Chapter 3 Player Analysis

3.1 Dataset

The data aggregated is scraped from the OUA website. Every box score per game per season is collected and aggregated so that there are player statistics for every season from 2014-15 to 2018-19 (this is because the Player Statistics came from the OUA website which has 2014-15 data).

3.2 The Goal

The goal is to use player statistics to gather insights on how players contribute to the game and how to categorize players using unsupervised learning.

3.3 Data Preparation

The data is a subset of the player data with certain filters on the number of games played and the minutes per game. There are dataframes for every season from 2014-15 to 2018-19 with players that have played at least 15 games of at least 20 minutes per game. The games are regular season games from the U Sports division, Ontario University Athletics conference. All the variables are totals for the season except for PPG (Points per game) and MPG (Minutes per game)

3.4 K-Means Clustering

First the data will be normalized in order to prepare the data for k-means clustering. This is helpful because some statistics have very different ranges e.g. the number of points compared to the number of steals. Therefore the variables will be comparable.

K-Means Clustering is a popular unsupervised machine learning algorithm. The goal of K-Means is to group similar data points in a dataset of unlabeled data. It does this by dividing the data into k clusters where each observation belongs to the cluster closest to the mean (cluster centroid) by using a distance metric (most usually Euclidean distance).

Since K-Means clustering is an unsupervised algorithm, this means that the number of clusters is not known. However, there are techniques that can be used to find an optimal number of clusters such as the gap method, silhouette method, within-cluster sum of squares method, D - index, etc. Different techniques and configurations of the techniques will be used for each season’s clustering for finding the optimal number of clusters.

3.4.1 K-Means Results

The technique that will be used to find the optimal number of clusters for the 2014-2015 season is the D-index method (Lebart et al. 2000). The D-index is based on clustering gain on intra-cluster inertia [8]. Intra-cluster inertia can be defined as:

Figure 3.1: Intra-cluster Inertia formula.

The clustering gain should be minimized. The optimal cluster configuration can be identified by the sharp knee that corresponds to a significant decrease of the first differences of clustering gain versus the number of clusters. This knee or great jump of gain values can be identified by a significant peak in second differences of clustering gain.

Figure 3.2: Finding the Optimal Cluster using D-index for the 2014-15 season.

In the plot of D-index, we seek a significant knee (the significant peak in D-index second differences plot) around 8, that corresponds to a significant increase of the value of measure. The number of clusters that the method suggests is 8 clusters.

Figure 3.3: Cluster Plot for 2014-15 Season. The axes are the Principal Components where Dim1 is the first PC and Dim2 is the second PC. The first PC explains 35.5% of the data and the second PC explains 18.5%.

Table 3.1: Average of each variable for each cluster for the 2014-15 season

	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5	Cluster 6	Cluster 7	Cluster 8
3PointMade	31.47	40.14	12.77	19.57	2.25	17.25	23.50	19.47
3PointAttempted	81.40	112.57	37.86	64.29	8.92	46.75	74.00	56.47
Assists	38.07	56.14	22.50	47.71	22.17	36.50	59.00	35.20
Blocks	4.33	6.29	3.64	5.86	15.25	21.25	4.50	4.13
DefensiveRebounds	59.60	64.86	44.18	81.86	79.83	128.75	94.00	58.00
FieldGoalMade	84.87	118.43	42.91	87.29	78.50	132.50	149.00	50.53
FieldGoalAttempted	194.00	278.14	104.55	209.29	157.50	264.75	304.50	135.27
FreeThrowsMade	44.80	58.57	20.86	55.71	40.50	64.25	99.50	29.40
FreeThrowsAttempted	59.87	73.57	32.59	75.00	62.83	94.75	137.50	40.67
Minutes	502.93	579.86	387.45	619.14	450.75	547.25	694.00	500.93
OffensiveRebounds	25.67	16.86	19.00	25.86	44.50	52.50	26.50	16.67
PersonalFouls	39.40	35.43	39.50	50.71	46.17	33.50	44.50	44.93
Points	246.00	335.57	119.45	249.86	199.75	346.50	421.00	149.93
Rebounds	85.27	81.71	63.18	107.71	124.33	181.25	120.50	74.67
Steals	19.60	21.86	13.00	23.57	12.50	16.75	27.50	20.53
Turnovers	34.47	40.14	28.55	48.43	30.50	47.25	57.00	34.27
Home	9.53	9.00	9.27	9.14	9.50	9.50	10.50	9.47
GamesPlayed	18.73	18.29	18.00	19.00	18.92	18.75	20.00	18.93
PointsPerGame	13.15	18.39	6.64	13.19	10.59	18.47	21.05	7.95
MinutesPerGame	26.85	31.74	21.53	32.60	23.81	29.20	34.70	26.53
3P%	0.37	0.36	0.30	0.29	0.18	0.37	0.32	0.38
FG%	0.44	0.43	0.42	0.42	0.50	0.50	0.49	0.38
FT%	0.74	0.79	0.66	0.76	0.64	0.70	0.72	0.72
TrueShooting%	0.56	0.54	0.50	0.52	0.54	0.56	0.57	0.49

