A controversial question about line calls

Discussion in 'Adult League & Tournament Talk' started by sureshs, Sep 23, 2013.

1. MongolmikeProfessional

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You are correct that you cannot see the line behind the ball. But the line is just that... it's a line, not a single point. You CAN see the line emerging from both sides behind the ball. Your eye/brain makes the computation that the diameter of the ball is past the line (in your example).

I'm not saying that its not a tough call, or people don't make mistakes. It's just that your example has been used before in other threads and it is valid only if the line is not a line. There is a perspective factor which our brains take into account.

2. tennixplRookie

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or you are mathmatically ignorant.

Mean error = 3.5 mm in your sited article. that means the average error. which means half the time the error is more than 3.5 mm, and half the time the error is less than 3.5mm.

and 3.5 mm is greater than 1/8th of an inch. more than half the time hawk eye is more than 1/8th of an inch off, by there own standard against using high speed cameras to determine that error.

sorry you don't understand math or experiments.

3. tennis_ocdHall of Fame

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lol. If Spielberg would've used "vector" graphics it'd be like a real T Rex!

Hawkeye isn't infinitely zooming in. It's a default level zoom for close balls; a computer fabricated cartoon graphic that represents the real life impact as closely as Jurassic Park equates to a family zoo trip.

To be sure, cool technology that permits a close mathematical guess of were the ball strikes. And it's great crowd theater for gasps and oooohs. Anything that close may well have been in or out. Think about why it isn't used on clay.

4. MongolmikeProfessional

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WHAT??!!

I call b.s. Looked real enough to me that I almost pi ssed myself!

5. tennis_ocdHall of Fame

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Just keep in mind that the Hawkeye graphic isn't real life. It's a cartooned "guess" of what happened. Like the weatherman's high tech mathematical modeled "guess" of tomorrow's weather.

6. TimeSpiralProfessional

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Lol. You guys are cracking me up!

Children know the definition of mean and median. That's grade-school level stuff. But apparently you do not.

Find the mean of the following data set: 1.5, 6.9, 2.3, 3, 3.5, 3, 2.5, 7, 3.6. Then, once you've done that, find me the "half" of these numbers that exceed the mean :twisted: Then, find me the median value. Just take a look.

Please explain to me, your issue with the following, from that HawkEye article:
1. During ITF testing in 2006 Hawk-Eye passed a number of stringent parameters, meaning that it would be the first electronic line calling system to be officially accredited.
2. Although the accuracy of the existing system has been proven to meet the ITF rules and regulations, the company is constantly developing and refining the system to raise the bar further still. Equally Hawk-Eye listens to feedback from customers and officials to ensure that Hawk-Eye remains the very best in the market in accuracy, reliability, speed and from a broadcast point of view.
3. ... a protocol remains if the officiating system is not able to provide an answer with utmost confidence, this is an extremely rare situation, where onsite operators are not 100% confident in the accuracy of the system for that given shot.

The level of accuracy and reliability have been proven to be significantly better than any potential competitors, proven by the system remaining (after 7 years) to be the only accredited system.
It's the best and most accurate system available.

Did you just suggest I keep in mind that a graphic is not real life? What does that even mean? Lol. Calculating the vector of a tennis ball is not--in any meaningful way--analogous to meteorology--I'm convinced I'm getting trolled now. Certainly you realize that an infinite zoom would never end, right? Hahahaha. I was identifying the graphic as a vector graphic, as to communicate it's ability to be accurate even when zoomed.

This is why you're not taken seriously, because you say ridiculous stuff like "cartoon graphic." It's not even clever, your attempt to diminish the value or accuracy with diction. It's the most accurate graphic simulation approved by the ITF.

Last edited: Sep 26, 2013
7. tennixplRookie

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Yes but so many here seem to think the brain doesn't enter into it. If you see it out its out otherwise its in. No thinking, no guessing, no statistical assumptions to determine if ball was in or out. They simply see and know with no thinking, no stress of the point altering there perceptions EVER. no focusing on trying to hit the ball at their feet at the baseline and that altered angle causing some doubt.

Even the desire to play fair may cause you too "see" more balls in and even when you are damn sure it was out, since you have an inkling of doubt you call it good. (my approach actually)

I played a guy this weekend who kept hitting ball long. one shot he hit right at my feet at the baseline. Now i knew it was out, but from my angle right above the bounce i can't see it out exactly, i can't accurately judge precisely where it bounced, i called it good, opponent was surprised and even the ref standing right on the line said " you gave him one there". my answer was "yep".

