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    • 2013 Publication

​A Statistical Analysis of the Packer Boys Varsity Basketball Team (2015-16)

Editor's Note: Victor A. ('17) conducted a statistical investigation of the boy's basketball team.
The 2015-16 Packer boys varsity basketball returned to former glory this year, a comeback that was two years in the making. With an in-league record of 8-4 (wins-losses), an out of league record of 11-0, and a 5-1 record throughout the playoffs, the team dominated through the whole season. They finished with three pieces of hardware: first place at the Dalton Invitational tournament, second place in the ACIS tournament, and first place in the NYSAIS C-Division tournament. In summation, the year was an absolute success for the team, a story of triumph and perseverance that will persist in the years to come.

But in some ways, this season was unprecedented. Although the team is no stranger to success, championship banners line the second floor gym, the two years preceding this one have left little to be positive about. Both years, the team finished the season losing more games than they won, without a shot in the state playoffs. In fact, they were barely a presence in the ACIS tournament. There was not a lot of turnover from those years either; most of the players returned and the JV players from the previous years filled out the rest of the slots. And to top it all off, the team lacked a height advantage most games. Many teams were not intimidated when they looked over to the other side during their warm ups. So, there was not much to expect this year.

So, that is precisely what this study is looking into. How does a mediocre team spring up to success in a year? George Boutis, head coach and father figure of the team, kept alluding to one key thing throughout the season: analytics. Over the past two decades, both in college basketball and the NBA, analytics has become a major part of the sport. And Boutis, too, looked to condense the fast-moving, high-paced, emotional high-school game into numbers (rebounds, assists, points, steals, blocks, free throws, three pointers) in the hopes that the game would become simpler. This makes sense: numbers are a reliable way to motivate your team and institute a game plan. In some ways, it is more effective to tell your team to “force contested twos” than to say “play hard on defense”. The numbers allow your team to set their eyes on a particular task. So, this study will analyze how key basketball statistics underlie the performance of the team and led to a successful season.

Over the past two decades, basketball analysts have been lamenting over the disappearance of the mid-range game. Long gone are the days of the dribble pullup jump shot or the iconic Michael Jordan back to the basket game. Instead, basketball has moved towards fast-paced offense with a preference for threes and layups, which makes sense; three is better than two unless it’s a sure thing. But let’s see how the team used the mid range this year.

During the regular season, at home the boys made 126 two pointers in the first half. The number of two pointers made fluctuated throughout the season, as expected. Wear and tear and fatigue would definitely come into play throughout the season and weaken the players’ legs, which means less lift on midrange shots and slower cuts. But then, players can always hit their second or third wind in the middle of the season to motivate them to perform better for longer. In the beginning of the year, the boys did not make as much two pointers probably due to nervousness; as games went on, the number steadily rises.

However, in the second quarter of the season, there is a steep drop, which is probably where the fatigue plays a role. It seems to fluctuate normally from that point until a second steep drop followed by a subsequent increase. The end of the yearis when a team starts to slow down and go through the motions; the basketball season is particularly long and this is commonplace amongst many teams. That explains the huge drop in two pointers. However, the steep increase can be explained as well. The team was having a particular successful season, and looking forward to the playoffs, their spirits were probably high, motivated them to finish strong. It is important to note that these are first half two point shooting numbers
The second half two pointer data shows similar fluctuation numbers patterns to the first half data. However, the peak is higher in the middle, which interesting. This means that at the beginning of the year, the team was prone to start better, but as the season went on, they were finishing games more efficiently. Perhaps this is due to the initial success the team had. Because they started hot at the beginning of the year, they slacked off at the start of games in the middle of the season, which forced them to play harder and better in the second half. Such a premise would make it extremely difficult to look at both data sets individually, but nonetheless, it is still significant. It is also interesting how much the shooting fluctuates in the second half data. It seems that one game the team is shooting very well in the second half, inside the arc, and then the next game, the team is shooting worse.
This trend could coincide with the first half data as well. Games where the team got off to a quick start, there was a less need to play the starters the whole game, so the number of two pointers made dwindled because the production of the players coming off the bench was not as high, which makes sense. Furthermore, games where the team shot badly inside the arc during both halves were most likely losses. Another interesting trend is that both graphs show increases at the end of the year, which was probably due to the new found energy for the playoffs as it was alluded to previously.  