Table 3.2: Players from 2014-15 season with assigned clusters.

Player	Team	Cluster
15-Zachary Angelini	Brock	1
10-Connor Wood	Carleton	1
23-Philip Scrubb	Carleton	1
23-Aaron Redpath	McMaster	1
32-Joe Rocca	McMaster	1
06-Caleb Agada	Ottawa	1
12-Aaron Best	Ryerson	1
21-Adika Peter-McNeilly	Ryerson	1
9-M Sahota	Toronto	1
22-Anthony Spiridis	Western	1
06-Mitch Farrell	Windsor	1
09-Alex Campbell	Windsor	1
21-Khalid Abdel-Gabar	Windsor	1
3-Richard Iheadindu	York	1
8-Nathan Culbreath	York	1
11-Johneil Simpson	Brock	2
14-Ryan Bennett	Laurentian	2
06-Will Coulthard	Laurier	2
08-Johnny Berhanemeskel	Ottawa	2
21-Greg Faulkner	Queen’s	2
7-Jahmal Jones	Ryerson	2
22-J Clarke	Toronto	2
2-Jamal Mucket-Sobers	Algoma	3
3-AJ Andre Barder	Algoma	3
4-Thomas Chalmers	Algoma	3
6-Adam Benrabah	Algoma	3
13-J.e Pierre-Charles	Carleton	3
05-Jonathan Wallace	Guelph	3
12-Michel Clark	Guelph	3
23-Jamar Coke	Lakehead	3
09-Luke Allin	Laurier	3
4-Joey Puddister	Nipissing	3
5-Marvin Ngonadi	Nipissing	3
7-Jerron Rhodes	Nipissing	3
01-Vikas Gill	Ottawa	3
05-Mehdi Tihani	Ottawa	3
09-Matt Plunkett	Ottawa	3
10-Cy Samuels	Queen’s	3
20-Ryall Stroud	Queen’s	3
8-D Ankrah	Toronto	3
07-Jedson Tavernier	Western	3
10-Nidun Chandrakumar	York	3
4-Phillip Cunningham-Gillen	York	3
5-Gene Spagnuolo	York	3
33-Matt Marshall	Brock	4
04-Daniel Dooley	Guelph	4
08-Dwayne Harvey	Lakehead	4
15-Tychon Carter-Newman	Laurentian	4
44-Sam Hirst	Laurentian	4
5-Jaspreet Gill	Waterloo	4
08-Quinn Henderson	Western	4
31-Guillaume Boucard	Carleton	5
21-Trevor Thompson	Guelph	5
22-Anthony McIntosh	Lakehead	5
24-Bacarius Dinkins	Lakehead	5
15-Aiddian Walters	Laurier	5
20-Kyrie Coleman	Laurier	5
10-Taylor Black	McMaster	5
22-Rohan Boney	McMaster	5
23-Marcos Clennon	Nipissing	5
04-Gabriel Gonthier-Dubue	Ottawa	5
15-Kadeem Green	Ryerson	5
07-Evan Matthews	Windsor	5
11-Thomas Scrubb	Carleton	6
7-D Johnson	Toronto	6
12-Rotimi Osuntola	Windsor	6
22-Nick Tufegdzich	York	6
6-Myles Charvis	Waterloo	7
12-Greg Morrow	Western	7
10-Sean Clendinning	Algoma	8
5-Brett Zufelt	Algoma	8
03-Gavin Resch	Carleton	8
21-Alex Robichaud	Lakehead	8
11-David Aromolaran	Laurentian	8
02-James Agyeman	Laurier	8
03-Garrison Thomas	Laurier	8
25-Adam Presutti	McMaster	8
6-Jordon Campbell	Nipissing	8
12-Tanner Graham	Queen’s	8
5-S Usher	Toronto	8
3-Jon Ravenhorst	Waterloo	8
7-Ben Davis	Waterloo	8
05-Tom Filgiano	Western	8
10-Mike Rocca	Windsor	8

Each cluster can be categorized as a type of player.