8. RetroSpinHall of Fame

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The briliance of HawkEye is it has managed to turn the worst aspect of a tennis match, unattractive arguing about line calls(that means you John MacEnroe), into a treat, watching the HawkEye graphic unfold.

Players accept a few things. One, it is not infallible, even though the graphic gives that impression. Two, a decision has to be made one way or the other. Three, errors should tend to even out over a match, tourney or season.

9. tennixplRookie

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yes and with a properly large sample size median and mean will converge.
and error is error, most accurate still has error. So in this case 100% accurate means they are 90% sure that the path they predict is within 3.5mm of being correct. meaning all systems were done properly and they didn't have too many known errors with a track.

I love hawk eye, i think it is a great tool and i would trust it more than the line judges. however people assume the technology is perfect and that the computer "knows" where the ball landed with 100% accuracy. The announcers certainly always treat it as though its gospel truth with no understating of the underlying algorithms that make it work.

That analysis it provided for shot speed and trajectories is produces is awesome. i wish they would show more of its analysis of player movement and ball bounces.

10. BdarbHall of Fame

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While deciding if a ball is in or out, I will consider, my knowledge of advanced statistics, FDA regulations of restaurants, Jurassic park, ml practice suits, as well as the metaphysical implications as to whether or not the ball is actually there..

God bless you all Tt. You get me through the work day

11. tennis tomHall of Fame

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So in who's favor does HAWKEYE decide when it's too close for it to make a call?

12. tennixplRookie

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BC if every one said "by golly chap you are correct" this wouldn't be much a of a message board.

don't forget the your relative theory knowledge, I mean with some of our serve speeds there is sure to be some time dilatation affects on eye perception.

13. tennixplRookie

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They don't, bc as time spiral says it is as accurate as any system so what it says, is what IS as far as line calls go. It doesn't favor anyone or any call. its prediction simply supersedes lineman and umps.

14. TimeSpiralProfessional

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I'm glad we've gone from you calling me "mathematically and experimentally ignorant" to actual conversation :twisted:

But I must ask: who is making this argument? I'm certainly not making that argument, and I'm not familiar with anyone who is. It's the classic adage: Don't let the perfect be the enemy of the good.

Correct--with the caveat that it is more (not as) accurate than other competing systems--however; the human beings on-site, operating the HawkEye system, will defer the call if the error thresholds in their system suggest that they cannot make the call within the acceptable margin of error. I've never seen this happen, but there is protocol in place in case it does.

15. MongolmikeProfessional

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I think another point that has to be taken into account with his example is he is trying to turn a 3 dimensional occurence into a 2 dimensional example.

Now if I was lying on my stomach on the baseline, and he was rolling a ball from the net towards the service line directly in front of me... yes, I would have a very difficult time judging if the ball was completely past the service line.

But that isn't tennis. The eye/brain is judging a ball traveling on a downward arc, which I think makes it easier to determine it's landing location. And to "give" an opponent a 6 inch leeway on calls is amazing to me, but IMO unnecessary.

16. tennis tomHall of Fame

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I think I've heard on TV when Hawkeye is used, the announcers will say it's degree of accuracy is one millimeter. IF, that's correct who's favor does the call go to if it's within that one millimeter +/- ?

17. tennixplRookie

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first quote 125 by you
"Dude ... You're just making stuff up."- You bolded my “more than 50% of the time Hawk Eye is worse than that” while you can argue median versus mean, like I said if they are doing a rigorous standard hopefully that means they have a large enough sample size where mean and median are really damn close, bc they should dis-include cases where no one would believe it accurate, anything more than a foot from where people see the ball land is a good starting point. So with no extreme outliers the mean and median are equal for this purpose. And since the error of HawkEye mean is larger than 1/8th, barring experimental incompetence, I am damn confident that more than 50% of the time they are worse than 1/8th of an inch

You bolded “and yes interpolation is a guess, its just a mathematical guess instead of a random one.”

Yes sorry it’s a guess, an educated one, a definable one, but still a guess. I have long arguments with physicists and engineers on best approach to filling in missing measured data. In our cases linear interpolation is a bad way to guess. For Hawkeye it’s probably not bad at all. But it is still a guess. Just because you can mathematically define the error, doesn’t suddenly make it not a guess of what reality is. Not saying you are, but so many people become bewildered at the application of math and take it as TRUTH with no regard to understanding what the math is really saying.

