# Idiotic Football Physics: The Highest Point

Picking on stupid things that sports commentators say is the ultimate “Fish. Barrel. BLAM!” sort of activity, but this morning on the way to drop SteelyKid at day care, Mike and Mike kept repeating one of the absolute dumbest things that football commentators say. They were talking about Larry Fitzgerald of the Arizona Cardinals, and praising his ability as a receiver. In particular, they heaped praise on his ability to “go up and get the ball at its highest point.”

That would be a pretty neat trick, if he could manage it. A football pass spends a second or two in the air– let’s call it two seconds for a long pass to a wide receiver like Fitzgerald. The trajectory of the ball looks like this:

For a pass that spends 2s in the air, its “highest point” is 4.9 m above the release point, or just over 16 feet. That release point is at least another 2m off the ground, putting the highest point of the ball off the ground at 6.9 m. To put that in persepctive, the world record for the pole vault is just 6.14 m. So,taking this football cliche literally would suggest that Larry Fitzgerald by himself can jump two and a half feet higher than the greatest pole vaulter in history could manage with the aid of a big long pole.

The issue here is pronoun trouble. Larry Fitzgereald doesn’t get the ball at its highest point, he catches it at his highest point. That is, he times his jump for the ball very well, so that he gets it in his hands at the very highest point his hands reach. Since he’s a pretty tall guy, that means that an opposing defensive back doesn’t have much chance of getting the ball before he does, which makes him a great wide receiver.

Now, you might say that 2s is a long time for a pass, and that’s true– I picked that number to make the math easier. But the basic point is still the same– the receiver is not catching the ball at its highest point. You wouldn’t want that, anyway– the highest point of the ball’s flight is roughly halfway along its trajectory from quarterback to receiver. If they really were catching the ball at the peak of its arc, they would be getting roughly half as much yardage as they could be.

There are cases where a football pass is caught at or before the peak of its trajectory, but they generally involve either a short fast crossing route, or Brett Favre flipping some crazy underhand thing to avoid a sack. The vast majority of the time, though, the pass is caught at the receiver’s highest point, which is well below the highest point reached by the ball.

1. #1 JohnV
January 8, 2010

The “catching it at its highest point” thing angers me greatly.

January 8, 2010

Mike and Mike are fucking douchebags. I can’t stand those pompous blithering fucks. All they do every single fucking day is suck the fucking dicks of every single pro sports star, executive, and hanger-on that they can possibly find. It’s fucking nauseating.

3. #3 6EQUJ5
January 8, 2010

You hear similar inanities in baseball. Professional ballplayers think the ‘action’ doesn’t show up until just before the ball crosses the plate, but the crosswise (vertical and/or lateral) acceleration due to spin, as well as the gravitational acceleration, acts throughout the trajectory and the deflection varies with the square of the time.

4. #4 Danny
January 8, 2010

You’re being pretty nit-picky here. I don’t think anybody is suggesting that “highest point” means the trajectory’s inflection point.

What they’re saying is that he’s catching the ball at the highest point _in_the_catchable_region_. Sure their wording is a bit sloppy, but (most–maybe not you) people understand what they’re trying to say. Believe it or not, they can communicate their point more effectively by speaking imprecisely and leaving a bit of inference to the viewer. If they got into any more technical precision, people would doze off and ignore them.

January 8, 2010

What they’re saying is that he’s catching the ball at the highest point _in_the_catchable_region_. Sure their wording is a bit sloppy, but (most–maybe not you) people understand what they’re trying to say. Believe it or not, they can communicate their point more effectively by speaking imprecisely and leaving a bit of inference to the viewer. If they got into any more technical precision, people would doze off and ignore them.

This doesn’t need extensive re-wording to fix, though. “His highest point” would capture the correct scenario, without even adding a whole syllable.

This is one of those cases where somebody made a mis-statement, and it’s been propagated. The other really good example is the tendency of sports announcers to say that a player has “gotten untracked” as if it were a good thing– some prominent announcer (I want to say Billy Packer, but that might be wrong) mangled the phrase “gotten on track,” and younger people started copying him.

6. #6 JohnV
January 8, 2010

Well when they leave the inference to the viewer it results in me inferring that they are buffoons.

Not sure why it would be so hard for an announcer to say “Larry Fitzgerald jumps and catches the ball at his highest point” instead of “Larry Fitzgerald jumps and catches the ball at its highest point” or why hearing it said correctly would put people to sleep (no extra words, the replacement word is the same length etc).

Of course, when people say “libary” and “nucular” and “mute point” and “ATM machine” and “genuses” I will usually correct that as well :p

7. #7 Danny
January 8, 2010

“His highest point” would capture the correct scenario, without even adding a whole syllable.

There’s a difference, though. Larry Fitzgerald can jump higher than everybody else. Everybody can jump and catch the ball at “their highest point”, but that wouldn’t make them special like Larry Fitzgerald. It’s important that his highest point is higher than everybody else’s highest point.

It’s not so trivial to exactly describe this situation, and to most people, it was straightforward to understand what they meant. If I were an announcer, I’d be able to sleep at night knowing this.

