(01-26-2019, 02:26 PM)JJJ Wrote: And this is why the CARDboard is so awesome. Learn something new every day!
There are concepts we fans have (like "too many steps") that aren't quite what the NCAA rules use. But if you keep reading the CARDboad, we might get it right.
The bounce should be roughly the same, not because of how air pressure affects the bounce, but because the amount of bounce is part of the definition of a legal ball. (Also remember that changes in temperature can affect air pressure, flexibility of the ball material (and playing surface), and thus bounce, but the temperature should be fairly constant in indoor basketball courts. Water vapor in air can affect the weight of the ball slightly, and probably its flight. Temperature has been indicated for issues with footballs. Humidity has been indicated for weight issues with baseballs.) The weight of the ball is also defined to be in a range.
NCAA WBB rules
Quote:Art. 7. The air pressure that will give the required reaction shall be stamped on
the ball. The ball shall be inflated to an air pressure such that when it is dropped
to the playing surface from a height of 6 feet measured to the bottom of the ball,
it will rebound to a height, measured to the top of the ball, of not less than 51
inches when it strikes its least resilient spot nor more than 56 inches when it
strikes its most resilient spot.
Art. 8. The circumference of the ball shall be within a maximum of 29 inches
and a minimum of 28½ inches.
Art. 9. The weight of the ball shall not be less than 18 ounces nor more than
20 ounces.
To me it seems less than optimal for the weight of the ball to vary as much as 10% (ie, +/- 5%)
and for the bounce to vary nearly 10% and still be in spec. (As for bounce, I have no idea how different the bounce height would be from the least to most resilient spot on a ball.)
The effects of the altitude are negligible on the mass of the air in the ball. The potential issue is going to be the drag on the ball. As with golf balls, the surface of the ball may impact the drag significantly. It also turns out that
backspin causes the ball to go further.
I was starting down the path to do some back-of-the-envelope physics. But when I started investigating drag's effect on a basketball, I figured someone else had already done this.
I ran across an
analysis that uses some NBA statistics mixed with some physical analysis (it was a follow up to this
May 2015 article). It isn't a research paper, so it wasn't peer reviewed and may have errors. He begins talking about drag and altitude about 2/3 way down. But, talking about sea level, he says "The drag force should only alter the path of a free throw by about 6 inches, which is probably at the limit of the
SportVU system's precision." I'm not quite sure why 6 inches wouldn't be extremely visible. If he means that the shot would be 6" shorter due to drag, then that would be immediately obvious except that the players compensate for it. If he means that the highest point of a free throw's path would be 6" higher after compensation, I think that would be pretty obvious.
Anyway, he goes on to show that the measured data shows that the shot arcs at the higher elevation sites showed less drag generally. But Cleveland seemed to have even less drag than Denver & Utah, while Boston had unexpectedly high drag than other sea level sites. (My first thoughts were wondering about effects of temperature, humidity, and circulation patterns in the venues. I remember that when the Astrodome first opened they would announce that the wind speed was 1MPH from the east, west, north, and south.)
Back to the Stanford performance... I expect everyone recognizes that the altitude is going to affect the flight of the ball. If the effect on a FT is 6", then the effect on a 3pt shot is probably 10" or a foot. (A WBB ball centered in the rim would have about 4.5" clearance all the way around.)
The players have to adapt to the difference. My belief is that Stanford didn't properly adapt. (In the TV replay of the game, I saw about 3 of the long shots that I felt were offline. The rest I thought were missed due to how far the ball went. However, don't trust those observations as I didn't make them rigorously.)
I would predict that teams that visit the high elevations have a drop in their 3pt% (on average) and that the 3pt% in the second half for visitors is better than the first half. I could hypothesize that Stanford's shooters were less flexible in their 3 point shooting than maybe they should be. I would suggest that the other 10 teams in the PAC-12 should schedule more 3pt practice time when they arrive at the mountain schools. I don't think this is something you can simulate at the home court.
For more recent & deeper analysis, you may want to look at
http://projects.rajivshah.com/sportvu/Traj_RNN.html
https://arxiv.org/pdf/1608.03793.pdf
http://www.yisongyue.com/publications/ni...ectory.pdf
(Neither "altitude" nor "elevation" appear in the PDFs, so I didn't dig into them at all.)