Today we answer one question, then turn things over to a fan with more fondness for math than I ever hope to possess.
The Canucks went down for good (in Game 5) to Anaheim last night, but they got another unbelievable performance from Roberto Luongo. I know you weren't big on Vancouver's playoff capabilities, but you've got to admit, their future looks good. Don't you?
Rory G., Victoria, B.C.
All year, I've been saying that (a) the Canucks didn't have enough firepower to score, (b) their defense corps wasn't among the league's elite, and (c) Roberto Luongo had yet proven himself in the playoffs. After Vancouver was eliminated by Anaheim, I stand by two of those three opinions.
Simply, Luongo was otherworldly in the Canucks' net. Check these stats out:
Â– In 12 games, Luongo faced 427 shots; the next closest on that list is Martin Brodeur, who's dealt with 308 in 10 games.
Â– Luongo also leads the list of post-season ice time among all goalies (847:26); Dominik Hasek is No. 2 at 636:05.
When you consider the Canucks were the fourth-worst scoring playoff team (an average of 1.75 goals-for per game), Luongo's heroics stand out all the more.
So yes, I think Vancouver's future looks bright. Dave Nonis is going to have to decide how to beef up his offense and deepen his defense, but clearly, he has the type of netminding that led teams such as New Jersey and Colorado to multiple Stanley Cups. Canucks fans have to feel good about that.
I know much has been written about the disallowed goal at the end of Game 4 of the Rangers/Sabres series. The official explanation is there was inconclusive evidence the puck completely crossed the goal line, with the rule of thumb being that white ice must be visible between the puck and the goal line for such confirmation.
However, it was also noted that the camera is not located directly above the goal line, but at the back of the net. Therefore, I generated the following example to prove that the rule of thumb is incompatible with the actual definition of a goal. More significantly, the correction for the distortion is simple, and one that any high school geometry student could complete.
According to the rulebook, the net is 48" tall, and the top of the net is 18" deep. This creates a right triangle with a height of 48", and a depth of 18". The ratio of the opposite and adjacent sides is 3 (opp/adj=3), resulting in an angle of 71.565 degrees at the goal line. This also results in a hypotenuse of 50.596".
The puck is 1" tall with a diameter of 3". If the puck is sitting flat on the ice and tangent to the interior side of the goal line, (which is as close as it could be to the goal line without actually covering any portion of it), this results in a new triangle of height 47" and depth 18". The angle from the front edge of the puck to the junction of the center of the back portion of the top of the net is tan^-1 (47/18)=69.044 degrees.
This means the angle created by extending the hypotenuse of this new triangle beyond the tangent end of the puck results in a new right triangle of height 1" with a top angle (at the top of the puck and hypotenuse) of 20.956 degrees, and the angle of the base and the hypotenuse of 69.044 degrees.
This means that the depth of the shadow, or portion of the goal line invisible to an observer positioned at the location of the camera when the puck is tangent to the red line is 0.383" (1/tan 69.044). This means that potentially 19.15%, or nearly 1/5, of the red line is invisible to the camera even when a goal is scored (i.e. the puck has completely gone over the red line).
How far would a puck have to progress beyond the red line in order for the white portion of the ice to be visible between the puck and the goal line? Taking our original triangle (which is formed by the interior edge of the goal line, the top back corner of the net, and a third point on the ice below that top back corner), when the hypotenuse is greater than 1" off of the ice, the ice in between the puck and the goal line will be visible.
What does this mean in practice? With a base angle of 71.565 degrees at the goal line, the hypotenuse is exactly 1" off of the ice 1/3 of an inch to the interior of the net from the back edge of the goal line.
What is the practical significance of all of this? Basically, it means that, in the absence of a camera positioned directly on the underside of the front crossbar (directly above the goal line), using the observation of white ice between the puck and the goal line as direct evidence that the puck has completely crossed the goal line is an incorrect standard.
Using such a standard, a goal can only result when the puck has crossed the goal line by more than a third of an inch - a different standard than for any other goal, wherein the puck only has to completely cross the line. Rather, the more appropriate standard would be to calculate how much of the red line must be visible to the camera when the puck is tangent to the goal line, and then applying that standard to the video.
For instance, knowing the goal is 2" deep, one can use the puck as a reference to gauge the distortion of the video, and then measure the amount of goal line visible. If the ratio of visible goal line exceeds the minimum standard, then this is concrete evidence that the puck has crossed the line.
Of course, the measurements provided here are simply suggestive, as I don't have the exact dimensions regarding the placement or size of the camera; but the NHL does. What I do think the above example represents, however, is the fact the angle of the camera, and the Â“white iceÂ” standard of the video replay officials, results in incompatible standards and distortions.
If the NHL really wants to get the calls right, a return to high school might be in order.
Really enjoy reading your columns. Keep up the good work!
You had me at hypotenuse. I think.
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