INFO-640 Final Project

An analysis of the 3 point shot
By Kailen Santos

2022-05-03

Background

Goals

Discover new trends in the modern era of basketball
Apply quantitative research on Basketball statistics to predict future of NBA stats
Identify where the position began to shift, if there is one

Research Question

Is there statistical significance corresponding to the relationship between NBA centers’ ability to attempt and make three-point shots at a high volume and the amount of playing time they have?

Cleaning

To collect and transform my data into a workable state, I used Python to both call the API and to save the data into a CSV.

q = "https://www.balldontlie.io/api/v1/players?per_page=100"

valid = True
page=1

#Instantiate variable lists to store player info
p_id=[]
f_name=[]
l_name=[]
t_id=[]
t_name=[]


#This loop allows for pagination until there are no pages left
while (page!=None): 
    #Build query string and request
    response = requests.get(q + f'&page={page}') 

    data = response.json()
    players = data['data']
    
    #Loop through response to filter out positions
    for line in players: 
        if (line['height_feet'] == None):
            if ((line['position'] == 'C') or (line['position']== 'F-C')):
                #Now that conditions are met, save player data
                p_id.append(line['id'])
                f_name.append(line['first_name'])
                l_name.append(line['last_name'])
                t_id.append(line['team']['id'])
                t_name.append(line['team']['full_name'])
            else:
                continue
        elif ((line['height_feet']*12+line['height_inches'])>=83):
            #Some players above 6'11" tall play center despite their position stating otherwise
            p_id.append(line['id'])
            f_name.append(line['first_name'])
            l_name.append(line['last_name'])
            t_id.append(line['team']['id'])
            t_name.append(line['team']['full_name'])
    #Assign next page value to page to check if != None
    page=data['meta']['next_page']
    #Sleep to avoid request limitations
    time.sleep(1)

d = {'player_id': p_id, 'first_name': f_name,
    'last_name': l_name, 'team_id': t_id, 'team_name': t_name}

#Finished player dataset
df = pd.DataFrame(data=d)
df_players=df

Once I had a dataset of all the centers in NBA history, I then gathered season average stats for each player by iterating through my list of player_ids to request data from every season between 1979-2021.

szn = 2021

while (szn >= 1979):
    
    df_init = df_players
    
    p_id=[]
    season = []
    mins = []
    fg3m = []
    fg3a = []
    fg3_pct = []
    oreb = []
    dreb = []
    reb = []
    ast = []
    stl = []
    blk = []
    
    
    my_q = build_q(df_players.player_id.tolist(), f"https://www.balldontlie.io/api/v1/season_averages?season={szn}")

    response = requests.get(my_q) 
    avgs = response.json()
    avgs = avgs['data']
    time.sleep(1)
    
    for i in range(len(avgs)):
        
        p_id.append(avgs[i]['player_id'])
        season.append(avgs[i]['season'])
        mins.append(avgs[i]['min'])
        fg3m.append(avgs[i]['fg3m'])
        fg3a.append(avgs[i]['fg3a'])
        fg3_pct.append(avgs[i]['fg3_pct'])
        oreb.append(avgs[i]['oreb'])
        dreb.append(avgs[i]['dreb'])
        reb.append(avgs[i]['reb'])
        ast.append(avgs[i]['ast'])
        stl.append(avgs[i]['stl'])
        blk.append(avgs[i]['blk'])
        
    df_temp = pd.DataFrame(data={'player_id': p_id, 'season': season,
                                'mins': mins, 'fg3m': fg3m, 'fg3a': fg3a,
                                'fg3_pct': fg3_pct, 'oreb': oreb, 'dreb': dreb,
                                'reb': reb, 'ast': ast, 'stl': stl, 'blk': blk})
    

    df_init = df_init.set_index('player_id').join(df_temp.set_index('player_id'))
    df_init = df_init.dropna()
    df_final = pd.concat([df_final,df_init])
    szn-=1