Cluster 1: Efficient Playmakers & Scorers This cluster of players have the most assists and the second most points per game. They have a big defensive impact through the number of steals they get and can control the tempo well and score.

Cluster 2: All-Around Players These players can get rebounds, pass and score well.

Cluster 3: Dominant Big Men These players are the most dominant big men in the league with the most rebounds (defensive and offensive), blocks, and points.

Cluster 4: Smart Catch & Shoot Players These players make the best decisions and turnover the ball the fewest. They do not dribble the ball much and are the most efficient shooters.

Cluster 5: Aggressive Defenders These players are aggressive and foul the most out of all the other clusters. They have a bigger impact on defense since they do not shoot well.

Cluster 6: Role Players These players contribute to many plays and work both offensively and defensively.

Cluster 7: Second Tier Playmakers These players are less dominant playmakers that can still score efficiently.

Cluster 8: Second Tier Small Players These players play small but do not shoot as efficiently as the other players or create as many plays.

3.4.2 2015-16 Season

For this season, the elbow method [9] will be used to find the optimal number of clusters. The elbow method looks at the percentage of variance explained as a function of the number of clusters: One should choose a number of clusters so that adding another cluster does not give much better modeling of the data. More precisely, if one plots the percentage of variance explained by the clusters against the number of clusters, the first clusters will add much information (explain a lot of variance), but at some point the marginal gain will drop, giving an angle in the graph. The number of clusters is chosen at this point, hence the “elbow criterion”. This “elbow” cannot always be unambiguously identified.

Figure 3.4: Elbow Method for finding the optimal number of clusters for the 2015-16 season

The number of clusters that will be used for this season is 6 for this season. Below are tables to show the average statistics for each cluster and also which players belong to which cluster.

Figure 3.5: Cluster Plot of 2015-16 Season

Table 3.3: Average of each variable for each cluster for the 2015-16 season

	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5	Cluster 6
3PointMade	14.85	22.62	18.75	13.16	31.75	44.57
3PointAttempted	48.15	67.88	55.75	41.84	86.00	133.29
Assists	39.38	57.12	43.25	24.91	40.62	52.71
Blocks	7.85	4.75	13.50	7.41	6.44	3.29
DefensiveRebounds	72.00	72.50	111.25	51.62	63.56	68.71
FieldGoalMade	101.38	56.25	150.50	48.56	85.62	111.14
FieldGoalAttempted	236.23	150.62	317.75	119.72	196.88	290.00
FreeThrowsMade	59.38	28.75	99.00	23.69	32.88	55.14
FreeThrowsAttempted	83.46	40.12	130.25	34.47	43.44	74.00
Minutes	564.00	620.00	631.50	419.31	490.81	639.14
OffensiveRebounds	30.77	25.75	44.50	21.50	18.19	14.57
PersonalFouls	44.92	48.88	47.25	39.56	38.44	35.57
Points	277.00	163.88	418.75	133.97	235.88	322.00
Rebounds	102.77	98.25	155.75	73.12	81.75	83.29
Steals	23.85	25.00	30.25	15.72	18.88	24.14
Turnovers	49.46	40.50	58.00	26.00	34.50	49.57
Home	9.69	9.62	9.75	9.31	9.25	9.71
GamesPlayed	19.08	19.38	19.00	18.38	18.25	19.43
PointsPerGame	14.58	8.47	22.02	7.34	12.99	16.58
MinutesPerGame	29.60	31.98	33.18	22.87	26.96	32.90
3P%	0.26	0.32	0.31	0.28	0.38	0.33
FG%	0.43	0.37	0.47	0.41	0.44	0.39
FT%	0.72	0.72	0.76	0.71	0.77	0.76
TrueShooting%	0.50	0.48	0.55	0.49	0.54	0.50

Table 3.4: Players from 2015-16 season with assigned clusters.

