While watching a basketball game,
one may be thinking what an easy sport it is, that it is so easy to throw a
shot through a circular room, but there is far more to the game than just this.
There is a lot in the game of basketball that pertains to mathematics, whether
one is taking a shot, driving to the hoop, pulling in a rebound, or the angles
one takes in the game. One can see lots of math in basketball by simply sitting
in on game film and scouting another team. Each player that is threat to the
opposing team has a set of statistics of shots taken and shots made, steals,
and rebounds. The basis on the game is statistics and there are percentages
that show how successful each player is in the game.
An equation that is used to
calculate the velocity a player would have to shoot to land the ball perfectly
in the basket is:
A basketball play tries to hit the basket at as close to a
right angle as they can which usually means the best strategy of this happening
is shooting at a 45-degree angle (Mathematics in Sports). Mathematics can also come into
play because there is another equation to find the range of the ball when it is
thrown at this angle, which is
One can graph this range function with distance as the x
axis in order to find the best angle and velocity to shoot a shot from a
certain distance on the floor. The graph itself is a curve increasing. The graph
is used to look at distance and get an idea of how hard a player has to throw
the ball in order for the shot to be made by looking at the speed and velocity (Mathematics
in Sports).
Another
part of the game of basketball that consists greatly on mathematics is
rebounding. The NBA has new cameras that can help track where rebounds land
from specific spots on the court. This new system logs where every missed shots
lands on the court and maps the location of where the shot was taken and where
the missed shot lands. The concept of rebounding depends on two things mostly:
distance and direction. Many coaches tell their athletes that the longer the
shot, the longer the rebound and this new system proves this concept directly. Direction also matters. Where the athlete
takes the shot affects where the rebound lands, this camera shows images such
as the one below:
This image shows where most right corner misses go. The
theory of weak side rebounding from the corner seems to be proven true by the
image shown above. There are also forces off the rim, that push the rebound off
in certain directions. The collision on the rim is very important in where the
rebound will land. For example, 56% of missed threes taken from the corner land
on the weak side. There is a lot of mathematics behind making this new camera
that can calculate these rebounding stats (Grantland).
Another
view on shooting in the game of basketball is to look at the radius of the ball
and see where the ball needs to go through in order for the shot to go into the
basket. When a shooter is shooting the ball they aim to not miss short of the
rim so the distance between the rim and the middle of the ball has to be
greater than the radius of the ball. The height of the person shooting also
comes into play here because the angle at which the ball needs to go into the
basket is different for differing heights. These sets up a model at which one
can find the exact angle they need to make the best shot for their shot to go
in. Now there are computer systems that use these certain equations to
calculate the best angle at which one’s shots go in. These computer systems go
into depth by looking at the height of the person and the angle the ball goes
in with. There is another model of looking at best chances of a ball going in
that is a similar idea where the best shot is one that goes exactly through the
center of the hoop, one calls this a swish. This strategy looks at two separate
graphs of two separate equations and then compares the feasible regions on each
graph to find the best angle and best strategy of making a basket.
As one
can see there is an immense amount of mathematics in the game of basketball
that can be far more complex than what is described here. There are many
equations, models, and graphs that can be used to find the best angle for a
shot taken and to find better strategies of where to pull in a rebound
depending on where a shot is taken. The game of basketball is far more complex
than just throwing a ball through a hoop (Modeling Basketball Free Throws).
Works Cited:
Gablonsky, Joerg, and Andrew Lang. "Modeling Basketball
Free Throws." Society for Industrial and Applied Mathematics. Web. 12 Nov.
2015.
Goldsberry, Kirk. "How Rebounds Work." Grantland.
14 Oct. 2014. Web. 12 Nov. 2015.
Wilson, Jim. "Mathematics in Sports." Mathematics
in Sports. Web. 12 Nov. 2015.
To be honest, the only time I ever watch basketball is during March Madness. My brother is a Duke fan and my dad is a NC state fan, you can imagine how hectic my household gets. I always knew there was math in basketball. The players shoot at different angles with different speeds. I now know that the perfect angle they go for is 45 degrees now. However I didn’t know there was a special way that players shoot the ball and where they stand to have a greater probability to get the rebound.