Here, we can see a snapshot of the data after cleaning:

glimpse(centers)

## Rows: 832
## Columns: 18
## Rowwise: player_id
## $ player_id  <int> 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,…
## $ first_name <chr> "Steven", "Steven", "Steven", "Steven", "Steven", "Steven",…
## $ last_name  <chr> "Adams", "Adams", "Adams", "Adams", "Adams", "Adams", "Adam…
## $ team_id    <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 3, 3, 3, 3, 3, 3, 3, 3,…
## $ team_name  <chr> "Memphis Grizzlies", "Memphis Grizzlies", "Memphis Grizzlie…
## $ season     <int> 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2006,…
## $ mins       <int> 14, 25, 25, 29, 32, 33, 26, 27, 26, 22, 34, 37, 37, 39, 36,…
## $ secs       <int> 46, 17, 10, 52, 43, 19, 40, 39, 17, 5, 51, 5, 27, 38, 15, 4…
## $ fg3m       <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.02, 0.00, 0.00, 0.00,…
## $ fg3a       <dbl> 0.00, 0.03, 0.00, 0.01, 0.03, 0.03, 0.05, 0.05, 0.01, 0.03,…
## $ fg3_pct    <dbl> 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.333, 0.000, 0.0…
## $ oreb       <dbl> 1.75, 2.84, 2.74, 3.51, 5.05, 4.89, 3.30, 3.67, 4.59, 2.29,…
## $ dreb       <dbl> 2.35, 4.63, 3.93, 4.15, 3.96, 4.61, 5.94, 5.19, 5.41, 2.67,…
## $ reb        <dbl> 4.10, 7.47, 6.66, 7.66, 9.01, 9.50, 9.24, 8.86, 10.00, 4.95…
## $ ast        <dbl> 0.53, 0.94, 0.78, 1.08, 1.16, 1.55, 2.32, 1.91, 3.37, 0.38,…
## $ stl        <dbl> 0.49, 0.54, 0.53, 1.11, 1.21, 1.48, 0.81, 0.93, 0.86, 0.35,…
## $ blk        <dbl> 0.70, 1.23, 1.11, 0.98, 1.03, 0.95, 1.08, 0.66, 0.79, 1.16,…
## $ full_name  <chr> "Steven Adams", "Steven Adams", "Steven Adams", "Steven Ada…

And a summary of the statistics:

summary(centers)

##    player_id         first_name         last_name            team_id     
##  Min.   :       3   Length:832         Length:832         Min.   : 1.00  
##  1st Qu.:     179   Class :character   Class :character   1st Qu.: 8.00  
##  Median :     325   Mode  :character   Mode  :character   Median :16.00  
##  Mean   :  832753                                         Mean   :15.47  
##  3rd Qu.:     460                                         3rd Qu.:22.25  
##  Max.   :24572055                                         Max.   :30.00  
##   team_name             season          mins            secs      
##  Length:832         Min.   :1996   Min.   : 0.00   Min.   : 0.00  
##  Class :character   1st Qu.:2012   1st Qu.:12.00   1st Qu.:15.00  
##  Mode  :character   Median :2017   Median :20.00   Median :30.00  
##                     Mean   :2015   Mean   :19.98   Mean   :29.78  
##                     3rd Qu.:2019   3rd Qu.:29.00   3rd Qu.:45.00  
##                     Max.   :2021   Max.   :39.00   Max.   :59.00  
##       fg3m             fg3a           fg3_pct            oreb      
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000  
##  1st Qu.:0.0000   1st Qu.:0.0200   1st Qu.:0.0000   1st Qu.:0.910  
##  Median :0.0200   Median :0.1300   Median :0.1820   Median :1.600  
##  Mean   :0.3171   Mean   :0.9279   Mean   :0.1872   Mean   :1.764  
##  3rd Qu.:0.4200   3rd Qu.:1.3225   3rd Qu.:0.3410   3rd Qu.:2.500  
##  Max.   :3.0000   Max.   :7.2900   Max.   :1.0000   Max.   :5.430  
##       dreb             reb              ast             stl        
##  Min.   : 0.000   Min.   : 0.000   Min.   :0.000   Min.   :0.0000  
##  1st Qu.: 2.285   1st Qu.: 3.265   1st Qu.:0.480   1st Qu.:0.2800  
##  Median : 3.790   Median : 5.410   Median :0.950   Median :0.4900  
##  Mean   : 4.148   Mean   : 5.912   Mean   :1.280   Mean   :0.5378  
##  3rd Qu.: 5.790   3rd Qu.: 8.162   3rd Qu.:1.685   3rd Qu.:0.7425  
##  Max.   :11.190   Max.   :15.990   Max.   :8.320   Max.   :1.9100  
##       blk          full_name        
##  Min.   :0.0000   Length:832        
##  1st Qu.:0.4300   Class :character  
##  Median :0.7950   Mode  :character  
##  Mean   :0.8933                     
##  3rd Qu.:1.2425                     
##  Max.   :3.6800

