Possible to prove mathematically that the football spot was bad?

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In summary: LBWs because if the ball is going to hit the stumps then it is an LBW.In summary, the referee spotted the ball after 4th down with seconds to go in the game with what appeared to be a "bad spot." If not for this, Michigan would have won the game. However, on the next play, Ohio State scored a touchdown that won the game.
  • #1
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In the 2016 Michigan vs Ohio State Football Game, the referee spotted the ball after 4th down with seconds to go in the game with what appeared to be a "bad spot." If not for this, Michigan would have won the game. On the next play, Ohio State scored a touchdown that won the game.

Would it be possible that photographic evidence exists to prove mathematically that the spot was bad? How much evidence would be required (such as camera angles, locations, etc.) to resolve this issue? Realistically, what would be the minimum amount of evidence required? Any estimate of the number of man-hours and other resources that would be entailed in seriously researching this?
 
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  • #2
Now, I have to disclose that my family is all OSU but my work colleagues are UM. Personally, I'm not into NCAA but care deeply about the Browns- I know from first-hand experience how frustrating 'bad' calls are.

Yes, it's possible to 'prove' where the ball should be spotted based on images- and there are enough cameras available already. It's also possible to prove, for example, when pass interference occurs based on images (ahem...). But the use of instant replay to 'correct' has to be balanced against the harm caused by constant interruptions of play, and there's a reason why some calls are not reviewable. I wonder if strenuous calls for more and more use of instant replay are in fact a projection of wishing for removal of all uncertainty in life.
 
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  • #3
Football games (or any sport) are not decided by one play... they're decided by the entirety of the game. It would waste far too much time to use instant replay on every single play, considering games already last so long. One bad call--- no matter how awful or momentum-changing--- will not decide a game.

But, yes, the photographic evidence certainly exists to place the ball accurately.
 
  • #4
Comeback City said:
Football games (or any sport) are not decided by one play... they're decided by the entirety of the game. It would waste far too much time to use instant replay on every single play, considering games already last so long. One bad call--- no matter how awful or momentum-changing--- will not decide a game.

But, yes, the photographic evidence certainly exists to place the ball accurately.
That's what I wanted to know.
 
  • #5
Why do you think it is that no one at Michigan's departments of Physics or Engineering has pursued this? Is it just that no one has thought of doing it? I would think that the Athletic department would be eager to fund a study like this.
 
  • #6
@Chestermiller
To clarify, are you asking why they haven't looked into more efficient ways to review? Or just why they haven't looked into this one specific play in the football game?
 
  • #7
I would assume that the football departments at major universities have every camera angle for every recent game in an archive. And the camera angles tend to be fixed. I would think if so inclined it would be easy to prove.
 
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  • #8
In many ways, the ideal thing wold be to have some 'intelligence' in the ball itself so that it could know its velocity and position at all times. Visual sighting is affected by the presence of bodies all over the vital areas of activity. A local hyperbolic positioning system using a suitable wavelength ( say 0.1m) could give all the information needed.
The problem would be (as it is with tennis, rugby and football) that only the higher league clubs could afford to run that sort of system.
Of course, the practice of arguing with and threatening match officials should be dealt with before any technical help that the Ref could use.
"Arguing with the ref? Back ten metres" sorts it out easily.
 
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  • #9
What is a bad spot? And was it 4th and inches or 4th and long?
 
  • #10
fresh_42 said:
What is a bad spot? And was it 4th and inches or 4th and long?
In this case, it was first down by an inch.
 
  • #11
The important thing in a game, or, for that matter, in a court of law, is not that the decision is correct.

The important thing is that the decision is made and accepted. The acceptance part is what motivates at least an appearance of fairness and correctness.
 
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  • #12
Chestermiller said:
In this case, it was first down by an inch.

They use camera technology now a lot in sports Tennis footy (soccer) rugby and cricket.

https://www.chroniclelive.co.uk/spo...news/video-referee-system-make-debut-14126254

https://www.nzherald.co.nz/sport/news/article.cfm?c_id=4&objectid=12164339

I think the reluctance in introducing them was a worry about how it would affect the flow of the game.