ReplyDeleteAs Tiffany stated at the beginning of her post most people think that basketball is an easy sport. I can attest that basketball is not an easy sport as I am personally very bad at it and I am generally good at most sports I play. The formula for the force needed to make a basket is something I need a lot of work with as most of my shots end up being to short. I found the new camera that detects where rebound will go from shots taken around the court to be interesting as it will give players who have access this this technology an advantage over other players who do not because they will have a better idea of where a missed shot will go. Although basketball is a very reactive sport so no matter how much you study it anything can happen mid play and change the angles and trajectory of the ball.
ReplyDeleteBasketball was, is and will always be the one sport that I look like a complete idiot trying to play. No matter what the laws of probability may say, I will miss every single free throw that I have to take. I mostly thought that this was attributed to my technique, which I may add, is severely lacking, and it turns out I was right. Tiffany does a really good job of showing the math behind normal capable human beings taking free throws. I found it really interesting how so many shots bounce off the rim to the right (if you are looking at the hoop from above). I would have thought that it would be the opposite way, because most people are right handed.
ReplyDeleteI used to play in basketball in high school and I have never though of all the math that is involved with it. When you are playing, these formulas to land the ball perfectly in the hoop are never running through your mind when you are playing. The other formulas that companies use to determine stats and where a rebound is most likely to land seem very interesting however. I think it’s rather intriguing that they producers of the NBA and others came up with these special cameras and formulas to figure everything out. I’m not sure how helpful it is for them to know where the rebound will land, but it is cool to know that they can figure it out when they want.
ReplyDeleteI know from my little experience on the incredibly intense and physically demanding intramural basketball team (shout out to Big Ed and the Boys, hey Devin), basketball is definitely not an easy sport. It’s so amazing to me that there is a way to calculate the velocity of shooting the ball, and I’m perplexed by thinking of how someone could’ve possibly devised such a formula. It’s really cool how there are now cameras used by the NBA that can track the distance and direction of a shot. This is one of many examples that clearly show us how incredible and advanced technology is, especially when it can be used in athletics in such a crucial and beneficial way (for the athletes, at least).
ReplyDeleteWith being a big sports fan, I have watched a fair amount of basketball over the years. There is a lot of math involved with basketball much like Tiffany discussed. Not only is the velocity of a players shot taken into account, the height of the player, the distance from the basket and the angle of the shot are all taken into account. It is almost a science to be able to get the ball through the hoop. With not being the greatest basketball player, I know how difficult it is to be able to actually score points in the sport. There are also statistics and percentages of how well a player shoots. The best players in the league don’t even shoot 50%, showing how tough it is to score in the NBA. I think basketball takes a lot of practice to be able to become good and a good shooter. Repetition is the best way to figure out the angle and velocity of the ball that needs to be used in order to get it in the basket and after a while, will become natural.
ReplyDeleteAs a basketball player I didn't think there would be anything math related that was involved, but as tiffany posted there is. I like how she used formulas to describe this it is much easier to see the formulas and how all of the numbers fit into it. This post took a lot of things that could effect the shot like velocity, height, and distance which was neat. It didn't just isolate a certain type of basketball player for this but instead all types of people that like to play the game. I think though however you could know all of this data, but yet still not be good. Even though knowing this might help, you still need to practice it because saying you can do something and actually doing it is a lot different.
ReplyDeleteI did a previous math project about different sports involving math and basketball was one of them. There can actually be some pretty complicated formulas to find the perfect shot at different areas of the court. There are a lot of factors being put into just one simple basketball shot. Of course professionals don't calculate this on the court, though, it would be interesting to maybe calculate these values at different areas and keep a mental note of the best angles to take at different areas on the court. It's really interesting how many fields of mathematics can be applied to different sports that you wouldn't think have any correlation to math besides statistics and scoring.
ReplyDeleteAfter reading the title of this post I got a little bit worried because I can honestly say I know nothing about basketball. I did think it was cool that Tiffany was able to take the sport she cares about and write about the mathematical side of it. I thought it was cool that there is an equation to calculate the best possible angle to shoot the ball. I'm curious to learn how they figured out that equation. Overall I thought this was a very cool post however it was hard for me to read since I don't know much about the sport.
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