Analysts make a huge fuss about home court advantage: teams usually shoot better in their own building because they are used to the balls, rims and lighting. Let’s see if this is true for the Packer team and if similar trends ensue. The first half numbers for two point shooting is interesting to say the least. Although the peak is very similar to the peak at home in the same category, it seems that the team’s two shooting on the road took a huge dip in the middle of the season. For several games, the team shot significantly worse than they shot in the beginning of the year, a product which is indeed probably due to unfamiliar balls and rims, but probably also the crowd as well. Also, in the first half, the team was probably shocked and timid; uncertain of what to expect in foreign domain.

The second half data for away games shows similar trends; the team started hot on the road and then fell to abysmal levels of shooting. It got worse in the second half for the team. While, in the first half, they stopped the bleeding, in the second half the downward trend continued for longer. Another interesting trend is the end of the season. Previously it was shown the boys got hot at the end of the season at home, but it is the opposite for the road. They finished the season making their least amount of two pointers all year in both halves. This could have been due to mental and physical fatigue at the end of the year. It is hard to gear up for games when you are on the road. But it was also due to the scheduling. The last few games of the season were at home. So, it is understandable that the excitement of finishing the year at home elevated the numbers as well.

But what about shot attempts? Was the team even taking a significant number of shots inside the arc or were they leaning more towards the rest of thebasketball world with a greater attention to threes? Let’s see what the numbers say. At home, in the first half, the team took a relatively high amount of shots inside the arc. However, in the second quarter of the season this number took a steady dip. Perhaps, they were giving up these shots for threes, or maybe even turnovers. Whatever happened the number went back up to normal level, until around the end of the season, when their two point attempts in the first half at home plummeted. This is an interesting drop that can be due to several components.
One, perhaps at the start of the game, Packer was less likely to drive to the hoop. A lot of teams are less aggressive in the beginning of games because of nervousness and regular jitters; it is natural. But, this should not be happening at the end of the year; teams, especially Packer, are usually hitting their stride around this point. Let’s continue to look for trends in the two point shot attempts in the second half; does Packer settle down and become more aggressive at this point in the game?

In the second half, though the numbers fluctuated, it was a lot more steady. It seems that for whatever reason, halftime speech, getting accustomed to the court, ball and light, or just settling down, the boys were more aggressive.
And it is a good thing that it did because at home, when the boys shot a relatively lesser amount of shots inside the arc, they lost. The only time this did not happen was at the end of the year, during the huge dip of shot attempts that we see in the first half. But this was probably offset by another category; perhaps Packer was playing phenomenal defense, or hitting a lot of threes instead. Nonetheless, the two point shot attempts at home indicate an intensity in the team’s gameplan in the second half: get to the rack and don’t settle. Let’s see how the numbers look on the road, where the team was habitually worse.
Away from home, in the first half, the shot attempts inside the arc is stable but much lower than the amount taken at home. This makes sense for many reasons. The boys are in an unfamiliar environment and the crowd is doing their most to shake their mental state; it is only natural that they are a bit antsy. But it is interesting that we see the same drop in the middle of the season in the road that we see at home. Perhaps this is indicative of the fatigue factor that was mentioned earlier. The boys must be tired after so many practices and games. Or perhaps this was an example of the boys settling. After a hot start, like Packer had, it is not unusual to settle for easier shots outside the arc. It would be interesting to see if this drop in two pointers coincides with a raise in three pointers.  
The boys two point attempts away from home in the second follows the same trend in the beginning of the year; it is lower than home attempts, though steady, and there is a drop in the middle of the year. But that drop is much more consistent in the second half of the season. For some reason, the boys continue to shoot less and less two pointers away from home, which is strange since this is an usually a proficient team inside the arc (based on the number of two pointers made during both home and away games). Perhaps, again it was due to fatigue; it is significantly harder to get into the lanes with weaker, tired legs. Or maybe something else is working for the boys. The three point shot has been alluded to more than once already, so let’s analyze that next.
As basketball evolves, the three point shot evolves with it. Teams throughout the country incorporate plays and offensive sets that are designated to spread the court and allow more three point shots to be taken. Several teams that Packer played against this year, not only used their three point shot to their advantage, but depended fully upon it to start and maintain their offense. Packer, however, was different. Packer shot almost four times as many two pointers than three pointers. They played a three-two (three wing players with two post players) lineup for the vast majority of the season. And they were successful. But the three point shot was definitely an integral part to the season and their success.
In the first half, at home, an interesting trend in the data surfaces. As the season goes on, the boys are making significantly more three pointers. By the last third of the season, they are making a good amount of threes, while still shooting thirty percent, which is a decent percentage from behind the arc. Why the increase in three percentage?
Perhaps, this is due to numerous shooting drills, and an improvement in technique. The year before, the team were horrid from behind the arc, so it was a point of emphasis to improve the form and the results. Perhaps towards the end of the season, the efforts were paying off. In the second half, the made shots follow a similar trend. As time goes on, the team is consistently making more threes. However, there is more fluctuation in this data set. Perhaps this is due to different strategies that are implored from game to game. This means that Packer is not simply chucking up threes against every team. Rather, they are assessing the situation and determining the amount of threes they should take depending on which team they are facing or whether or not shots are falling. It could also mean that the team was full of streaky shooters, hot one night, but not shooting the ball quite well on the next. Away from home, the boys start slow and then as the season goes on, they seem to catch their stride. Especially, in the middle third of the season. Perhaps this is supportive of the claim that they picked and chose who to shoot against depending on the lineup of the other team and the way the game was going. This effective use of strategy is one of the key components in the number of wins for the team. This intriguing strategy is also indicative of the team’s ability to go inside and out on a regular basis, a mantra that is integral to the team’s success on the court.