You bolded “Hawk eye thing is nothing but probability”
Um perhaps you should look up what probability is, bc the whole interpolation and error thing, is basically probability. What is the likely hood the ball is at position x between our measured points of A and B, say it with me…………. P-R-O-B-A-B-I-L-I-T-Y. Okay in fairness since it is a lot of measurement and computer algorithms Hawkeye is more than JUST probability, but that of course wasn’t my point

See simply saying I am “making stuff up without proving it is the beginning of that not having a conversation you cite.

As far as who is making the argument…. You
Quote 125
“I can triangulate exact locations and recreate an accurate simulation”

“Exact” and “accurate” sounds a lot like you are making that argument. but I'll admit i am professionally biased about the use of those words, bc people say them and really think them to be true.

18. tennixplRookie

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They ignore the error, bc its a lower error than any other method.

plus you would confuse ppl if you threw that in there. look at how we are arguing here, you think if they threw that up and said well "I know Hawkeye shows the ball was in by a millimeter, but since that is within our error please disregard, the out call stands"

ain't gonna happen, the system must appear infallible.

19. AvlesHall of Fame

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I don't think it works that way. My guess is that Hawkeye always makes a call, but there's a possibility that its call could be off by a millimeter in either direction.

20. sureshsBionic Poster

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Vector graphics means that instead of the old row by row pixel-based method, the math is based on polygons (lines and curves). So you can draw the line between points A and B without worrying about if A,B and points in between are actually real pixels.

However, when the line is rendered on a real display, pixels have to be taken into account, say by Bressenham's algorithm which actually looks like a staircase rather than a line.

21. sureshsBionic Poster

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It doesn't care that is too close. It just puts it out there. We accept it with the error. If it shows that it is 1 mm out with a margin of error of 1.5 mm, it will still be considered out. Otherwise, you will have to call it both in and out, and nothing will be gained.

22. schmkeHall of Fame

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The important point here is that they do not decide, like some recreational/league players like to do, that it was too close to call so lets replay the point.

23. tennis_ocdHall of Fame

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You don't get it. Nothing is being "zoomed." It is a predetermined algorithm that is posting a cartoon-like graphic. IT IS NOT REALITY.

In real life that close ball could be in or out. Feel free to tout some mythical accuracy and ignore why it isn't used on clay.

24. LuckyRLegend

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Sorry to come late to your post.

Your graphics (including the video that the second set of stills came from) are really apples and oranges from real life player (not linesman) line calling.

The reality of realtime matchplay is that you don't have access to super slo mo video replay. You are correct that the amount of court contacted by a very high RPM topspin shot is lengthy, as your graphics describe. But the amount of time of this contact is not appreciably different than that of the average Rec or Club groundstroke. And for calls made in realtime it is literally a blink of an eye.

You are using the fact that the human eye in realtime, cannot distinguish between Federer's shot's initial conact point and final contact point, to conclude (correctly, I might add) a call based on seeing court inbetween "at contact" could be wrong. I don't dispute your initial logic, since I agree that the human eye cannot parse that difference. However, that level of error IMO falls squarely into the baseline error associated with human eye observations. No other player-called regimen for making line calls is going to be superior to it and many if not most would be inferior to it.

25. sureshsBionic Poster

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Even on clay, players argue about where the "mark" ends

26. sureshsBionic Poster

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That is one important point.

But even more fundamental is the fact that all computer vision and image processing algorithms are probabilistic. Hawk Eye is no different from Google driver-less car deciding whether there is a car in front of you.

In the same way, human vision processing is also probabilistic and interpolative. That is how optical illusions fool people.

27. tennis_ocdHall of Fame

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Exactly. Those very close balls may be determined by a mathematical calc with as little as a 51% probability of being correct. The system must make a binary IN or OUT call* and, for shear theater, self-generates a cartoon-like graphic that many appear to believe is real life.

Tennis isn't the only sport that uses hawkeye system and some of its failures are legendary. Other sports default to humans as final arbitrators; tennis umps are held to hawkeye (Think back to Nadal, Youzhny, and chair a few years ago when they all believed ball was out and mark confirmed. Ump was forced to go with hawkeye costing Nadal the set.)

It isn't used on clay because, well, they aren't going to highlight its inaccuracy. Even so, I agree that, on the whole, it's more accurate than human eyes; it does remove some of the enjoyable match banter.

*(There are supposed failure modes if the system simply breaks down on some weird shot -- perhaps camera blockage? but I've never seen it happen.)