Analysis

To begin exploring my data, my first thought was to fit a linear model to identify the best predictors for playing time

## 
## Call:
## lm(formula = mins ~ ., data = subset)
## 
## Coefficients:
## (Intercept)    player_id         fg3m         fg3a      fg3_pct         oreb  
##   3.243e+00   -1.581e-07    7.748e+00   -1.850e+00    4.854e-01   -1.256e+01  
##        dreb          reb          ast          stl          blk  
##  -1.372e+01    1.491e+01    1.434e+00    4.021e+00    3.315e+00

## 
## Call:
## lm(formula = mins ~ ., data = subset)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.5560  -2.4811  -0.2939   2.2751  12.6629 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.243e+00  3.249e-01   9.981  < 2e-16 ***
## player_id   -1.581e-07  3.855e-08  -4.102 4.50e-05 ***
## fg3m         7.748e+00  1.722e+00   4.501 7.76e-06 ***
## fg3a        -1.850e+00  6.320e-01  -2.927  0.00352 ** 
## fg3_pct      4.854e-01  7.770e-01   0.625  0.53238    
## oreb        -1.256e+01  2.812e+01  -0.447  0.65533    
## dreb        -1.372e+01  2.812e+01  -0.488  0.62560    
## reb          1.491e+01  2.812e+01   0.530  0.59601    
## ast          1.434e+00  1.749e-01   8.199 9.29e-16 ***
## stl          4.021e+00  5.750e-01   6.994 5.55e-12 ***
## blk          3.315e+00  2.907e-01  11.404  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.754 on 821 degrees of freedom
## Multiple R-squared:  0.8615, Adjusted R-squared:  0.8598 
## F-statistic: 510.6 on 10 and 821 DF,  p-value: < 2.2e-16

Upon first inspection, looks like 3-Point field goal attempts is a solid variable to look into. Out of curiosity, let’s see the change in the correlation matrices from both 2010 and 2021 to compare.

2010 Data

2021 Data

Now we can hone in on the 3-Pointers made to see how that statistic has influenced playing time over the years