The second half follows a similar trend to the first half three point shooting on the road. The boys shot poorly in the beginning of the year, but then started shooting well around the middle of the season. However, the end of the season at home shows very erratic shooting. They boys shoot very well and then finish shooting very poorly. Perhaps, this is due to the nature of the three point shot; it comes and goes. This is why so many analysts are still skeptical of the three pointer; unless you have a good group of sharp-shooters, it is not very good to depend on. Or perhaps the three pointer is following the general trend of the team’s production: as the season goes on, they become less productive due to fatigue. Or maybe the drop is due to a simultaneous drop in three point attempts. Perhaps, the team found a lot of success inside the arc and thought it better to be more aggressive. Let’s look at the three point shot attempts both at home and away during the regular season to gain more insights.
At home, in the first half of basketball games, the team seemed to vary in the number of shots taken from outside the arc; their attempts fluctuated significantly. This is very interesting because it strengthens the argument that the team focused on different points of attack in different games. Perhaps against bigger teams the team shot more, whereas against smaller teams, the team looked to get the ball inside more. However, the trend from other data sets continues in this one as well; the team started shooting less and then built up as the season continued.
In the second half of home games, the data looks very different. Again, the team starts slow, and then picks it up as the season continues. But then the attempts drop suddenly. Perhaps this was due to being aggressive in the second half, taking less outside shots in order to get to the rim for easier shots near the basket. This is very likely because in the second half, teams are a lot more urgent; they are much more willing to make aggressive plays to win basketball games. However, this trend does not continue. In other games, the team shoots a steady amount of three pointers. So maybe during that first drop in three pointers is attributed to the uncertain nature of the three point shot in general. Maybe the team could not depend on them to fall that day, so they decided to go inside more.
The three point shot attempts on the road in the first half resembles the three point shot attempts at home in the second half. The team started slow and then started shooting more frequently and steadily in the middle of the season, which persisted until the end.
This makes sense; it is common for teams to want to settle on the road for a lot of reasons that were all mentioned in the preceding paragraphs: nervousness, uncertainty, foreign crowd noise, balls and lighting. It is no surprise that this resulted in less aggressive play and more shots from outside the arc.The data set for away games in the second half breaks the trend. The team saw the same rise in three point shooting, but afterwards, instead of the amount of shots continuing, they dropped significantly around the end of the season. Although unprecedented, perhaps this relates to similar reasoning as before: as games were ending, close to playoff time, the boys were more urgent, looking for better shots closer to the basket. And because of this newfound aggressiveness, the number of shots from outside the arc diminished.
Some coaches attest that the team that gets to the line more wins more games. This may be true. Shooting free throws may fundamentally increase your chances of winning basketball games because it slows the game down, allows you to get easy points, and allows you to set up your defense on the other side of the court, mitigating the other team’s fast break attack. Not to mention, getting to the line gets the other team in foul trouble as well. So let’s see how team fared from the line this year, and what the data may elude to.
In the first half of home games, the team was very erratic from the line from game to game. Some games they would shoot free throws at a high clip, but other games not so much. The reason for this may be more cryptic. Maybe there is no outright reason, other than the ball just was not falling. However, at the end of the season, the made free throw number becomes steadier. Perhaps, this is when the team hit its stride at the charity stripe.

