TROM BARRASSO and so many others posted many seasons above 3 GAA and SAVE% in the low 900's and high 800's and were starters. Look at BRODEUR'S numbers in the 90's and you will see why he is one of THE BEST no GAA above 3 EVER. The guy who wrote this and claims Brodeur is a fraud is FUCKING RETARDED and KNOWS DICK about goaltending. IF BRODEUR CAN POST THOSE NUMBERS IN THE 90's HE IS ONE OF THE BEST AND NOT A FRAUD.

Unknown said...

IT IS JUST EASIER TO PLAY IN THE NEW EQUPITMENT THESE DAYS. I HAVE NOTICED A HUGE INMPROVEMENT IN MY PERSONAL GAME DUE TO THE NEW EQUIPTMENT ALMOST IMMEDIATELY. I USED 90's GEAR UNTIL 2009 AND THE DIFFERENCE ONCE ADJUSTED WAS ASTOUNDING. IT IS THE GEAR. SAD BUT TRUE.

Unknown said...

AGAIN ABOUT BRODEUR... His SAVE%'s all ABOVE 900 every season. His career average isn't INCREDIBLY high but it is still Above average. ALSO LOOK AT HOW MANY GAMES HE WOULD PLAY A SEASON IN THE 90's At least 70 most seasons. Oh and BTW... HE WAS AND IS BETTER than Patrick Roy when it comes to numbers and games played. There is a reason why NEW JERSEY would never let Brodeur go. The only FRAUD = the GUY WHO WROTE THIS ARTICLE.

Anonymous said...

That's preposterous. Goalie technique has been revolutionized. You can blame the gear all you want, but watch the goalies from the past. They are flopping all over the place, diving and pad stacking.

Sure, the new gear helps with the butterfly, but the technique came first.

There's so many more goalie schools now, the young generation is learning fast. With the widespread of YouTube tutorials online, any young goalie can easily learn a lot.

Unknown said...

Lets be serious here. There are no more five foot eight goalies in the league like Vernon or Irbe. Imagine if gretzky tried to score that hasn't winning shot on Vernon against a goalie the size of Luongo.
Sure technique and better pass technology has improved the position.
Then again the average nhl goalie takes up 60% of the net buy just standing there.
So please do not dictate discredit size, it does matter.

Tom said...

Someone above mentioned that the leg pads have changed. I think this is a huge point. When goalies used to go down on their knees the pads were underneath them. It was the side of the pad that was blocking the puck. Now the pads flip to the side. Instead of a 3" barrier, there is now a 12" (or so) barrier. (I am actually curious to know when this change in pad style changed. My google searches just keep turning up recent news about pads needing to be shorter.)

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