I think they are great, adds another dimension and tension while the electronic ref is being "consulted"

In cricket you only have so many times you can challenge the human ref with the camera ref, say for LBW.

The camera and software track the trajectory of the ball to see if it would have hit the stumps or not on the replay.

Not easy as swing spin and air density all have to be factored in as well as velocity and where the ball pitches.
 
  • #13
Chestermiller said:
In this case, it was first down by an inch.
One inch is tough, but not impossible precision with video. There was one a year or two ago where the ref slipped an index card between the ball and the pole to tell.
 
  • #14
Comeback City said:
Football games (or any sport) are not decided by one play... they're decided by the entirety of the game.
Coaches say this a lot and while it seems true in hindsight and at a high level, IMO it isn't true in the progression of the game. The reason is that the strategy changes as the game progresses because the risk/reward calculus depends on the current score and time remaining to correct an old or new mistake. This is true to a great extent in most games/sports, but seems to be more true in American football than in most because of how easy it is for one big play to make a big difference in a close game. It also creates substantial opportunities for the team behind to come back and win, since the team ahead often adopts a very low risk/low reward strategy that backfires against the high risk/high reward strategy of the team behind.

That said, it is difficult to evaluate the game-altering ability of an early play due to how much of the game can be changed by one changed play.
It would waste far too much time to use instant replay on every single play, considering games already last so long. One bad call--- no matter how awful or momentum-changing--- will not decide a game.
It's only the close plays that need to be challenged, but as @sophiecentaur said, a move to electronic officiating would take care of both the accuracy and time issues.
 
  • #15
@russ_watters
Obviously, plays towards the end of the game have a heavy influence on the outcome of a game. But how did they get to that close score at the end of the game? How did they get to that 4th down on the goal line with 3 seconds left? Why not just play a 5-minute game so every play is a big play? The "big plays" you speak of are only "big" because they're closer to the end, and thus get more attention from everyone invested. From playing and watching many sports, I can tell you that many games are decided right at the beginning. A few quick goals in a soccer game can set up for the possibility of a comeback at the end, but that comeback doesn't happen too often.
 
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  • #16
Sport is not Science and people behave irrationally. Worse still is the way that commentators describe games in terms of logic.
Then there’s “what a great goal that would have been”
 
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  • #17
Guys,

My goal was purely scientific and was not focused either on the pros and cons of instant replays, officiating, or announcing a game. It was much more primordial than that. I wanted to find out if it would be possible to ruin the "win" for hated rival Ohio State fans by "proving" scientifically that the spot was bad and that they really "lost the game." This is part of the never-ending feud between Michigan and "Duh" Ohio State University.

Chet
 
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  • #18
"Proving" the actual location of the ball at the end of the fourth down doesn't really help, unless you also "prove" that the ball was spotted correctly at the start of the play (that is, the third down spot wasn't incorrect). And so on, with the second and first downs. Maybe the entire series of downs was off by an inch either way.
 
  • #19
gmax137 said:
"Proving" the actual location of the ball at the end of the fourth down doesn't really help, unless you also "prove" that the ball was spotted correctly at the start of the play (that is, the third down spot wasn't incorrect). And so on, with the second and first downs. Maybe the entire series of downs was off by an inch either way.
You're talking mathematics and I'm talking hatred of Ohio State. Get the picture? I don't care if it is exactly mathematically correct as long as it ruins things for them.
 
  • #20
Chestermiller said:
I don't care if it is exactly mathematically correct as long as it ruins things for them.
Got it! :wink:
 
  • #21
Unfortunately, recent advances in sports broadcasting such as improved camera angles and high definition video have made it possible to very accurately measure the speed of a runner or thrown ball. You see this all the time as the announcers discuss how quickly a ball leaves the quarterbacks hand or how fast a running back cuts to avoid a tackle. As we all know by now, the more precise information we have about the balls velocity, the more uncertain we are forced to be about the balls position. So sadly, we will soon never be able to disprove any bad spots.
 
