More basketball analysis

Reader Jorge has also looked at these amazing basketball shots. (here is my last basketball analysis) Jorge claims that at least one shot seems fake. He is referring to the following video (at around the 2:20 mark).

ARRGH Ok, new plan. For some dumb reason, youtube won't let me embed this video. Well, here is a link - Amazing Basketball Shots: The Legendary Shots 4 (at least I can link to the right time). It is even dumber that you can't embed it, but youtube gives you the download option. Oh well.

Let me tell you the part that Jorge has an issue with. This guy on a ladder throws a basketball through the hoop. The ball then bounces back up and through the hoop again. Here is an annotated screen shot.

i-f04fb7e5fcb83c78fd24176cbd8e64d7-2010-08-19_ball_shot_1.jpg

So, what is the problem? Jorge claims that there is evidence of video-fakery - primarily by looking at the ball and the goal-pole. He also claims that the ball would not bounce that way if it wasn't spinning. So, what do I think? First, I tend to think things like this are real. Maybe someone would go through the trouble to fake it, but who knows. Could something like this be faked? I assume so - probably by shooting the ball through and then later bouncing a ball into the goal and combining the two.

First let me address the spinning-bouncing part. I think Jorge is correct in that a non-spinning ball on a flat surface would not bounce back. However, I am not certain the ball is not spinning. The video is not clear enough to show the spin. I would assume there would be some spin from the way he threw the ball. Enough about the spin.

Ok, is there anything I can look at to see if this particular clip is real or fake? Fortunately, this clip is a good one to analyze.

  • The camera is stationary
  • The camera is perpendicular to the motion of the ball
  • The camera is far enough away (at least it seems) so that there are no perspective problems

It would be nice if the video was in a little higher resolution, but I guess it is ok. Also, since the background is simple and stationary, this makes the great candidate for the autotracker feature of Tracker Video analysis.

In this analysis, I picked the height of the goal to be 3 meters. This is likely wrong because I get the wrong value for the acceleration while the ball is free falling. Oh well - that is ok. The goal could really be at any height. Here is a plot of the ball after it goes through the goal a second time. The nice thing about this is that it shows a couple of bounces.

i-5d7101dec88cb04bdd563c32b1d5df9c-2010-08-19_data_tool.jpg

This is a plot of the vertical velocity after it goes through. The slope of the three lines is around the same value (which is good - because they are all cases of free fall). What I want to get from this is an estimate of how the speed changes after a bounce. The first bounce hits at about 7.5 m/s (going down) and leaves at about 5.3 m/s going up. For the second bounce, it hits at 5.3 m/s and leaves around 4 m/s.

The ratio of the speed before and after the bounce should be a constant. This constant is called the coefficient of restitution. Let me calculate the coefficient (CR) for these two bounces.

i-c90ba0c536aabf8f00882a1c828b1f55-2010-08-19_la_te_xi_t_1.jpg

Ok, so it is in the 0.7-ish range. Now, what about the bounce after it went through the goal the first time? Here is a plot of the velocity of the ball.

i-6e8efb93fa0c2c69917809313af02b93-2010-08-19_data_tool_1.jpg

This doesn't look too great. The velocity after the bounce looks fine. Before the bounce, I think there was a problem with the ball moving fast. This means that there aren't many data points to look at. How about I look at position data instead of velocity data?

i-88f5598619dca3c5ce2e48d97cc844d3-2010-08-19_data_tool_2.jpg

If I fit a quadratic function to the position data, it mostly agrees that the velocity before impact is around 13 m/s. The velocity after the bounce is 8.5 m/s. This gives a coefficient of restitution of:

i-b5cb1ea36338c1cfbb96c2490f8d1809-2010-08-19_la_te_xi_t_1_1.jpg

The coefficient seems a little different. Is this different enough to say that the before motion and the after motion don't go together? I am not sure. That collision with the floor seems to be different than the other two bounces. The coefficient of restitution can't possibly be an always the same constant for a basket ball. Imagine shooting it a mach 1 speeds. Would it bounce off with 0.7 times the original speed?

Where does this leave this? I know if you look at individual frames, some things can look funny. But I am just not enough of a video compression expert to really comment on those. So, I guess I will leave it where I started. There is nothing that says it has to be fake. I am sure you could get a basketball to do that motion.

Pre-emptive comments:

  • Why do you do this? Why do you analyze some video and at the end say "well, it could be real or fake?" - answer: I am really looking for some piece of evidence that says it HAS TO BE FAKE (or probably)
  • So, are you saying it is fake or not fake? answer: see above.

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Actually, it looks to me as if the driveway is slightly raised compared to the front door, and that there is a slanted seam at just about the point the ball hit. I suspect that is what gave it the back-momentum it needed.

@Aaron,

You are correct. Thanks for posting those links. (I have been burned before - hint: giant water slide jump)

When I looked at the actual video, it is clear that the garage floor on the right is maybe one brick higher than the one on the left. The driveway slopes down from the edge of the garage door to the side door. This is hard to see in your frame grab because of the line you drew.

Estimate that angle and see if the bounce angle is more likely. It is also more reliable than the familiar problem of dribbling on a joint.

What is suspicious is the nearly constant downward v.

By CCPhysicist (not verified) on 22 Aug 2010 #permalink

In response to Ahcuah, take a look at the shadow when the ball hits the grounds. Any variation in the angle of the surface from the horizontal is negligible. Also, any anomaly on the surface that is large enough compared to the basketball to significantly affect its trajectory should be clearly visible.
In response to CCPhysicist, I don't think that a constant downward velocity is suspicious for the initial throw. Is 13 m/s an unreasonable terminal velocity for the basketball?