Player	Team	Cluster
10-Sean Clendinning	Algoma	1
24-Bacarius Dinkins	Lakehead	1
11-David Aromolaran	Laurentian	1
44-Sam Hirst	Laurentian	1
12-Matt Chesson	Laurier	1
03-Leon Alexander	McMaster	1
23-Aaron Redpath	McMaster	1
13-Marcus Lewis	Nipissing	1
21-Adika Peter-McNeilly	Ryerson	1
07-Ben Davis	Waterloo	1
10-Peter Scholtes	Western	1
22-Anthony Spiridis	Western	1
08-Nathan Culbreath	York	1
33-Matt Marshall	Brock	2
03-Nick Burke	Lakehead	2
21-Alexandre Robichaud	Lakehead	2
02-Simon Mikre	Laurier	2
04-Joey Puddister	Nipissing	2
06-Dylan Phillips	Waterloo	2
05-Tom Filgiano	Western	2
10-Mike Rocca	Windsor	2
13-Dani Elgadi	Brock	3
06-Devin Johnson	Toronto	3
12-Greg Morrow	Western	3
09-Alex Campbell	Windsor	3
05-Brett Zufelt	Algoma	4
06-Nathan Riley	Algoma	4
13-Reng Gum	Algoma	4
25-Tyler Brown	Brock	4
15-Drew Walford	Guelph	4
31-Jack Beatty	Guelph	4
10-Nick Simon	Laurentian	4
32-Joseph Sykes	Laurentian	4
03-Garrison Thomas	Laurier	4
04-Trevon McNeil	McMaster	4
21-David McCulloch	McMaster	4
22-Rohan Boney	McMaster	4
05-Marvin Ngonadi	Nipissing	4
07-Jerron Rhodes	Nipissing	4
09-Kalil Langston	Nipissing	4
01-Vikas Gill	Ottawa	4
05-Mehdi Tihani	Ottawa	4
09-Matt Plunkett	Ottawa	4
13-Nathan McCarthy	Ottawa	4
13-Sammy Ayisi	Queen’s	4
20-Ryall Stroud	Queen’s	4
06-Roshane Roberts	Ryerson	4
22-Juwon Grannum	Ryerson	4
05-Sage Usher	Toronto	4
09-Manny Sahota	Toronto	4
21-Daniel Johansson	Toronto	4
06-Alex Coote	Western	4
07-Jedson Tavernier	Western	4
15-Micah Kirubel	Windsor	4
22-Tyler Persaud	Windsor	4
04-Philip Gillen	York	4
05-Gene Spagnuolo	York	4
03-Andre Barber	Algoma	5
14-Ryan Bennett	Brock	5
03-Gavin Resch	Carleton	5
10-Connor Wood	Carleton	5
31-Guillaume Boucard	Carleton	5
41-Kaza Kajami-Keane	Carleton	5
04-Daniel Dooley	Guelph	5
05-Jonathan Wallace	Guelph	5
11-Taylor Boers	Guelph	5
05-Troy Joseph	McMaster	5
12-Tanner Graham	Queen’s	5
04-Ammanuel Diressa	Ryerson	5
12-Aaron Best	Ryerson	5
04-Devon Williams	Toronto	5
11-Marko Kovac	Windsor	5
11-Tommy Hobbs	York	5
11-Johneil Simpson	Brock	6
05-Henry Tan	Lakehead	6
21-Anthony Iacoe	Laurentian	6
06-Will Coulthard	Laurier	6
11-Mike L’Africain	Ottawa	6
03-Jon Ravenhorst	Waterloo	6
13-Isiah Osborne	Windsor	6

3.4.3 2016-17 Season

Figure 3.6: Silhouette Method for finding the optimal number of clusters for the 2016-17 season

The Silhouette method suggests 2 as the optimal number of clusters for this season. This is possibly separating the players into forwards/centers and guards. Below are tables to show the average statistics for each cluster and also which players belong to which cluster.

Figure 3.7: Cluster Plot of 2016-17 Season

Table 3.5: Average of each variable for each cluster for the 2016-17 season

	Cluster 1	Cluster 2
3PointMade	16.67	25.09
3PointAttempted	51.80	73.85
Assists	30.02	42.82
Blocks	4.92	9.18
DefensiveRebounds	53.12	83.88
FieldGoalMade	55.86	101.97
FieldGoalAttempted	136.37	234.88
FreeThrowsMade	24.86	50.88
FreeThrowsAttempted	37.14	71.27
Minutes	452.90	559.09
OffensiveRebounds	20.53	30.91
PersonalFouls	35.53	44.12
Points	153.24	279.91
Rebounds	73.65	114.79
Steals	16.88	23.67
Turnovers	28.86	47.39
Home	9.14	9.70
GamesPlayed	18.43	19.12
PointsPerGame	8.34	14.70
MinutesPerGame	24.59	29.24
3P%	0.28	0.30
FG%	0.41	0.44
FT%	0.68	0.71
TrueShooting%	0.50	0.52

Table 3.6: Players from 2016-17 season with assigned clusters.

