Mathematics plays a huge role in
basketball, from the shooting percentage to how much time a team has to score
in. An article written by Brian Skinner talked about the probability that a
given shot will do in, equality of future shots the team is likely to generate,
and the number of seconds left before the players must either shoot or forfeit
the ball to the opposing team. Skinner’s equations show that if two teams shoot
with different times left on the clock that the team that shoots with extra
seconds has a better shot selection which turns into a winning strategy.
Professional basketball player
Lebron James is now apart of the new Big 3; himself, Kevin Love, and Kyrie
Irving. James can and will score from anywhere on the floor. His highest
scoring spots are in the paint and is average outside of it. Although, he still
leads the league in close-range efficiency with 75 percent of them are inside
eight feet.
This shows how much he scores in the paint compared to
anywhere else on the floor. He doesn’t just score from inside the paint,
although his scoring percentage is at it’s highest in the paint, he does score
from mid-range shots and some three-point shots. With percentages of 47%
mid-range shots and 41% three pointers. James is a stronger scorer on the left
side of the floor compared to the right.
Another
professional basketball player whose name is Kevin Love also enjoys scoring
from the left side of the floor. He is by far NBA’s most active shooter form
the three-point line on the left side.
This diagram shows that he is most active on the three-point
line but can also score efficiently inside the paint as well. He is increasing
in his ability to score from everywhere on the floor, especially behind the three-point
line.
The third
component in the Big 3 is Kyrie Irving. He has become one of the go-to
playmakers for Team USA. Irving has been one of basketball’s most creative
scorers despite drama within the league. Unlike James and Love, Irving scores
from all over the floor and is very efficient. He moves and opens up the floor
for his team and himself, showing that like James and Love he is above average
on the left floor but with his inside game along with his outside game.
With James and Love joining a team with Irving, his usage
will begin to diminish which will lead him to take fewer self-created tough
jump shots than his previous season. On the bright side he will have a higher
efficiency with catch-and-shoot shots than off the dribble. So his chart will
begin to look more orange and red which means he will be more above average on
his shot selection.
Having the Big 3 on the same team in
Cleveland, they will become one of the NBA’s productive scoring teams. Although
with the combination of the three, their inside game will be stronger which
will leave the outside game for the other players on Cleveland.
The left side of the floor will be dominant for Cleveland.
They will score a majority of their points from outside the three-point line
and inside the paint. Scoring on the right side will have to come from the
other players on the team according to this chart, the Big 3 loves the left
side of the floor, so the team will have to balance it out unless only scoring
from the left side will win them ball games.
Within
mathematics in basketball rebounding plays a huge factor. This article is based
upon the question of “Where do rebounds go?” Last regular season of the NBA
players missed over 100,000 shot attempts. Missed shots means rebounds, missed
shots result in the outcome of the game. Rebounding is a huge potential to the
game of basketball. Rebounding is very unpredictable, missed shots means that
the ball can hit the rim or background and bounce anywhere.
Almost 80
percent of all NBA rebounds happened within eight feet of the hoop. Thinking
about rebounding should include three simple rules: distance matters, direction
matters, there will be randomness.
Referring
to the distance matters rule, longer shots lead to longer rebounds is supported
by basic physics. “The tracking system enables us to visualize the distance
effect like never before.” The further out you shoot the longer the rebound. Within
the paint, on average, the rebound will go about 5.4 feet from the basket.
Within 18 feet from the three-point line and the lane, on average, the rebound
will go from 6.1 feet to 6.5 feet from the basket. Finally within the
three-point line, on average, the rebound will go from 7.3 feet to 8.3 feet
from the basket.
Referring
to the direction matters rule, rebound locations depend on the angle the shot
was taken at. For example, if a player misses a shot from the right corner, the
rebound on average will come back in the same direction or will go on the
opposite side of the basket. “Consequently, a basketball traveling from left to
right will continue on its path unless it hits the rim, in which case the rim
exerts a force on the ball.” The ball has to hit the rim in special ways to
change its path of direction.
Referring
to the there will be randomness rule, some times a player doesn’t know which
way the ball is going to land after hitting the rim on a shot. This rule
includes the other two rules; distance matters and direction matters.
In conclusion mathematics
is very essential in the game of basketball and is very hard to explain in
fewer than 1,200 words. There are many more characteristics to basketball that
involve mathematics. The majority of the game is mathematics related but it was
hard to pick out the most essential ones and put them into words within an
essay.
References
Cowen, R. (2011, August 2). The Mathematics of Basketball.