Visualizing the data

3-Point attempts over time

Fitting a linear model to determine how 3-Pointers affect playing time

Timeline depicting change in 3-Point attempts over the years

## List of 93
##  $ line                      :List of 6
##   ..$ colour       : chr "black"
##   ..$ size         : num 0.5
##   ..$ linetype     : num 1
##   ..$ lineend      : chr "butt"
##   ..$ arrow        : logi FALSE
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_line" "element"
##  $ rect                      :List of 5
##   ..$ fill         : chr "white"
##   ..$ colour       : chr "black"
##   ..$ size         : num 0.5
##   ..$ linetype     : num 1
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_rect" "element"
##  $ text                      :List of 11
##   ..$ family       : chr ""
##   ..$ face         : chr "plain"
##   ..$ colour       : chr "black"
##   ..$ size         : num 11
##   ..$ hjust        : num 0.5
##   ..$ vjust        : num 0.5
##   ..$ angle        : num 0
##   ..$ lineheight   : num 0.9
##   ..$ margin       : 'margin' num [1:4] 0points 0points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : logi FALSE
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ title                     : NULL
##  $ aspect.ratio              : NULL
##  $ axis.title                : NULL
##  $ axis.title.x              :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 1
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 2.75points 0points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.title.x.top          :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 0
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 2.75points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.title.x.bottom       : NULL
##  $ axis.title.y              :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 1
##   ..$ angle        : num 90
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 2.75points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.title.y.left         : NULL
##  $ axis.title.y.right        :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 0
##   ..$ angle        : num -90
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 0points 2.75points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.text                 :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : chr "grey30"
##   ..$ size         : 'rel' num 0.8
##   ..$ hjust        : NULL
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.text.x               :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 1
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 2.2points 0points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.text.x.top           :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : num 0
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 2.2points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.text.x.bottom        : NULL
##  $ axis.text.y               :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : num 1
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 2.2points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.text.y.left          : NULL
##  $ axis.text.y.right         :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : num 0
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 0points 2.2points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ axis.ticks                : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ axis.ticks.x              : NULL
##  $ axis.ticks.x.top          : NULL
##  $ axis.ticks.x.bottom       : NULL
##  $ axis.ticks.y              : NULL
##  $ axis.ticks.y.left         : NULL
##  $ axis.ticks.y.right        : NULL
##  $ axis.ticks.length         : 'simpleUnit' num 2.75points
##   ..- attr(*, "unit")= int 8
##  $ axis.ticks.length.x       : NULL
##  $ axis.ticks.length.x.top   : NULL
##  $ axis.ticks.length.x.bottom: NULL
##  $ axis.ticks.length.y       : NULL
##  $ axis.ticks.length.y.left  : NULL
##  $ axis.ticks.length.y.right : NULL
##  $ axis.line                 : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ axis.line.x               : NULL
##  $ axis.line.x.top           : NULL
##  $ axis.line.x.bottom        : NULL
##  $ axis.line.y               : NULL
##  $ axis.line.y.left          : NULL
##  $ axis.line.y.right         : NULL
##  $ legend.background         : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ legend.margin             : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
##   ..- attr(*, "unit")= int 8
##  $ legend.spacing            : 'simpleUnit' num 11points
##   ..- attr(*, "unit")= int 8
##  $ legend.spacing.x          : NULL
##  $ legend.spacing.y          : NULL
##  $ legend.key                : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ legend.key.size           : 'simpleUnit' num 1.2lines
##   ..- attr(*, "unit")= int 3
##  $ legend.key.height         : NULL
##  $ legend.key.width          : NULL
##  $ legend.text               :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : 'rel' num 0.8
##   ..$ hjust        : NULL
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ legend.text.align         : NULL
##  $ legend.title              :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : num 0
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ legend.title.align        : NULL