28. tennis_ocdHall of Fame

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And that the pros play to an OUT call within perhaps 51% certainty

29. newpballLegend

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There are cases and it has happened.

For instance a first service where the ball touches the net and then bounces near the sideline. The path length of the ball which is tracked by Hawk-eye is significantly shortened because it touches the net cord and can be relatively erratic. There may not be enough samples for Hawk-eye to determine if the ball was in or out.

30. tennixplRookie

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huh? 51% probability of being correct, um that is crap probability for a system. you are correct on the theater part though, but it makes people feel like the system actually knows what it its doing.

Legendary? um one if the Ump and players were in agreement why was hawk eye even called up? did it say the ball landed in jersey from new york or something?

its not used on clay probably for other reasons, its sheer usefulness in a whole lot of other areas would be enough. though if it is bc of clay it might have something to do with a clay puff ball in air right after contact that might screw up the system. not that the system is sooo bad but that it does not perform to enough of a specification on a particular surface to be used.

Yes there are times when shot spot isn't available for reasons of error. i remember some hard court match where a review was called and it couldn't be done bc the system brain farted. though only once so far.

though for the record i will not admit to agreeing with newpball

31. tennis_ocdHall of Fame

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Legendary in other sports.... Tennis is more mildly amusing. You can search youtube for hawkeye failures.

In Nadal/Youzhny case, ball likely clipped the net on way to sideline. Deciding point in first set tie-break. All involved later acknowledged they thought ball was out. If ball's flight was disturbed by net I don't find it at all surprising that the hawkeye "guess" was off. Cartoon graphic and announcer both are able to tout in by 1 mm. lol.

32. sureshsBionic Poster

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Nothing wrong in that. Even military radars do the same thing - at their heart is a probabilistic calculation of where a target is, because radio signals are subject to noise, interference, diffraction, etc. The green thing they show on the screen is a cartoon.

Last edited: Sep 26, 2013
33. newpballLegend

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Getting mad at Hawk-eye, priceless! :grin:

Reminds me of Star Trek: The Deadly Years:

SPOCK: Doctor, you heard the computer's analysis of Captain Kirk's physical age. Do you agree with it?
MCCOY: It's a blasted machine, Spock! You can't argue with a machine.

:grin:

34. sureshsBionic Poster

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Machines are better than people. Just ask the auto industry. They would make robots do all the work if they could do it without political repercussions.

I would much rather be driven by a Google car than most people I know.

35. tennixplRookie

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I'd rather be driven by most people i know then trust a car designed by google or engineers i know , gosh knows what the car would do on pi day.

36. TimeSpiralProfessional

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I wish you would use the multi-quote feature. It's really nice. With that being said, since you insist on quibbling, let's have at it.

Are you really gonna ding me for using the word exact when framing a hypothetical question about the results or a triangulation process? Lol. That's rich and you know it.

What kind of points do you lose for using the word dis-include? Lol. Who am I arguing with? I mean, you're the one calling me out on word usage, remember?

So let's go further. If you have regular conversations with physicists and engineers about interpolation techniques (uhm, okay, your position makes even less sense now, assuming that's true), then why are you being disingenuous with your word selection? You know you are.

You're using the word guess to specifically undermine the viability of the system, and you know it. If you're gonna ding me on the definition of exact, I'm gonna ding you on the definition of guess (Hint, it's not the result of an equation). A guess means you are making your prediction without sufficient information. So, I'm calling red-hot, pants on fire BS.

An educated guess is an idiom with a slightly different meaning, but you've used guess so many times now, it's obvious what you're trying to communicate. Why not say, "experimentally verified prediction?" Why not say, "Accurate within ITF standards and guidelines?" Why not say, "Mathematically predicting?" I would argue all of those descriptions are more accurate than your various guesses.

You're also being disingenuous when you say it's wrong by more than 1/8" 50% of the time. You know the context of this thread is close line calls. HawkEye tracks the ball throughout the entire match. It could very well be the case that the majority of line calls in a match that call upon HawkEye is better than 1/8". Maybe it's vice versa. Either way, we're specifically talking about close line calls. Bear in mind: you might be right, but I still think you're framing this unfairly.

Now you're making the claim that I'm arguing that HawkEye is 100% accurate? Sigh ... What am I even doing responding to this? No. I'm on record--in this thread--citing and discussing the margins of error! Ha. Disingenuous, again.

