Lecture 26 – Visualizing Two Numerical Variables

Data 6, Summer 2021

from datascience import *
import numpy as np
Table.interactive_plots()

Our first dataset today comes from Basketball Reference. It contains per-game averages of players in the 2019-2020 NBA season.

Run the cell below to load it in, select the relevant columns, and do some data cleaning.

Note: Most of the interesting data comes from the "better" players in the league; we will only look at players who averaged at least 10 points per game in the season. This isn't perfect, since there were plenty of good players who averaged less than 10 points per game.

nba = Table.read_table('data/nba-2020.csv') \
           .select('Player', 'Pos', 'Tm', 'PTS', 'TRB', 'AST', '3PA', '3P%') \
           .where('3PA', are.not_equal_to(0))

def remove_code(name):
    return name[:name.index('\\')]

def get_court(pos):
    if 'G' in pos:
        return 'Guard'
    else:
        return 'Forward'

nba = nba.with_columns('Player', nba.apply(remove_code, 'Player'),
                       'Pos', nba.apply(get_court, 'Pos')) \
         .where('PTS', are.above(10))

nba

Player	Pos	Tm	PTS	TRB	AST	3PA	3P%
Bam Adebayo	Forward	MIA	15.9	10.2	5.1	0.2	0.143
LaMarcus Aldridge	Forward	SAS	18.9	7.4	2.4	3	0.389
Jarrett Allen	Forward	BRK	11.1	9.6	1.6	0.1	0
Giannis Antetokounmpo	Forward	MIL	29.5	13.6	5.6	4.7	0.304
Carmelo Anthony	Forward	POR	15.4	6.3	1.5	3.9	0.385
OG Anunoby	Forward	TOR	10.6	5.3	1.6	3.3	0.39
D.J. Augustin	Guard	ORL	10.5	2.1	4.6	3.5	0.348
Deandre Ayton	Forward	PHO	18.2	11.5	1.9	0.3	0.231
Marvin Bagley III	Forward	SAC	14.2	7.5	0.8	1.7	0.182
Lonzo Ball	Guard	NOP	11.8	6.1	7	6.3	0.375

... (163 rows omitted)

A description of each column:

• 'Player': name
• 'Pos': general position (either Forward or Guard)
• 'Tm': abbreviated team
• 'PTS': average number of points scored per game
• 'TRB': average number of rebounds per game (a player receives a rebound when they grab the ball after someone misses)
• 'AST': average number of assists per game (a player receives an assist when they pass the ball to someone who then scores)
• '3PA': average number of three-point shots attempted per game (a three point shot is one from behind a certain line, which is between 22-24 feet from the basket)
• '3P%': average proportion of three-point shots that go in

Review – bar charts and histograms

Bar charts

nba.group('Pos', np.mean).select('Pos', 'PTS mean', 'TRB mean', 'AST mean')

Pos	PTS mean	TRB mean	AST mean
Forward	15.6297	6.68901	2.41099
Guard	16.7463	4.00244	4.45244

nba.group('Pos', np.mean).select('Pos', 'PTS mean', 'TRB mean', 'AST mean').barh('Pos')

Histograms

nba.hist('PTS', density = False, bins = np.arange(10, 40, 2.5),
         width = 400, height = 600)

nba.hist('TRB', density = False, group = 'Pos', bins = np.arange(17),
         xaxis_title = 'Rebounds',
         title = 'Distribution of Rebounds')

/opt/conda/lib/python3.8/site-packages/datascience/tables.py:920: VisibleDeprecationWarning:

Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray

Scatter plots

example_data = Table().with_columns(
    'x', np.array([1, 4, 4, 3, 6]),
    'y', np.array([-1, 2, 8, 0, 1])
)

example_data

x	y
1	-1
4	2
4	8
3	0
6	1

example_data.scatter('x', 'y', s = 50, width = 500, height = 500)

nba

Player	Pos	Tm	PTS	TRB	AST	3PA	3P%
Bam Adebayo	Forward	MIA	15.9	10.2	5.1	0.2	0.143
LaMarcus Aldridge	Forward	SAS	18.9	7.4	2.4	3	0.389
Jarrett Allen	Forward	BRK	11.1	9.6	1.6	0.1	0
Giannis Antetokounmpo	Forward	MIL	29.5	13.6	5.6	4.7	0.304
Carmelo Anthony	Forward	POR	15.4	6.3	1.5	3.9	0.385
OG Anunoby	Forward	TOR	10.6	5.3	1.6	3.3	0.39
D.J. Augustin	Guard	ORL	10.5	2.1	4.6	3.5	0.348
Deandre Ayton	Forward	PHO	18.2	11.5	1.9	0.3	0.231
Marvin Bagley III	Forward	SAC	14.2	7.5	0.8	1.7	0.182
Lonzo Ball	Guard	NOP	11.8	6.1	7	6.3	0.375

... (163 rows omitted)

Example 1

nba.scatter('PTS', 'AST')

Observation: On average, as the number of points a player averages increases, the number of assists they average also increases.

