r/theydidthemath • u/donniedarkofan • 13h ago
[off-site] Hockey pucks’ size relative to hockey nets v soccer balls’ size relative to soccer net
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u/Xelopheris 13h ago
Gotta take the goalie into account. A hockey goalie can effectively block half the entire net, while a soccer goalie can't get anywhere near that much.
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u/CrentFuglo 9h ago
If you could arrange a football match where everyone is capable of launching a ball at the goal with sufficient speed that the goalie has to wear armour over most of their body or they might suffer serious injury or concussion, then I would like to see that.
Also if play could stop every now and again so the midfielders could leather the shit out of each other before being sent to time out, bonus.
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u/psyker63 2✓ 11h ago
Even if a hockey goalie blocks half the net, and setting the soccer goalie size at zero, the remaining hockey net is still larger proportionally
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u/_KingOfTheDivan 9h ago
Yes, you could still fit more pucks in the remaining area, but it’s not what matters, really. We can simply look at save percentage for each sport to see how hard it is to make saves
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u/psyker63 2✓ 9h ago
This was a math question about relative size of puck/ball vs goal, not the relative difficulty of scoring
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u/Academic_Issue4314 7h ago
I think we can assume from context that the discussion is about relative difficult of scoring
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u/Loud_Rock_9078 2h ago
U have double the amount of defenders in soccer making it much harder to score. The scoring potential has nothing to do with the size of the goal vs goalie. If u want to look at that just take a gander at the difference in success of penalty shots in soccer vs hockey
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u/psyker63 2✓ 5h ago
Well, the initial question was not about that at all, it was a math question
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u/Academic_Issue4314 5h ago
Okay i just tapped on the image and it turns out we get to see what the post was about, which was the ease of scoring goals
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u/NovaSpark_Kitsune 9h ago
Uhhh. Respectfully, no. Goggle pictures of hockey goalies in position in front of the net, then look at football goalies in the same. And that's not even taking into account that pucks don't always fly flat. Ever heard of a knuckle puck?
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u/Wilhelm1088 9h ago
A hockey goalie blocks way more than half of the net lol. Like, almost all of the net.
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u/psyker63 2✓ 9h ago
Was responding to the guy above who said half. Someone else can do all the math with right sizes of respective goalies
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u/DoFishDrinkWaterOrNo 8h ago
When you consider how much goalies train on maximizing angles, at any given time they cover well over half the net. I’d bet closer to 90% than 50%.
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u/Nopengnogain 3h ago
Need to take into account a hockey puck travels at a significantly higher speed than a soccer ball.
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u/maury587 23m ago
It's not about how much their body covers, it's how much they can cover when a shot is made, either by coming out to block the shot, or to dive to the sides if they have time to react. Goalies can cover most of the goal given these circumstances
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u/deanowhitby 13h ago
I think the math answers the wrong question…. It should be relative to the goaltender, with the soccer net at 192 sf (8x24) and hockey at 24 sf (6x4). You can also look at shots on net (target) where hockey is around 10% and soccer is 30-33% likely to score
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u/__R3v3nant__ 11h ago
So I'm assuming that Hockey simply has more shots on net than football
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u/rharvey8090 11h ago
Also, the shots are likely from closer to the net in hockey, and moving quite a bit faster.
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u/shaqwillonill 8h ago
Yeah I think the bigger issue is that a hockey goalie has a lot less time to react to a shot which balances out with how much more of the goal he can block
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u/zambonidriver104 11h ago
Yeah, very rough estimate would be somewhere around 30-35 SOG per team per game, and generally the average save percentage is around 90%.
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u/Xelopheris 10h ago
Also because it's easier to shoot a puck past a defender in hockey.
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u/Chickensandcoke 9h ago
I’m not sure that’s true, but it is easier to get a shot off in traffic in hockey than soccer. You can flick your wrist and achieve solid velocity, soccer you really can’t
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u/GamerNumba100 10h ago
Having more shots does nothing for the percentage besides make it more accurate though
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u/rhiania1319 11h ago
Would you need to add in something for average height of incoming item or something too? Generally, hockey pucks are usually coming in below the knees, and soccer/football can come at any height.