Player	Team	Cluster
06-Nathan Riley	Algoma	1
13-Reng Gum	Algoma	1
09-Daniel Cayer	Brock	1
14-Ryan Bennett	Brock	1
25-Tyler Brown	Brock	1
03-Marcus Anderson	Carleton	1
42-Eddie Ekiyor	Carleton	1
04-Daniel Dooley	Guelph	1
05-Jonathan Wallace	Guelph	1
11-Taylor Boers	Guelph	1
15-Drew Walford	Guelph	1
44-Ahmed Haroon	Guelph	1
03-Nick Burke	Lakehead	1
05-Henry Tan	Lakehead	1
21-Alexandre Robichaud	Lakehead	1
44-OJ Watson	Laurentian	1
02-Matthew Minutillo	Laurier	1
04-Chuder Teny	Laurier	1
08-Vlad Matovic	Laurier	1
10-Owen Coulthard	Laurier	1
12-Elliot Ormond	McMaster	1
44-Lazar Kojovic	McMaster	1
06-Jordon Campbell	Nipissing	1
07-Jerron Rhodes	Nipissing	1
10-Ismael Kaba	Nipissing	1
21-Justin Shaver	Nipissing	1
22-Jaaden Lewis	Nipissing	1
09-Matt Plunkett	Ottawa	1
10-Brandon Robinson	Ottawa	1
15-Brody Maracle	Ottawa	1
24-Adam Presutti	Ottawa	1
05-Isse Ibrahim	Queen’s	1
08-Jesse Graham	Queen’s	1
13-Sammy Ayisi	Queen’s	1
14-Keevon Small	Ryerson	1
15-Myles Charvis	Ryerson	1
22-Juwon Grannum	Ryerson	1
04-Reilly Reid	Toronto	1
05-Sage Usher	Toronto	1
21-Daniel Johansson	Toronto	1
07-Ben Davis	Waterloo	1
05-Eric McDonald	Western	1
07-Jedson Tavernier	Western	1
11-Cam Morris	Western	1
13-Ian Smart	Western	1
20-Nikola Farkic	Western	1
20-Lucas Orlita	Windsor	1
22-Tyler Persaud	Windsor	1
10-Nidun Chandrakumar	York	1
10-Sean Clendinning	Algoma	2
22-Jermaine Lyle	Algoma	2
11-Johneil Simpson	Brock	2
13-Dani Elgadi	Brock	2
10-Connor Wood	Carleton	2
41-Kaza Kajami-Keane	Carleton	2
24-Bacarius Dinkins	Lakehead	2
10-Kadre Gray	Laurentian	2
11-David Aromolaran	Laurentian	2
23-Nelson Yengue	Laurentian	2
12-Matt Chesson	Laurier	2
13-Tevaun Kokko	Laurier	2
11-Connor Gilmore	McMaster	2
21-David McCulloch	McMaster	2
22-Rohan Boney	McMaster	2
13-Marcus Lewis	Nipissing	2
05-Jean Emmanuel Pierre-Charles	Ottawa	2
06-Caleb Agada	Ottawa	2
12-Tanner Graham	Queen’s	2
04-Ammanuel Diressa	Ryerson	2
21-Adika Peter-McNeilly	Ryerson	2
06-Devin Johnson	Toronto	2
03-Jon Ravenhorst	Waterloo	2
04-Simon Petrov	Waterloo	2
20-Mike Pereira	Waterloo	2
23-Justin Hardy	Waterloo	2
42-Nedim Hodzic	Waterloo	2
08-Eriq Jenkins	Western	2
12-Omar Shiddo	Western	2
05-Micqueel Martin	Windsor	2
10-Mike Rocca	Windsor	2
11-Jayden Frederick	York	2
20-Brandon Ramirez	York	2

3.4.4 2017-18 Season

Figure 3.8: Finding the Optimal Cluster using D-index for the 2017-18 season.