January 8, 2010

It’s not so trivial to exactly describe this situation, and to most people, it was straightforward to understand what they meant. If I were an announcer, I’d be able to sleep at night knowing this.

9. #9 ms physics
January 8, 2010

Count me out of most people. When I read “its highest point,” I also assumed half-way through the trajectory. Then again, I don’t care for sports commentators and watch TV sports on mute.

10. #10 jnc
January 8, 2010

“For a pass that spends 2s in the air, its “highest point” is 4.9 m above the release point, or just over 16 feet.”
————————–
Doesn’t the maximum height depend on velocity of the ball, among other things?

Oh, and 4.9m, eh? Not 4.8? Not 5.125? And, the only thing more annoying than listening to sportscasters is to read pseudo-exactness in numbers that are just pulled out of the air.

11. #11 Danny
January 8, 2010

Count me out of most people. When I read “its highest point,” I also assumed half-way through the trajectory. Then again, I don’t care for sports commentators and watch TV sports on mute.

For the record, we’re not going to get a representative sample of the football-watching audience on a physics blog. This point is pretty “mute”, eh JohnV?

January 8, 2010

Doesn’t the maximum height depend on velocity of the ball, among other things?

Yes, but there is some initial velocity for which a pass will spend two seconds in the air. During those two seconds, the ball will be subject to a nearly constant acceleration due to gravity, which is usually within a few percent of 9.8 m/s^2.

One second of travel (the time needed to reach the maximum height, the other second being the time needed to fall back down from that height) subject to a constant acceleration of 9.8 m/s^2 corresponds to a distance of 4.9 m vertically, independent of the horizontal travel.

It’s basic Newtonian physics.

Air resistance complicates things a little bit, but for a reasonably tight spiral pass, it’s probably not that big a factor. Certainly not enough to bring the maximum height down to the level where a human could jump that high.

13. #13 JohnV
January 8, 2010

Yeah but Newton pulled that stuff out of thin air with that apple deal. /rimshot

14. #14 --E
January 8, 2010

jnc@#10:

Physical constants and equations of motion make it easy to tell how high an object went if you know how long it was in the air. The principle that all things fall at the same rate in a vacuum was figured out centuries ago.

Now, Chad obviously went for the ultimate simplifying assumptions: 1. there is no air resistance; and 2. g really is constant 9.8 m/s^2 at all points on Earth.

Given those assumptions, Chad’s calculation is correct. The speed at which the QB throws the ball will determine how far the ball goes horizontally in that two-second time; if he throws harder, it will travel further. But the question is about the vertical component, which is (in a vacuum) solely dependent on time and gravity.

15. #15 --E
January 8, 2010

Whoops, I’m saying “speed” when I should be saying “velocity,” which is a vector measure. The angle at which the QB throws the ball determines the distance it goes.

16. #16 Dr. Pain
January 8, 2010

Your argument is based upon a false premise.

The fundamental principle of passing in the NFL is to minimize the time of flight of the ball. NFL quarterbacks throw hard, flat trajectories. An NFL receiver doesn’t catch a pass at the point where it would hit the ground but much nearer the apex of flight. A ten yard pass hits probably another ten to fifteen yards down field when it misses the receiver.

For the same reason, your 2 second time of flight is a gross overestimate (except perhaps for a Hail Mary heave to the end zone). I’m pulling this out of my butt, but I think if you timed a 10-20 yard pass in the NFL it would be in the air for 500 ms or less.

Not that Mike & Mike aren’t idiots (they are) but there’s something to what they (and Charles Woodson) was saying.

17. #17 Matt Springer
January 8, 2010

@#11,

Hard, flat trajectories are common but not universal. Really it depends on the location of the defenders; sometimes the QB has to get it over the head of a defender to a receiver somewhat farther downfield. A flat trajectory in that situation is an interception waiting to happen. Even with an open receiver, the flatness is constrained by arm strength.

That a guy like Sean Payton can do this kind of calculation in about two seconds despite the constant threat of being smashed at any moment is pretty astonishing.

January 8, 2010

The fundamental principle of passing in the NFL is to minimize the time of flight of the ball. NFL quarterbacks throw hard, flat trajectories. An NFL receiver doesn’t catch a pass at the point where it would hit the ground but much nearer the apex of flight. A ten yard pass hits probably another ten to fifteen yards down field when it misses the receiver.

First of all, “flat trajectory” is an oxymoron. Every trajectory is parabolic, or near enough as makes no difference.

Second, as Matt says, the range of a typical pass is highly variable. Also, the relevant range here is the distance at which the ball returns to the launch point (roughly 2m above the ground) not the point at which it hits the ground.

Finally, the ten-yard across-the-middle routes that are closest to “flat” trajectories are typically not the ones where jumping ability comes into play. The plays where “catch the ball at its highest point” is dragged out are the jump-ball plays, where the receiver makes a leap to catch the ball near the sideline or in the corner of the end zone. The normal use of “catch the ball at its highest point” is during a slo-mo replay that clearly shows the ball on a downward trajectory into the receiver’s hands.