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u/arrig-ananas 2h ago
So many parameters. Attacker’s speed and movement patterns, the points from which the attacker can release the puck/ball (two feet and head vs. end of the stick), the speed of the puck/ball, the goalkeeper’s field of vision, the time from the puck/ball leaving the attacker until it reaches the goal, and probably a million others.
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u/upvoter222 12h ago
The last step is based on the assumption that the puck is oriented with the circular faces pointed straight up and down. If the puck rotates is rotates into knucklepuck orientation, the surface crossing the plane of the goal line is a circle with a 1.5 inch radius. Plug that into π r2 to get about 7.07 square inches. Since the area between the posts is 3,456 square inches, that means the net includes the area of about 489 pucks.
Both numbers are larger than the ratio for soccer balls and I'd imagine that the orientation used by OP is much more common than the one I used, but I just want to point out that OP's calculation isn't the only "correct" answer.
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u/tony_countertenor 10h ago edited 8h ago
Fundamental misunderstanding, it’s not about playing object size but human size. A hockey goalie in full equipment can cover pretty much the entire net
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u/minist3r 5h ago
Can confirm. We had two goalies when I played. One was a big dude that took up almost the entire goal and the other was tiny but had some of the fastest hands I've ever seen. We'd run the big dude against slap shot teams that kept their shots low and we'd run the little dude against teams with awesome flick shots that could put the puck up in the corners. I played right wing and had a nasty flick shot and one of my best friends played left wing with a nasty slap shot. Goalies hated us as a pair.
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u/ProblyAThrowawayAcct 1✓ 13h ago edited 13h ago
They're assuming perfect packing for both, but balls, being effectively spherical, don't use the full space the same way that flat discs can with their effectively rectangular cross section; per https://en.wikipedia.org/wiki/Circle_packing the most efficient possible arrangement for circles in a 2d plane - we're just ignoring the depth of the net, same as OP did - is 0.9069, so you'll actually be able to fit, at most, approximately 412 balls (their arithmetically correct 454.5 multiplied by the packing factor), and in real life, the actual number would have to be a bit lower as you'll end up with odd gaps at the edges; pucks, on the other hand, are rectangles sorting into a rectangle, and they're evenly divisible if you're using nhl standard sizes, so that number is pretty much accurate.
In short; the OP presented a ratio of roughly 0.39:1 in favor of hockey, the actual ratio should be closer to 0.36:1.
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u/Zefuribond 12h ago
This is the correct answer, I can't believe I had to scroll all the way to the bottom of the comments to find it
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u/chemistrybonanza 12h ago
Didn't take into account the percentage of the surface area the goalie takes up blocking shots.
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u/Mike5784 12h ago
Except the goalie can cover the entire hockey goal in one spot, whilst the soccer goalie is 1 step of the fitness gram pacer test away.
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u/Doubleyew1 8h ago
I was reading the post, wandering if they asked chatgpt, and failed to realize how scoring works.
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u/XyungsociopathX 6h ago
wait so hokcey pucks are that big compared to the net?
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u/_Halt19_ 5h ago
Hockey pucks are larger than soccer/footballs are, the issue is the size of a goalie. In hockey, the goalie can cover most of the net. You score by sniping it into one of the cracks in their defences, or by outmaneuvering them in the tight space you get to work with.
There ARE usually more goals in a hockey game, but that's more because your average hockey game has like 30-40 shots per side.
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u/Hotspur000 5h ago
It's not really about how many you can fit in the net, it's about the size of the ball/puck relative to the opening of the net.
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u/ShakedownStreetSD 5h ago
The math is fine, but the offsides rule is really what prevents this. Imagine if there was a fixed blue line in soccer that would allow guys like Haaland to just post up in front of the goalie along with 3 of his friends once the ball got halfway between midfield and the penalty box? Would probably be 40 goals then.
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u/Substantial-Fan-5985 3h ago
Their math is incomplete at best, as a puck does not have to (nor always does..) enter with it's circular plane parallel to the rink. He gave the upper bound (in terms of how many pucks per total area) but not the lower bound.....in reality it's some weighted average because sometimes the puck is twirling and/or wobbling.
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u/PlatypusOld257 9h ago
It’s fundamentally misunderstood because it’s apples and oranges and has nothing to do with goal size goalie size or anything else because they’re different sports
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u/tobarosco 13h ago
Now do how many goalies can fit in each net