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  • #22
Chestermiller said:
My goal was purely scientific
Chestermiller said:
I'm talking hatred of Ohio State
Pick one or the other.
 
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  • #23
I'm still dissatisfied with the answers I've gotten to my question. So let me be a little more precise with my problem statement:

How would a team of scientists apply present-day technology to the existing video evidence, both official and unofficial (the latter from available cell phones and other video devices in the stands) to ascertain as closely as possible the 3D geometric location of the leading edge of the football at the moment that J.T. Barrett's knee (or other body part acceptable for establishing the end of the play) first touched the ground? What precision could be expected?
 
  • #24
UK Soccer introduced 'goal line technology' for the Premier League and some other competitions, but its coverage is 'goal mouth only'. However, when there's been a mid-field incident, eg leading to a yellow or red card and possible 'totting up' penalties such as multi-match bans, a player may appeal after the match based on multi-angle media footage. Of course, when ref says 'GO', the player had better go quietly...

Admittedly, there is a human element. Some soccer players have a reputation for being very, very easy to trip. Deliberately 'diving' when tackled is a serious offence, but hard to prove during the game. When one such player 'goes down' easily, perhaps too easily, the tackler is more likely than not to receive the benefit of the doubt...
 
  • #25
Nik_2213 said:
UK Soccer introduced 'goal line technology' for the Premier League and some other competitions, but its coverage is 'goal mouth only'. However, when there's been a mid-field incident, eg leading to a yellow or red card and possible 'totting up' penalties such as multi-match bans, a player may appeal after the match based on multi-angle media footage. Of course, when ref says 'GO', the player had better go quietly...

Admittedly, there is a human element. Some soccer players have a reputation for being very, very easy to trip. Deliberately 'diving' when tackled is a serious offence, but hard to prove during the game. When one such player 'goes down' easily, perhaps too easily, the tackler is more likely than not to receive the benefit of the doubt...
You do realize we are talking about American football here, not soccer, right?
 
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  • #26
Chestermiller said:
You do realize we are talking about American football here, not soccer, right?
I think he was just giving another example, although American football definitely has more plays that could be considered worthy of video review.

Your question is tricky... officials are generally able to review placement calls in a matter of a couple minutes in games, but it sounds like you’re asking to find an exact coordinate position of the ball. Someone mentioned a tracking system in the ball and how that would make this a lot easier. But based solely on footage, it could take maybe an hour of video analysis of ALL videos available at that moment to determine placement with precision reasonable to what the human eye can distinguish. I could be wrong but that’s how I see this situation.

Maybe another UM person could give you a better answer... Go Terps! 🐢
 
  • #27
A tracker inside the ball won't help work out where the carrier's knee touched the ground.

And please change the title of the thread - American Football has no axioms and so it is not possible to prove anything about it mathematically.
 
  • #28
pbuk said:
A tracker inside the ball won't help work out where the carrier's knee touched the ground.
If the tracker is time-synced with the game clock then one could visually determine at what time the carrier's knee hit the ground and then use the tracker to determine the coordinate position at that time.
 
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  • #29
Chestermiller said:
I'm still dissatisfied with the answers I've gotten to my question. So let me be a little more precise with my problem statement:

How would a team of scientists apply present-day technology to the existing video evidence, both official and unofficial (the latter from available cell phones and other video devices in the stands) to ascertain as closely as possible the 3D geometric location of the leading edge of the football at the moment that J.T. Barrett's knee (or other body part acceptable for establishing the end of the play) first touched the ground? What precision could be expected?

It doesn't matter- you lost :)

(sorry, couldn't resist)
 
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  • #30
You should be aware that the video systems that 'project' the line of scrimmage & first down target etc are all based on knowing exactly where a series of cameras are in relation to the field: angles to the corners, elevation, etc. That system is inherently accurate and precise enough to position the ball after each play, so long as a view of the ball at the end of the play is available.
 
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  • #31
I always figured RFID sensors in the ball (tips, around the perimeter traced by the semiminor axis, etc.) plus sensors embedded in the field to track them would be able to do this pretty accurately. As mentioned before, syncing the position to the game clock would mean that instant replay would allow the precise location of the ball to be known at the point of any frame of video.