Two seconds is probably an overestimate for those sorts of plays, but not by a factor of 4. And it makes the math considerably easier.

19. #19 Danny
January 8, 2010

The only thing idiotic about this entire discussion is the post assuming an idiotic interpretation of what the announcers said.

20. #20 chris y
January 9, 2010

If they really were catching the ball at the peak of its arc, they would be getting roughly half as much yardage as they could be.

Very true, but if you’re concerned about maximum yardage, you don’t want them to catch it at their highest point either – scooping it up near ground level would give the longest pass. Trouble is though, if they tried to do that somebody would intercept it first, so what you really need is to take the ball at the lowest point at which you can be confident that it won’t be intercepted.

Or maybe they could just take the pass where they can and get on with the game.

21. #21 CCPhysicist
January 9, 2010

The “flat trajectory” folks need to calculate how far an 80 or 90 mph baseball drops while traveling about 22 yards. The answer is more than 3 feet.

A flat trajectory is an illusion created by our brain’s ability to remove the ‘normal’ drop of a projectile as part of our ability to learn how to hunt and survive.

I don’t understand what 6EQUJ5 meant, since the fact that the deflection increases with t^2 is precisely why the ball moves more during the last part of its trajectory than the first part. In round numbers, it deflects as much in the last 1/3 of its flight as it does in the first 2/3 of its flight, and you have to start your swing before it has traveled 2/3 of the way to the plate.

And Danny is a sycophant. What they said required no interpretation. It was wrong. It only makes sense if you run it through my patented Bent Mooseburger “I’m listening to idiots” filter.

22. #22 neil b
January 9, 2010

Since “his highest point” came up, the skill involved is: being able to catch a fast football with your arms held high. That is not easy, compared to the classic torso catch.

23. #23 Jim Thomerson
January 10, 2010

So long as we are being picky, a time of 2 seconds is one significant figure; so your answer using that number has one significant figure, not two.

24. #24 DSMV
January 11, 2010

OK, “at its highest point” is a lousy sports cliche.

Unfortunately, the most correct alternative is “He catches the ball at the highest point at which his catching of the ball is possible. Furthermore, that point is higher than the highest catching height of most, if not all, DBs”. That is accurate but much too wordy.

“He catches the ball at his highest point” isn’t so great. After all, I catch the ball at my highest point, but that’s only 8 or so feet off the ground. Most tall receivers can reach that flat-footed. So, I suspect that if the pat phrase were to become “..at his highest point” we would be treated to annoyed blog posts on the subject of the inaccuracy of a tired sports trope in about 6 months.

I play competitive Ultimate and the local phrase to praise a similar ability is “wow, that kid can read AND sky (jump)”. “Read” refers to the ability to know when and where the disc is arriving to co-incide with your own maximum reach/leap. This is trickier with an airfoil like a disc than it is with a ball, especially with wind.

25. #25 peter chatterton
January 11, 2010

I have a question about the diagram. That doesn’t look much like a parabola to me and I thought thrown balls were supposed to follow that kind of path. Maybe I’m wrong on both points?

Peter

26. #26 Jud
January 11, 2010

Idiotic question from layperson: Wouldn’t the maximum height of a parabolic arc of sufficient length to require 2 seconds to travel at deceleration/acceleration of 9.8m/s^2 depend on the shape of the arc, and thus on the initial angle at which the ball was thrown? (In other words, are there not multiple shapes of parabolic arcs with equal lengths?) Not that this means anything to your problem with the word usage of Mike & Mike, and every other football announcer I’ve heard.

The one that drives me nuts is “Better than any 3rd baseman in the league,” forgetting the “other” that should go between “any” and “3rd.”

27. #27 Anonsters
January 14, 2010

But could Larry Fitzgerald do this all by himself?

28. #28 Koozies imprinted
January 15, 2010

If it were to happen, my guess is it would be by Friday.”
Don’t guess, report the facts, blogger.

Kiffin repeatedly said in his news conference that he was going to take his time and it’s a slow process. It doesn’t even sound like your ‘guess’ is a good one, again…

29. #29 JC Denton
May 15, 2010

If you think that’s bad, I’m watching a replay of last year’s UT vs Baylor game, and on a pass that spends about 50 yards in the air before being caught by the receiver, the announcer says “…at the apex of the throw, Shipley makes the play”.

30. #30 sierrapaul
December 18, 2010

Another dumb term that football announcers often use is “turnover ratio”, meaning a team’s takeaways minus turnovers. For example, if a team has 21 takeaways and 15 turnovers for the season, then this is equal to 21-15 = +5, but it is NOT a ratio, it is a MARGIN. A ratio is a fraction like 2/5 or 7/3. In a ratio, the operation is DIVISION, but in what is commonly referred to as “turnover ratio”, the operation is SUBTRACTION. It should be referred to as TURNOVER MARGIN. This is really 3rd grade math, nothing more. But we are largely a nation of mathematical ignoramuses (sp?), unfortunately.

31. #31 sierrapaul
December 18, 2010

Sorry, 21-15 = +6, not +5. That’s actually kind of funny that I did that!!