Example 2

nba.where('Pos', 'Forward') \
   .scatter('TRB', '3PA',
           xaxis_title = 'Rebounds Per Game (TRB)',
           yaxis_title = 'Three-Point Attempts Per Game (3PA)',
           title = '3PA vs. TRB for Forwards',
           width = 800,
           height = 500)

Observation: on average, as the number of rebounds a player averages per game increases, the number of three point attempts they average per game decreases.

Quick Check 1

nba.where('3PA', are.above(2)) \
   .scatter('PTS', '3P%',
            xaxis_title = 'Points Per Game (PTS)', yaxis_title = 'Three-Point Percentage (3P%)',
            title = '3P% vs. PTS for Players with at least 2 3PA',
            width = 700, height = 500)

Observation: on average, as the number of points per game a player averages increases, three-point percentage neither increases nor decreases. (In other terms – it appears that PTS and 3P% are uncorrelated.)

More customization

Point size

nba.scatter('PTS', '3P%', s = 40)

nba.scatter('PTS', '3P%', s = 40, sizes = '3PA')

Point color by grouping

nba.scatter('TRB', '3PA', group = 'Pos', s = 30)

Observation: Guards tend to have fewer rebounds and more three-point attempts than forwards, who tend to have more rebounds and fewer three-point attempts.

Labels

nba.where('PTS', are.above(25)) \
   .scatter('PTS', 'AST',
           labels = 'Player',
           s = 30,
           width = 500,
           height = 500)

nba.where('PTS', are.above(20)) \
   .scatter('PTS', 'AST',
           labels = 'Player',
           s = 30,
           sizes = '3PA',
           title = 'Players Averaging at least 20 PTS')

Line plots

nba_yearly = Table.read_table('data/nba-league-averages.csv') \
                  .select('Season', 'PTS', 'FGA', '3PA', '3P%', 'Pace')
nba_yearly = nba_yearly.with_columns('Season', np.arange(2021, 1979, -1))
nba_yearly

Season	PTS	FGA	3PA	3P%	Pace
2021	111.7	88.3	34.7	0.367	99.2
2020	111.8	88.8	34.1	0.358	100.3
2019	111.2	89.2	32	0.355	100
2018	106.3	86.1	29	0.362	97.3
2017	105.6	85.4	27	0.358	96.4
2016	102.7	84.6	24.1	0.354	95.8
2015	100	83.6	22.4	0.35	93.9
2014	101	83	21.5	0.36	93.9
2013	98.1	82	20	0.359	92
2012	96.3	81.4	18.4	0.349	91.3

... (32 rows omitted)

Our second dataset also comes from Basketball Reference. This dataset contains team-based average statistics for each year.

A little bit about our new dataset:

• 'Season': the second calendar year for each season (e.g. 2018 refers to the 2017-18 season)
• 'FGA': the average number of field goal attempts (shot attempts) per game
• 'Pace': the average number of times a team had possession of the ball per game

Example 1

nba_yearly.plot('Season', 'Pace')

Observation: The league slowed down in the late 90s and early 2000s, but is speeding back up.

Example 2

nba_yearly.plot('Season', '3PA',
               yaxis_title = 'Three-Point Attempts (3PA)',
               title = 'Three-Point Attempts Per Season',
               width = 700)

Observation: The three-point shot has rapidly increased in popularity over the past decade.

Example 3

nba_yearly.select('Season', 'FGA', '3PA')

Season	FGA	3PA
2021	88.3	34.7
2020	88.8	34.1
2019	89.2	32
2018	86.1	29
2017	85.4	27
2016	84.6	24.1
2015	83.6	22.4
2014	83	21.5
2013	82	20
2012	81.4	18.4

... (32 rows omitted)

# Notice how we only supplied `plot` with a single argument
nba_yearly.select('Season', 'FGA', '3PA').plot('Season')

Quick Check 2

champ = nba_yearly.take(np.arange(1, 7)).select('Season', 'PTS', '3PA', 'Pace').with_columns(
    'Champion', np.array(['LAL', 'TOR', 'GSW', 'GSW', 'CLE', 'GSW'])
).select(0, -1, 1, 2, 3)

champ

Season	Champion	PTS	3PA	Pace
2020	LAL	111.8	34.1	100.3
2019	TOR	111.2	32	100
2018	GSW	106.3	29	97.3
2017	GSW	105.6	27	96.4
2016	CLE	102.7	24.1	95.8
2015	GSW	100	22.4	93.9

champ.select('Season', 'Pace').barh('Season')

champ.scatter('PTS', 'Pace', s = 100, labels = 'Champion')

champ.scatter('PTS', 'Pace', s = 100, labels = 'Season')

champ.select('Season', 'PTS', 'Pace').plot('Season')