Here is my quote, in context:
And finally, I bolded “Hawk eye thing is nothing but probability” because I'm calling you on BS. "Nothing but" are qualifiers you are using to diminish the viability of the system. If I'm wrong, tell me so, but I don't think I am. And when you say "nothing but," you are wrong. It's a bunch of stuff, like high speed cameras, operators, non-probabilistic math, and all sorts of other stuff. Probability is part of the system--of course!--but when you qualify it by saying "nothing but," you're attempting to confuse the layman, and that's not cool (and you know it!)

At least you added "-like" to cartoon, making you slightly less incorrect.

I do get it. You just don't get that I get it, which is fine. When I say a vector graphic can be zoomed without losing clarity, I'm just stating a factual attribute about vector graphics. That's how they can show a far away version of the ball mark, and then zoom in on the ball mark (when you're watching TV) and the representation still be accurate.

I can appreciate getting Zen as much as the next guy. But listen, Morpheus, HawkEye is an instrument used to measure reality; like your eyeballs, and brain. But as humans, our given instruments have limitations. So we develop instruments to overcome those limitations, like cameras and computers. So yes--you could probably find some scale where the reality is wildly different than whatever data you collected through and instrument, but we're talking about tennis, dude. Lol.

***Side Note: I enjoy arguing things like this. It's intellectual exercise. It's super easy, and tempting, to take stern rebuttals, or rebukes as angry, or personal, or me trying to slight you. Most of the time, it's not that. I just try to be straight and to the point, which comes off blunt. Maybe I need to lighten the tone? But, when I do that I get dinged on using the word exact. Sigh.

37. newpballLegend

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Come on folks, let's stop the bickering, it is already bad enough that some people cannot accept it when a ball is called out.

Peace, and enjoy tennis!

38. FayProfessional

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Gosh wish I met more people like you. Some will play fair, but there is always a team or two that wants to win without letting their racquet do the talking ~

39. tennis_ocdHall of Fame

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I "experimentally verified prediction" you're right.

40. TimeSpiralProfessional

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But you know, if you're being colloquial then your diction is much less important than during an argument. But, I guess you know that already. :twisted:

41. TimeSpiralProfessional

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It's either have a lively discussion about line calls and tech system changes in our game, or endless this, ad infinitum ...

42. tennixplRookie

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Yes sorry about the not being able to multi-quote properly. you'd be surprised what makes my computer lock up. But let’s quibble away, the name of the thread invites quibbling

Yes I will ding you bc it’s not exact. Where do you think the error in the interpolation comes from? They don't know exactly where the ball is. My issue is with people’s perception of the ‘perfection’ of computer analysis and mathematical analysis in these cases, ppl who see that graphic really do think it’s "perfect". You mentioned weather forecasting in response to someone else, well Hawk Eye isn't anywhere near that bad, it just isn't fraught with as many assumptions and errors, but still has them.

I don't know how many points I lose for dis-include instead of exclude. What’s the point scale? Either way the meaning conveyed doesn't change from exclude to dis-include. Just shows my inability to purge my regular vernacular of idiomatic computer programming terms You intent from “exact” to “well kind of within error” does change the meaning of what is said. You want exact change or kind of close? Within a few cents…dollars, tens of dollars, how exact is acceptable?

So let's go further. If you have regular conversations with physicists and engineers about interpolation techniques (uhm, okay, your position makes even less sense now, assuming that's true), then why are you being disingenuous with your word selection? You know you are. [/QUOTE]

No I am not; I guess you know something about me that I don’t know about me.…….Or wait I interpolate you know something about me that I do not. I am more certain than a guess and have evidence and data points.

I am not undermining the value of the system, I laud the system, I said I would trust it more than a lines man, call after call. Perhaps you should read an entire post and determine my context. So I say it’s a great system but it’s just a guess and should be dis-regarded???? Is that what you read?

One can put an equation to anything, it does not make it any more viable than a "guess pulled out of ones behind" but again since you seem to not garner my favor for Hawk Eye, Hawk Eye uses a perfectly reasonable estimation technique to "guess" where the ball is in travel. T

I am not being disingenuous at it being more than 1/8th of an inch wrong. 3.6mm is bigger than 1/8th an inch. The link you gave from hawk eye its self says this, so unless you are making the argument that the median is much larger than the mean in this case my point is valid, but since I assume it is an "experimentally validated model" they wouldn't inject huge error data points to pull the median to be so much larger than the mean, and if they are rigorous and do more than ten data points, the two should converge.

