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Casting Doubt On the Hawkeye Ball-Calling System
Human judgment by referees is increasingly being supplemented (and sometimes overridden) by computerized observation systems. nuke-alwin writes "It is obvious that any model is only as accurate as the data in it, and technologies such as Hawkeye can never remove all doubt about the position of a ball. Wimbledon appears to accept the Hawkeye prediction as absolute, but researchers at Cardiff University will soon publish a paper disputing the accuracy of the system."
I've seen in Hockey and Football broadcasts the ability to track the ball or puck realtime thru some system inside the playing piece (puck or football.) It seems to work pretty decent to me.
Still waiting on Serviscope_minor to wake up to fucking reality and realize that Jessica Price isn't going to fuck him.
Why not use a radio transmitter in the tennis ball (or soccer ball or whatever) to record its exact position? I am certain this has been discussed and I wouldn't be surprised if it's already in use. The article's "Hawkeye" just works by optical analysis.
It's been tried in soccer. The latest attempts were prior to the last couple of World Cups IIRC, but the systems were plagued with problems, not the least of which was the survival of the transmitter.
http://www.gizmag.com/go/2790/
"Anyone that has ever gotten an idea based on any of my work and done something better with it-good for you."--J.Carmack
Sorry, but you don't know what you're talking about.
Any system of equations with more equations than unknowns is called overdetermined. If you have 5 cameras and 3 coordinates, that leads to an overdetermined system.
The accuracy of the cameras matters, because if the reported measurements were completely accurate, then some of the equations in the system would be linearly dependent on others, and as long as the cameras are intelligently placed, there would be precisely one solution.
Observation errors in the camera measurements however produce an inconsistent set of equations, hence the usual problem of overdetermination.
No it doesn't. When you combine observations, there is ALWAYS the question of what criterion do you use to combine them. That's ARBITRARY. The GPS is no exception: some ARBITRARY method of combining observations is used.
By far the most popular criterion is least squares, which is simple but not as robust to perturbation as least absolute deviation for example.
I don't know what you mean by complementing the equations. A fitting method is used when there are too many equations, and you'd like to essentially ignore the redundancy embodied in them, by introducing another criterion. Is that what you mean? The criterion is arbitrary, so there is no universal way of complementing equations. People pick the criterion they like, usually the one that involves least effort on their part.
Precisely. These multiple averaging methods give different answers. Which one is right? There isn't one. In particular, none of them is more accurate than a human. Just different.
For those that didn't care to RTFA, the study is in the journal 'Public Understanding of Science' and (gooly who would have guessed) doesn't have anything to do with the summary written. They argue that uncertainties in measurement that normally don't impact the layman now need to be presented in an understandable way. They worry that people will wrongfully become too trusting of the systems that do have appreciable error in rare circumstances.
To inject my own opinion on the matter, I've had a little bit of experience with Vicon motion capture systems which appear to use similar technology to the Hawkeye system. The main problem with the system (when it works) isn't any problem with accuracy or precision. In fact, it's awesome. The problem is that the output is a little noisy and suffers from occasional jumps and hiccups. With proper filtering these are eliminated and the output is amazing. I can only imagine the problem is much easier when you're tracking a single ball rather than tens of tiny reflective makers such as with the Vicon system.
You gotta find first gear in your giant robot car
If the errors are random and follow a normal distribution (two big ifs, I admit) then even in one dimension, the error is reduced by a factor of 1/sqrt(N) where N is the number of measurements.
The same general idea applies to higher dimensions. If you can avoid systematic errors then the more measurements you take, the more accurate your final result will be. If you are interested in the gory details of the higher dimensional case, you should take a look at singular value decomposition.
We don't see the world as it is, we see it as we are.
-- Anais Nin
Since we're only dealing with three dimensions, why would any number of satellites > 3 be more precise for GPS?
;-)
Because we are dealing with reality as well - where no measurement is perfect.
Geometrically, three sats indeed are enough, but in reality:
More measurements -> smaller error bars -> better position.
The alternative to more sats would be not to move and to take more measurements over time.
But that would render GPS useless for most applications
Additional trouble with the "stay and wait" method: Those nasty satellites move over time,
introducing different errors that can not be eliminated as easily by simple averaging.
That's also why ultra precise GPS surveying records the satellite data and waits for the week it takes
to make the actual orbital data (as measured, and not just as predicted) available before computing
the position, thereby elimiating (well, at least reducing) another source of error.
In statistics, the only thing beating multiple measurements is even more measurements.
Because that's not the issue. You'll always have uncertainty in systems. The study argues that the public perceives these systems as infallible, and therefore believe that technology can provide a final, absolute arbitration. The study is commenting on this tendency in lay people (i.e., people without specialized knowledge of the system), and warns against the corollaries that stem from such assumptions. Also, the title is bad: they are merely looking at the issue through the lens of Hawk-Eye, they're not looking at Hawk-Eye specifically. You may note that there is no analysis of the hawk eye system beyond a basic discussion of its function.
The reason it isn't officially used in cricket is because it would be used to predict the path of the ball had someone's legs not interrupted it. Whereas in tennis it is simply used to account for where the ball actually went.
Obviously just tracking a ball is a more definite science than the prediction of something that didn't happen (but could have). Especially as anyone who knows about cricket will tell you is that the path of the cricket ball is 'mysterious'.
I once heard a cricket commentator interviewing the inventor of Hawk-eye (a Mr Hawkins) and asked him how accurate the system was - he said something along the lines of "in testing it has been incredibly accurate" which I found quite weak as I was expecting tolerances of so many mm deviation per second.
In cricket it is only used as a commentary tool generally proving that the umpires get it 'right' most of the time anyway.
If this were really happening, what would you think?
But one has to ultimately question, whether, by gaining mathematical precision, we lost some human touch of sport that makes it enjoyable to play and watch. Fun can't be generated with a mathematical formula. And sometimes sitting on the couch and thinking "OMG that referee is such a dumbass" is part of the fun as well.
Watched the Aussie Open or Wimbledon in the last couple of years? I, and most other observers, consider that Hawkeye makes the game more enjoyable, and whilst probably isn't 100% accurate, is better than having players constantly whinging at the line judges and a constant feeling of 'unfairness' being held by a player because they think the human linejudge made a significant mistake (and maybe they did). Hawkeye won't make a SIGNIFICANT mistake.
== Jez ==
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Wimbeldon, IIRC, has a limit of 3 appeals. Just as an example.