The trend from the line is the same in the second half as well. The team is very erratic from game to game, though there is one key difference. After the halftime break, in the beginning of the year, the team made less free throws. Perhaps, this was due to halftime rustiness, or again, just the ball not going in. It is also interesting that the made free throws became steady at the end of the season.
Away from home, in the first half, the free throw rates are very interesting. Instead, of getting better as the year goes on, like in other data sets, the team actually gets significantly worse. Perhaps, it was due to a lack of calls on the road. Perhaps, they were not used to the rims and the balls in the opponent's gyms. Perhaps, once again, shots were not falling. But for a decline like this, one that persists throughout the whole season in the first half, there is probably more to it than that. Does the trend continue on into the second half?     In the second half, the team makes a consistently small amount of free throws. Unlike the first half, the team starts bad and stays bad. Maybe the same reasons are involved: a lack of calls on the road, weird environments and crowd noise. However, it is interesting that a team that shot free throws so poorly on the road was able to win so many games. One would think, and several coaches would agree, that the team that shot the best from the line would have the greater chance of winning, but in Packer’s case, this may not always be true.
Free throw attempts can be just as telling as free throw makes. But the data from home games in the first half seems to coincide with the overall trend: erratic free throw shooting. The attempts from game to game varied immensely. It seems that at home the boys would get more calls to go their way, but that does not seem to be the case in all games. Perhaps, they were less aggressive in the first half, which is prone to happen.
In the second half of home games, although the shot attempts still varied from game to game, they shot significantly more often. Perhaps this was due to the fact that they were more aggressive in the second half due to their urgency. However, the data set ends on an downward trend. Could this also be a result of fatigue?
The free throw attempts in the first half of away games are a lot more steady. The team starts well, takes a big dip and then stays consistent throughout the year. This is interesting because as the attempts were consistent, the shooting was not. If you remember, the team shot poorly from the line during away games. So, this data suggests that the team was a rather poor free throw shooting team on the road. Again, this is strange because most people believe that free throw shooting is essential to winning basketball games, but apparently in Packer’s case, it is not.     In the second half, the team, this even better in the first half at getting to the line. This suggests that the poor shooting was not due to shotty officials, because the free throw shooting rates remained the same throughout the season. However, this confirms the team’s poor shooting on the road. Perhaps this trend of the team shooting poorly on the road is consistent throughout the season, but for the team to be so successful, they must have done something else to perform so well.
rebounding and inside play is so pivotal and focused upon, let’s see what the numbers say.
At home in the first half, the team rebounded at a very steady rate. It seems that even through their erratic shooting, their rebounds were consistent.
In the second half of home games, the trend regresses. They no longer rebound at such a high and consistent clip. Instead they are more erratic, rebounding less. Although, they pull a lot of boards around the middle of the season, they cannot keep the effort going. The disparity between the first half and second half rebounding is perplexing. Perhaps it is a direct result of the shooting; in the first half the team shoots relatively poorly, so they have more opportunities to rebound. But after they have settled in the second half and their shots start to fall, they rebound less.
On the road, in the first half, the rebounding numbers look similar to the numbers at home in the second half. They are consistently low, except for a jump around the end of the season.
Something that coach Boutis said often that impacted his team was “the team that wins the paint, wins the game.” And with two all-star forwards controlling the paint most of the game, that feat became a reality for the team, and was one of the bigger reasons for the team’s success. However, this does not undermine the rest of the team’s rebounding prowess. In fact, for this reason, coach also coined the term “Wakin Rebounds” to commemorate guard Mike Wakin (class of 2015) and the importance of rebounding from the perimeter. So, on a team where