Though as an aside if they really do use linear interpolation to determine where the ball lands that is exactly where the system would show maximum error as the line has a discontinuous point and has an undefinable derivative. So whatever error is present that is where it would be most likely to occur. Who cares if hawk Eye tracks a full inch error when the ball is mid-flight over the net, four feet above the net?

yes whatever technique, once they use the equipment, is probability. And nothing but! It’s not a bad thing, but it is what it is. If once they have data points it is something more than probability please do enlighten?

So I am confusing ppl about guess, and you are confusing people about exact. At least guess is a super class of interpolation, exact is not a super class of almost.

Yes that was a poke. But you did say "exact" and can "accurately" determine bounce when in fact it is not exact and can only determine probabilistically where the ball bounced. To the layman you claim I confuse with guess then you are doing the same thing here. see my previous example.

Why do you respond? I don't know, perhaps bc you have ordained "disingenuous" of my stance and feel compelled to prove it. But I wouldn't assign any probability to that chance , I'd hate to guess!! (yes I am just poking you there about our ideas of proper usage of guess) or perhaps it is related to you side note. I get the sense we would have a lot less interesting “argument” in person as an actual back and forth discussion would remove the disagreement

A note to others, the error associated with Hawk Eye is the same type of error you have in your brain between seeing, thinking, comprehending and deciding. For those who say it is in or out, no doubt, there is a gray area where you don't know and your brain guesses where the ball was. It is why you just call balls as best you can and live with the other person’s calls. But understand that the stress of the situation like the OP was talking about can affect any one of the steps to making that in or out call. Call them as you see them, however we would probably all be surprised by how often we would be wrong on an in or out call that is close, that’s why you call it good and move on because we don’t want to be favoring ourselves unfairly.

hope we entertain and cause some neuron activation.

43. FayProfessional

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New River, AZ, usa
That is a great way to play. That way for the most part people feel GOOD about playing tennis!

So given that if I see a ball of mine is out clearly, I give the opponent the point, especially if they haven't play long. So one time I am playing doubles with someone ranked well above me and I knew my serve was clearly long so I reached for a ball to send a second serve and the woman across the net played it and said "I called it good so it is our point."
All I could do is stand there with jaw dropped and finally said "Oh, you want to play that way do you." and smiled

Thinking to myself, why would a 4.0 woman want to play two 3.0 people like that (it was social, drop in tennis) ....

Some people are just so competitive that they want to win no matter what the situation or whom they are playing against, which of course takes the fun out of it for those who try to play fair as best they can.

44. TimeSpiralProfessional

Joined:
Jul 9, 2013
Messages:
1,291
Location:
Gotham City
On the record: HawkEye is not exact.

Clarification: I should have said "an accurate location of the ball" in my hypothetical statement. I apologize to those who may have misunderstood the meaning of my example.

You covered your mistake nicely with this gem.

I have no reason to suspect that you would lie. I believe your story, in which case I will make a suggestion: be more careful with your words. When discussing the most accurate computerized line calling system, maybe whip out something a little better than "guess." I mean, I doubt you would say the linesmen are guessing; and they don't even have the benefit of multiple high speed cameras being piped into high-tech software specifically designed to track the ball.

To be completely forthcoming, I may have unwittingly combined your position with tennis_ocd's. You're both in similar camps--at least to some extent--and have similar handles.

I still take issue with "just a guess" in this context--I think it's horrible communication--but you've explained yourself well enough for me to be okay with, I guess.

I don't have access to their algorithms, but I'm assuming the gaps their filling are extremely small ones. If you're taking 60 frames per second (it could be much higher, I really don't know) from multiple angles, and you record the entire flight path, including the bounce phase, you have a fairly well populate list of discrete data points. Not much can happen in between those data points, which is probably why the margin of error is so small.

No point in splitting hairs here. Yes, at some point the uncertainty principle kicks in, and the wave/particle duality prevents us from knowing the exact location and the velocity of a subatomic particle. :twisted:

However, seeing as how life needs to continue to operate, and we tend to live life in the scale of human beings, I assumed it is understood that acceptable margins of error are determined within that context for various systems, like bridges, anti-locking brake systems, planes, electrical systems, HawkEye line calling systems, etc ...

I seriously doubt anyone was confused about my usage of exact, and if they were, I'm on record clarifying.

Again? How many times did you address the "exact" point in this response?

Agreed. I would have won much sooner.

Haha. Nice one to end on.

I'm the most amazed and interested in the bounce phase of the entire process. It would be interesting to see the training a linesman gets and how they address the bounce phase.