The optimal number of clusters suggested by the D-index method is 5 for this season. This is possibly separating the players into the actual posistions (Point Guard, Shooting Guard, Small Forward, Power Forward, and Center). Below are tables to show the average statistics for each cluster and also which players belong to which cluster.

Figure 3.9: Cluster Plot of 2017-18 Season

Table 3.7: Average of each variable for each cluster for the 2017-18 season

	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5
3PointMade	46.75	16.23	23.72	28.11	29.50
3PointAttempted	127.75	49.32	71.44	85.00	86.33
Assists	57.92	33.95	41.36	64.17	85.33
Blocks	3.83	6.68	10.04	11.06	11.33
DefensiveRebounds	70.17	60.45	74.40	93.22	137.00
FieldGoalMade	133.00	53.00	81.40	109.00	156.33
FieldGoalAttempted	309.83	129.64	189.52	255.67	340.33
FreeThrowsMade	58.42	20.86	36.56	55.17	117.17
FreeThrowsAttempted	75.50	33.68	52.52	77.28	144.00
Minutes	606.67	496.41	571.40	703.78	750.17
OffensiveRebounds	22.17	23.73	26.32	30.72	40.17
PersonalFouls	49.33	44.00	47.08	52.89	54.00
Points	371.17	143.09	223.08	301.28	459.33
Rebounds	92.33	84.18	100.72	123.94	177.17
Steals	26.50	17.73	19.88	31.11	27.67
Turnovers	48.58	31.09	34.00	49.33	65.33
Home	11.25	11.36	11.44	11.56	11.50
GamesPlayed	22.25	22.50	22.72	23.22	23.17
PointsPerGame	16.82	6.44	9.88	13.00	19.95
MinutesPerGame	27.36	22.11	25.22	30.34	32.43
3P%	0.37	0.27	0.29	0.30	0.27
FG%	0.43	0.41	0.43	0.43	0.46
FT%	0.77	0.64	0.71	0.71	0.82
TrueShooting%	0.54	0.48	0.52	0.52	0.56

Table 3.8: Players from 2017-18 season with assigned clusters.

Player	Team	Cluster
10-Ian Nash	Algoma	1
11-Johneil Simpson	Brock	1
35-Cassidy Ryan	Brock	1
10-Yasiin Joseph	Carleton	1
08-Mor Menashe	Lakehead	1
06-Ali Sow	Laurier	1
11-Tevaun Kokko	Laurier	1
11-Miles Seward	McMaster	1
22-Jaz Bains	Queen’s	1
04-Manny Diressa	Ryerson	1
10-Marko Kovac	Western	1
12-Omar Shiddo	Western	1
07-Pedro Costa	Algoma	2
09-Kascius Small-Martin	Brock	2
03-Marcus Anderson	Carleton	2
15-Drew Walford	Guelph	2
03-Darnell Curtin	Lakehead	2
24-Litha Ncanisa	Laurentian	2
03-Ntore Habimana	Laurier	2
25-Andre Toic	McMaster	2
05-Marvin Ngonadi	Nipissing	2
07-Jerron Rhodes	Nipissing	2
10-Ismael Kaba	Nipissing	2
12-Gage Sabean	Ottawa	2
15-Brody Maracle	Ottawa	2
04-Harry Range	Queen’s	2
10-Filip Vujadinovic	Ryerson	2
20-Nikola Farkic	Western	2
15-Damian Persaud	Windsor	2
21-Lucas Wood	Windsor	2
10-Gene Spagnuolo	York	2
11-Prince Kamunga	York	2
13-Nana Adu-Poku	York	2
15-Ricky Hudson	York	2
09-Cailum White	Algoma	3
13-Reng Gum	Algoma	3
22-Jermaine Lyle	Algoma	3
15-Daniel Cayer	Brock	3
25-Tyler Brown	Brock	3
13-Munis Tutu	Carleton	3
42-Eddie Ekiyor	Carleton	3
05-Jonathan Wallace	Guelph	3
11-Taylor Boers	Guelph	3
21-Anthony Iacoe	Laurentian	3
02-Matt Minutillo	Laurier	3
10-Matt Quiring	McMaster	3
02-Sean Stoqua	Ottawa	3
03-Calvin Epistola	Ottawa	3
05-Jean Emmanuel Pierre-Charles	Ottawa	3
06-Mike Shoveller	Queen’s	3
07-Quinton Gray	Queen’s	3
05-Roshane Roberts	Ryerson	3
11-Christopher Barrett	Toronto	3
21-Daniel Johansson	Toronto	3
22-Nikola Paradina	Toronto	3
15-David Ramon Prados	Waterloo	3
09-Henry Tan	Western	3
05-Anthony Zrvnar	Windsor	3
08-Gianmarco Luciani	York	3
06-Nathan Riley	Algoma	4
04-Daniel Dooley	Guelph	4
23-Nick Burke	Lakehead	4
11-David Aromolaran	Laurentian	4
23-Nelson Yengue	Laurentian	4
04-Kareem Collins	McMaster	4
13-Marcus Lewis	Nipissing	4
22-Jaaden Lewis	Nipissing	4
10-Brandon Robinson	Ottawa	4
12-Tanner Graham	Queen’s	4
07-Myles Charvis	Ryerson	4
08-Jean-Victor Mukama	Ryerson	4
04-Reilly Reid	Toronto	4
05-Sage Usher	Toronto	4
20-Justin Hardy	Waterloo	4
08-Eriq Jenkins	Western	4
11-Marcus Jones	Windsor	4
20-Lucas Orlita	Windsor	4
13-Dani Elgadi	Brock	5
10-Kadre Gray	Laurentian	5
21-David McCulloch	McMaster	5
04-Simon Petrov	Waterloo	5
42-Nedim Hodzic	Waterloo	5
10-Mike Rocca	Windsor	5