However, in the second half, the numbers are much more consistent. Not only, does the team rebound more but there is barely a drop off throughout the whole season. Perhaps the reason for the consistent rebounding on the road is because of the poor shooting again. They experienced bad results shooting the ball on the road, so they must have had more opportunities to crash the glass.
But along with rebounding, assists are also indicative of a team’s success. Assists can show ball movement, offensive efficacy and even team chemistry. Throughout the season, the team was numerously applauded on their chemistry and good-natured teamwork. Perhaps, their assists numbers can do these claims justice.
In the first half during home games, the numbers are good but fall near the beginning and end of the season.

However, during the second half, the numbers are much lower. Perhaps, one on one play dominated late game situations. It is much harder to have ball movement in the later stages of the game, because it is much more important for to get the ball in the basket.

Away from home, in the first half, the numbers reflect that of the first half. The guys pass the ball very well, though shy away from it at times.
In the second half of these games, the team shows signs of similar play. This was definitely a team that passed the ball well and often. It seems the praise from numerous sources was well earned. However, the steep drop at the end of games is concerning. Perhaps this reflected a drop in the performance of the team at the end of games as well.
A good defense defines many successful team especially when the old and familiar adage is mentioned: defense wins championships. And even in an age when high-powered shooting and spread offenses dominant many gameplans, a stout defense is still the backbone of good basketball. Now, we have already seen how rebounding and assists have impacted the Packer team that shot the ball below average this year. But, how did defense, especially blocks steals and deflections, affect the team’s play as well.At home, in the first half, the team turned the other team over often. Steals are very important to the game of basketball. The art of turning the other team over while also keeping the ball in bounds in order to get a fast break opportunity on other end. These high steal numbers in the first half of home games are indicative of active, locked-in defense to set the tone for the rest of the game.

In the second half of home games, the rate of steals is significantly lower, but that makes sense. After intense first half defense, teams would probably more tentative and careful with the ball, which leads to a lower amount of play making and less points. So, even though the numbers are lower, the results are still fantastic.
And in the first half of away games, the boys came out the same way. Intense defense led to a high amount of steals which set the tone for the rest of the game. This probably led to a lack in aggressive play from the other team and an increase in fast break points for Packer. For a team that does not shoot particularly well, defense is essential, and seeing these steals numbers definitely explains Packer’s success.
In the second half of these away games, the trend continues. Because the boys played great defense in the first half, the other team did their work for them in the second half. Staunch defense led to scared play by their opponent’s offense. But it is interesting to see, that the numbers did not decline that much; the team was still working hard on defense.
In 7th grade, my middle school coach, Thomas Stokes, told me that blocking shots out of bounds was the most worthless play in basketball. The other team keeps the ball and they get an opportunity to regroup and run an efficient out of bounds play. And the morale boost for the shot blocker actually acts as a distraction to the overall defense and hampers the success of the team. However, coach Boutis has emphasized “Bill Russell post defense.” Instead of blocking the ball in the stands, post players are persuaded to tip the ball to themselves in the air and then make the quick outlet pass, thus keeping the ball in bounds and giving the team an opportunity for a fast break. So let’s see how blocks contributed to the team’s success.
At home, in the first half, the team blocked a relatively high number of shots. It seems that their first half intensity on the defensive end was two-fold, blocks and steals.

In the second half, the team may have been even better at blocking shots. Perhaps, as the opponent’s offense became more tentative worrying about ball pressure and steals, their offense became more predictable, which led to more blocked shots and rebounds. This means that the team’s defensive pressure at home games persisted through the whole game. Perhaps this is the reason for their poor shooting at home in the second half.
On the road, in the first half, the block numbers were also relatively high. It seems the team’s defense did not change on the road in the same way that their shooting did.

In the second half, the defense persisted. The team continued playing fierce defense from start to finish.