Of course, placing the sensors could be tricky, but it would be a fun thing to try.

Obligatory edit to support my own almae matres:
Go Illini!
Gig 'Em!
(But mostly Go Illini!)
 
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  • #32
pbuk said:
A tracker inside the ball won't help work out where the carrier's knee touched the ground.

And please change the title of the thread - American Football has no axioms and so it is not possible to prove anything about it mathematically.
Thanks for the unsolicited advice on terminology. Here's an axiom for you: it's a bad idea to try to make a PF moderator appear ignorant.
 
  • #33
pbuk said:
And please change the title of the thread - American Football has no axioms and so it is not possible to prove anything about it mathematically.

I bet you're popular at parties.
 
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  • #34
boneh3ad said:
I bet you're popular at parties.
I wouldn't make that comment at a party. Or in the "General Discussion" forum here - but this is a Physics forum where technical questions are asked and technical answers given.
 
  • #35
pbuk said:
I wouldn't make that comment at a party. Or in the "General Discussion" forum here - but this is a Physics forum where technical questions are asked and technical answers given.

Would you accept "use mathematics to reduce the uncertainty of a football spot to triviality" as an alternative proposal?

Give me a break. You can have an intelligent discussion without being a pedant.
 
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<h2>1. Can the football spot be proven to be bad using mathematical equations?</h2><p>Yes, it is possible to use mathematical equations to prove that the football spot was bad. This can be done by analyzing the trajectory of the ball and the position of the spot to determine if it was placed incorrectly.</p><h2>2. What kind of mathematical principles can be used to prove the football spot was bad?</h2><p>Principles from geometry, trigonometry, and physics can be used to prove the badness of the football spot. These principles can help calculate the angle and distance of the ball's trajectory and compare it to the intended spot.</p><h2>3. Is it necessary to have a mathematical background to prove the football spot was bad?</h2><p>While a mathematical background can be helpful, it is not necessary to prove the badness of the football spot. There are tools and software available that can assist in the analysis and calculation of the ball's trajectory and spot placement.</p><h2>4. How accurate is a mathematical proof compared to other forms of evidence?</h2><p>A mathematical proof can be very accurate and reliable in determining the badness of a football spot. It provides concrete and measurable evidence that can be replicated and verified by others. However, it should be used in conjunction with other forms of evidence for a more comprehensive analysis.</p><h2>5. Can a mathematical proof be used in a court of law to dispute a bad football spot call?</h2><p>Yes, a mathematical proof can be used as evidence in a court of law to dispute a bad football spot call. It can be presented by a qualified expert witness and can carry significant weight in the decision-making process. However, the final decision is ultimately up to the judge or jury.</p>

1. Can the football spot be proven to be bad using mathematical equations?

Yes, it is possible to use mathematical equations to prove that the football spot was bad. This can be done by analyzing the trajectory of the ball and the position of the spot to determine if it was placed incorrectly.

2. What kind of mathematical principles can be used to prove the football spot was bad?

Principles from geometry, trigonometry, and physics can be used to prove the badness of the football spot. These principles can help calculate the angle and distance of the ball's trajectory and compare it to the intended spot.

3. Is it necessary to have a mathematical background to prove the football spot was bad?

While a mathematical background can be helpful, it is not necessary to prove the badness of the football spot. There are tools and software available that can assist in the analysis and calculation of the ball's trajectory and spot placement.

4. How accurate is a mathematical proof compared to other forms of evidence?

A mathematical proof can be very accurate and reliable in determining the badness of a football spot. It provides concrete and measurable evidence that can be replicated and verified by others. However, it should be used in conjunction with other forms of evidence for a more comprehensive analysis.

5. Can a mathematical proof be used in a court of law to dispute a bad football spot call?

Yes, a mathematical proof can be used as evidence in a court of law to dispute a bad football spot call. It can be presented by a qualified expert witness and can carry significant weight in the decision-making process. However, the final decision is ultimately up to the judge or jury.

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