##  $ legend.position           : chr "right"
##  $ legend.direction          : NULL
##  $ legend.justification      : chr "center"
##  $ legend.box                : NULL
##  $ legend.box.just           : NULL
##  $ legend.box.margin         : 'margin' num [1:4] 0cm 0cm 0cm 0cm
##   ..- attr(*, "unit")= int 1
##  $ legend.box.background     : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ legend.box.spacing        : 'simpleUnit' num 11points
##   ..- attr(*, "unit")= int 8
##  $ panel.background          : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ panel.border              : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ panel.spacing             : 'simpleUnit' num 5.5points
##   ..- attr(*, "unit")= int 8
##  $ panel.spacing.x           : NULL
##  $ panel.spacing.y           : NULL
##  $ panel.grid                :List of 6
##   ..$ colour       : chr "grey92"
##   ..$ size         : NULL
##   ..$ linetype     : NULL
##   ..$ lineend      : NULL
##   ..$ arrow        : logi FALSE
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_line" "element"
##  $ panel.grid.major          : NULL
##  $ panel.grid.minor          :List of 6
##   ..$ colour       : NULL
##   ..$ size         : 'rel' num 0.5
##   ..$ linetype     : NULL
##   ..$ lineend      : NULL
##   ..$ arrow        : logi FALSE
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_line" "element"
##  $ panel.grid.major.x        : NULL
##  $ panel.grid.major.y        : NULL
##  $ panel.grid.minor.x        : NULL
##  $ panel.grid.minor.y        : NULL
##  $ panel.ontop               : logi FALSE
##  $ plot.background           : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ plot.title                :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : 'rel' num 1.2
##   ..$ hjust        : num 0
##   ..$ vjust        : num 1
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 5.5points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ plot.title.position       : chr "panel"
##  $ plot.subtitle             :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : num 0
##   ..$ vjust        : num 1
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 0points 0points 5.5points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ plot.caption              :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : 'rel' num 0.8
##   ..$ hjust        : num 1
##   ..$ vjust        : num 1
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 5.5points 0points 0points 0points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ plot.caption.position     : chr "panel"
##  $ plot.tag                  :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : 'rel' num 1.2
##   ..$ hjust        : num 0.5
##   ..$ vjust        : num 0.5
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ plot.tag.position         : chr "topleft"
##  $ plot.margin               : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
##   ..- attr(*, "unit")= int 8
##  $ strip.background          : list()
##   ..- attr(*, "class")= chr [1:2] "element_blank" "element"
##  $ strip.background.x        : NULL
##  $ strip.background.y        : NULL
##  $ strip.placement           : chr "inside"
##  $ strip.text                :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : chr "grey10"
##   ..$ size         : 'rel' num 0.8
##   ..$ hjust        : NULL
##   ..$ vjust        : NULL
##   ..$ angle        : NULL
##   ..$ lineheight   : NULL
##   ..$ margin       : 'margin' num [1:4] 4.4points 4.4points 4.4points 4.4points
##   .. ..- attr(*, "unit")= int 8
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ strip.text.x              : NULL
##  $ strip.text.y              :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : NULL
##   ..$ angle        : num -90
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  $ strip.switch.pad.grid     : 'simpleUnit' num 2.75points
##   ..- attr(*, "unit")= int 8
##  $ strip.switch.pad.wrap     : 'simpleUnit' num 2.75points
##   ..- attr(*, "unit")= int 8
##  $ strip.text.y.left         :List of 11
##   ..$ family       : NULL
##   ..$ face         : NULL
##   ..$ colour       : NULL
##   ..$ size         : NULL
##   ..$ hjust        : NULL
##   ..$ vjust        : NULL
##   ..$ angle        : num 90
##   ..$ lineheight   : NULL
##   ..$ margin       : NULL
##   ..$ debug        : NULL
##   ..$ inherit.blank: logi TRUE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  - attr(*, "class")= chr [1:2] "theme" "gg"
##  - attr(*, "complete")= logi TRUE
##  - attr(*, "validate")= logi TRUE

Conclusion

What did we learn?

The 3-Point shot has become more exponentially more prevalent in the last decade
Centers were hardly even attempting 3-Pointers, let alone making any 20 years ago
As it stands, the players with the most playing time also are attempting more 3s on average
My predictive model estimates that in order to maximize minutes, a center must be comfortable with attempting at least one 3-pointer in a game

Thanks for your time!

pairs <- read.csv('centers_final.csv') %>%
  select(season, mins, fg3m, reb, ast, stl, blk)

pairs <- pairs %>%
  filter(season==2021)

pairs <- pairs %>%
  select(mins, fg3m, reb, ast, stl, blk)

ggpairs(pairs, title="Correlation Matrix w/ ggpairs")