A Scholarly Look at the Mathematics of Getting Buckets
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Mathematics is perhaps the greatest tool humans have in the pursuit of knowledge. The study of numbers can standardize and quantify nearly every aspect of the universe with incredible accuracy. Problem solving is made easy by the analysis of numbers, if you know how to look at the data and interpret the results.
Advanced statistics in sports have been around for roughly the last twenty years. They were often cast aside in favor of conventional wisdom in both casual and professional circles. Then, the Oakland A’s happened in the MLB. The famous 2002 Oakland team, portrayed in the film Moneyball, legitimized advanced statistics in the realm of baseball due to its more rigid, structured nature when compared to other sports. It wasn’t until Daryl Morey (an MIT grad with a degree in computer science and an emphasis on statistics from Northwestern University) became general manager of the Houston Rockets in 2007 that advanced stats became widely acknowledged in the NBA. Basketball advanced statistics had their first true champion in 2015 when the Golden State Warriors were victorious over the Cleveland Cavaliers in the NBA Finals. This shocked the basketball world and led to a seismic shift in the way basketball is played.
Principles of advanced statistics are simple and easy to comprehend. Efficiency, efficiency, efficiency. Efficiency is the name of the game with advanced statistics. The goal of the offense is to score the most points off of the least amount of shots, while the goal of the defense is to eliminate excess opportunities for the offense and have as many takeaways as possible. Three point shots and layups are the weapons of choice for an efficient offense because of their increased point output per shot and high conversion/foul rate, respectively.
Albany High School is not safe from the seismic changes to the game of basketball. At an Albany High School Boys Varsity basketball game on December 13, 2016, the Falcons took roughly 75% of their shots from three-point territory or the painted area in the first quarter. They shot an amazing 100% from the paint and 43% from behind the arc. They scored 2 points per shot from inside the paint and .86 points per shot from downtown. Their opponents during the same time period took 85% of their attempts from three-point land or the paint. However, they shot 33% from the paint, scoring .67 points per shot from that segment of the court and a dismal 12.5% from three with .375 points per shot. It is no wonder that Albany High left the quarter with a commanding lead and momentum on their side.
There are other stats that can be used to explain occurrences on the court and value of individual players. The following numbers come from the first half of the December 20, 2016 Falcon Boys game. Effective field goal percentage is a number that accounts for the difficulty and increased reward of three point shots. It essentially adds a multiplier to three point shots made, with the theory being that a shot worth more points can safely have a larger margin for error. The following table shows the effective field goal percentage of each player that saw the court in the first half:
|Player||Effective FG Percentage||Shot Attempts|
Two players performed especially well in this category(even when considering the small sample size), Coons and Bertrand. This indicates that these players do the most with their opportunities on offense.
Offensive and Defensive Rating project points for a given lineup out over 100 possessions to standardize scoring and points allowed. It allows for the contributions of players that don’t traditionally show up on a stat sheet to be quantified by using possessions to control for different lengths of time. Here is a table of all lineups and their Offensive and Defensive Ratings.(You want high Offensive and low Defensive
ORTG=(100(PTS)/POSS) DRTG=(100(PTS allowed)/POSS)
|Lineup||Offensive Rating||Defensive Rating||Possessions|
|Gaddy, Choudhri, Nixon, Bertrand, Coons||72.2||88.8||Offense:18
|Wallace, Nixon, Jorge, Coons, Bertrand||100||33.3||Offense:2
|Wallace, Gaddy, Bertand, Coons, Jorge||133.3||0||Offense:3
|Wallace, Gaddy, Bertrand, Nixon, Jorge||80||100||Offense:5
|Wallace, Gaddy, Nixon, Coons, Jorge||0||200||Offense:2
|Choudhri, Coons, Gaddy, Nixon, Jorge||0||100||Offense:2
Two lineups are exceptional and two are lackluster(with two being neutral. The second and third lineups are incredibly efficient, while the last two are rather suboptimal, and the first and fourth lineups are neither particularly bad nor particularly good(neutral). The only player that occurs exclusively in neutral and excellent lineups is Bertrand, yet again.
The final stat that will be assessed is points per one hundred possessions for and against. This is actually calculated the same as Offensive and Defensive Rating, however, instead of lineups, the calculation uses all points scored or allowed while a specific player is on the floor. This allows the viewer to see the overall effect an individual has on the game by projecting relatively small samples out to a large, uniform number.
|Player||Points for||Points against|
Once again, the big standout is Bertrand. He was the only player to have more points scored than allowed while he was on the floor. This indicates that despite not having eye popping points, blocks, steals, etc. he still makes a very massive and underrated contribution to his team.
Advanced stats are not the be all end all for sports; all of the players have a role on a team, which is why they are on it. Advanced stats don’t tell us that one player is definitively better than another; they tell us that a player makes an unsung impact on the floor that positively affects the trajectory of the team. They simply are another way of understanding what’s going on during a game by reading between the lines.
There is a hidden side to everything, and math is our portal to understanding this unknown entity.