So, what did the team do that made them the most successful on the road and at home throughout the game. Although, these point totals were high, it seems that they could not reliably depend on their shooting; it was much too erratic. On the road, they shot poorly in their first half, inside and outside the arc. And throughout the season, at home, though they started the year shooting well, they could not continue to perform at such a level, probably due to fatigue. The team probably couldn’t depend on free throws either. Throughout the year, their free throw shooting was rather poor, despite the fact that they got to the line a lot. So, if the team couldn’t rely on their offense, which is ironic seeing that three people averaged double digits this year, then they had to rely on their defense. And the numbers support this; the team’s blocks and steals numbers persisted throughout the year. They consistent on the road and at home, for the entire game. And this directly correlated to their rebounding as well. The more steals and blocks the team had, the more they rebounded as well, which suggests that fierce defense was stifling the other team’s offense, forcing them into bad shots and ending their positions quickly. And this probably facilitated their offense; since they were mediocre shooting the basketball, they needed defense and fast breaks to jump start their offensive attack. So, it seems that defense really does wins championships. Will the Packer basketball team continue to pursue and emphasize staunch defense to win, or will other teams catch up and force them to shoot more? Next season will definitely be a very interesting one.


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        • The 43rd Figure
        • The Clock
        • The Collatz Conjecture
        • Constructing a Soccer Ball
        • Determining how Ballparks Affect Batter's Ability to Create Hits
        • The Rotating Conundrum
        • Pythagorean Puzzle
        • Mathematic and Scientific Explorations
        • Kinetics Lab
        • Math in the Restaurant Business
        • Math as a Vessel for Social Change
        • Sustainability of Bottled Vs. Tap Water
        • Thoughts on the Lottery
        • Understanding Player Efficiency Rating
      • Scientific Research >
        • Communicating With Computers
        • The Mystery of Asthma
        • The Nanoscopic War Against Cancer
        • Phytochemistry
        • Solving the energy crisis with Intermediate Band Solar Cells
        • A Pain That Never Ends
        • Rapamycin Resistance
        • Ampacity of a Single Core Horizontal Cable
        • Morphological Properties of Texting Acronym Formation
        • cGAS and STING Expression
      • Reactions and Responses >
        • Can Humans Survive the Climate Crisis?
        • My Experience as a Teacher's Assistant
        • Ted Talk Responses
        • Teens For Food Justice
      • Artistic Creations >
        • Chandelier
        • Deltoidal Hexacontrahedon
        • Dodecahedron Card Trick
        • Eye of the Triangle
        • Free Radric Delantic Davis
        • The Grid
        • What Does A Randomly Composed Song Sound Like?
        • Science Wing Mural
    • 2014 Publication >
      • Cover Photo
      • Artistic Creations >
        • Art Using the Fibonacci Sequence
        • Computer Generated Architecture and Designs
        • Mathematical Landscape
        • Math Art
        • Math in Music
      • Historical and Current Explanations >
        • Algae Bio-Fuel
        • An Energy Alternative
        • Clean Energy In Transportation
        • Calorie Restriction
        • Creating Energy in the Modern World
        • Dietary Intervention Impact on Gut Microbial Gene Richness
        • Earthly Applications for NASA Technology
        • Explaining Relative Motion
        • Exploring Artificial Inteligence
        • Gamma Function
        • How Leaves Work
        • Hydrogen Fuel Cells
        • Music and Brain Development
        • Programming Calculators
        • The Science of Microsatellites
        • Sci-Fi Taser
        • Sloane's Gap
        • Sustainable Energy: Why Some Ideas Shine Brighter than Others
        • Understanding The Galvanic Cell
        • The Virus: Our Unforeseen Philosopher's Stone
        • What Are Fuel Cells and How Do They Work?
      • Mathematic and Scientific Explorations >
        • Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons
        • Big Bang
        • Dictyostelium Discoideum
        • The Future of Solar Cell Technology
        • And Many More...
      • Reactions and Responses >
        • Alternative Energy Sources, New but Unused
        • An Insight Into the Curious World of Ethnobotany
        • Challenging What We Think We Know
        • The Current State of American Education
        • Discovering New Numbers
        • Interview With an Architect
        • Life of Pi Response
        • Mathematical Art Video Commentary
        • Missing from Science Class
        • The Museum of Math
        • The Inside Scoop on a Real Mathematician
    • 2013 Publication