Retrieved August 2, 2011, from http://news.sciencemag.org/2011/08/mathematics-basketball
Goldsberry, K. (2014, January 1). The Shape of Cavs to
Come: How Lebron, LOVE
, and Kyrie Might Fit Together. Retrieved January 1, 2014, from http://grantland.com/the-triangle/lebron-james-kevin-love-kyrie-irving-cavs-offense/
, and Kyrie Might Fit Together. Retrieved January 1, 2014, from http://grantland.com/the-triangle/lebron-james-kevin-love-kyrie-irving-cavs-offense/
Goldsberry, K. (2014, January 1). How Rebounds Work.
Retrieved January 1, 2014, from http://grantland.com/features/how-rebounds-work/
It's amazing how efficient basketball players can be in their shooting. Lebron having a 75% chance of scoring within 8 feet is just incredible. Like you explained in your blog, physics can play a role in where the ball goes after a rebound. depending on where it hits the rim, the ball can fly anywhere. However, I doubt NBA players take the time to calculate the angles and measure how far the ball will go. It is awesome to see how math can be incorporated into scenarios like basketball.
ReplyDeleteThis was interesting to read; I never knew that basketball contained that much mathematics. I think that it's incredible that 80 percent of the rebounds are made only 8 feet away. It seems like the players would have to consider the different angles before going to play a game so that they have a better chance of making the hoop. I also thought that the Big 3 was interesting especially that they're all on the same team.
ReplyDeleteBeing a basketball player I knew that there was math involved but its crazy to actually think about it because you don't while you are on the court. You would think that all this could be useful to coaches and players but I've never had a coach talk to me about math during practice.
ReplyDeleteSports analysts have used this kind of stats to determine player efficiency when breaking down teams and what you showed in the post did just that. As a basketball fan myself, I understood how you explained the shot selection as well as the probabilities of making it for each of them on different areas of the court. The physics was rather simple: long shot, long rebound which is something the analysts always say in a close game.
ReplyDeleteI enjoyed how clear and detailed your post was. I enjoyed reading the statistics of the three different players and the three players combined. Having played basketball, I can relate and see the patterns in the shot charts. I also liked the physics part of the summary which I thought was a nice touch to the post. Great Summary!
ReplyDeletei felt like the vast majority of your paper was just the statistics of certain players providing little to no insight as to the math of the game. i disagree with some of the explanations you gave regarding the "physics" of basketball. On the pro-side however...
ReplyDeleteAlthough I cannot respect Lebron in any way, I thought this was an interesting read. I had never really thought of math in basketball because I don't play, but your facts seem to make sense. For example a longer shot would lead to a larger rebound because it takes more force to get the ball to the basket. I think it's interesting that all of the "Big Three" are better scorers from the left side. It should be easier to defend this team knowing this fact
ReplyDeleteI hate to be the guy that gets all technical, but I don't think the notion that there's a lot of math in basketball is justifiable. Yes, you can calculate the percentage of shots made and you can explain the optimal shot with physics. However, I don't think that basketball players are thinking about the physics behind their shot. The way I see it, the "math" behind this is essentially showing their behavior and the result is essentially just stating how good they are at different positions and that can most likely be attributed by their training.
ReplyDeleteI'm gonna have to agree with Robby here, I got the player statistics but no Math, and physics was little from what I would expect. For example, like the ball in the game is a projectile, if you had maybe talked about the relationship between the distance and the force the player needs to throw the ball such that it lands in the hoop (the initial velocity of the ball), or the initial velocity vs the angle at which the ball is thrown which will ensure the ball lands in the hoop. Or maybe talk about how the speed of a player running towards the hoop affects his accuracy as apposed to the one standing at one sport, as well the the forces required by the respective players to drive the ball into the hoop. I don't know much about basketball but this was sort of what I expected the post would at least talk about
ReplyDeleteIntriguing how randomness, distance, and direction take part in basketball. I knew many factors took place, but it is also based on their skill and practice. Great use of statistics and references
ReplyDeleteI agree with Robby it seemed like most of the paper was statistics of certain players and not a lot of math to the game. Although your topic was an interesting one. You did a good job with the details and including pictures. You did a good job explaining the physics to it.
ReplyDeleteI thought it was actually pretty cool reading the statistics you had. It was nice to read what math is involved in basketball. I thought you did a good job including those pictures because it helped me understand more things. Overall this is a good blog to me.
ReplyDeleteI was little interested in the statistics of the player, but really interested in the topic you mentioned in the beginning about the players and the time limits on scoring. I think that you should have gone in to a little more depth on this topic. The idea of what the time on the shot clock would be for the highest percentage of shots being made intrigues me.
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