3.4.5 2018-19 Season

Figure 3.10: Finding the Optimal Cluster using D-index for the 2018-19 season.

The optimal number of clusters suggested for the 2018-19 season is 4. Below are tables to show the average statistics for each cluster and also which players belong to which cluster.

Figure 3.11: Cluster Plot of 2018-19 Season

Table 3.9: Average of each variable for each cluster for the 2018-19 season

	Cluster 1	Cluster 2	Cluster 3	Cluster 4
3PointMade	25.24	75.50	18.74	38.00
3PointAttempted	79.55	205.75	58.26	106.56
Assists	51.12	70.75	29.81	53.06
Blocks	9.03	4.25	6.85	11.12
DefensiveRebounds	83.12	96.00	60.33	114.81
FieldGoalMade	91.48	192.75	62.52	132.25
FieldGoalAttempted	215.67	435.75	150.70	308.19
FreeThrowsMade	40.79	105.00	28.93	81.19
FreeThrowsAttempted	58.48	130.75	40.74	108.38
Minutes	613.58	775.25	478.74	708.94
OffensiveRebounds	28.67	22.00	20.56	36.44
PersonalFouls	52.00	48.50	40.37	50.38
Points	249.00	566.00	172.70	383.69
Rebounds	111.79	118.00	80.89	151.25
Steals	24.64	31.00	15.96	24.69
Turnovers	37.42	68.00	29.00	50.12
Home	11.55	11.50	10.33	11.38
GamesPlayed	22.73	23.00	20.52	22.88
PointsPerGame	11.00	24.88	8.65	16.80
MinutesPerGame	27.05	33.72	23.51	30.99
3P%	0.29	0.36	0.29	0.33
FG%	0.43	0.44	0.42	0.43
FT%	0.69	0.79	0.70	0.75
TrueShooting%	0.51	0.57	0.51	0.54

Table 3.10: Players from 2018-19 season with assigned clusters.

Player	Team	Cluster
03-Elijah Butler	Algoma	1
08-David Bokanga	Algoma	1
15-Daniel Cayer	Brock	1
25-Tyler Brown	Brock	1
11-Tj Lall	Carleton	1
13-Munis Tutu	Carleton	1
42-Eddie Ekiyor	Carleton	1
22-Rasheed Weekes	Guelph	1
08-Lock Lam	Lakehead	1
23-Nick Burke	Lakehead	1
21-Anthony Iacoe	Laurentian	1
02-Matt Minutillo	Laurier	1
03-Ntore Habimana	Laurier	1
05-Jackson Mayers	Laurier	1
11-Justin Hill	Nipissing	1
03-Calvin Epistola	Ottawa	1
07-Mackenzie Morrison	Ottawa	1
10-Brandon Robinson	Ottawa	1
07-Quinton Gray	Queen’s	1
23-Jayden Frederick	Ryerson	1
09-Evan Shadkami	Toronto	1
11-Christopher Barrett	Toronto	1
21-Daniel Johansson	Toronto	1
22-Nikola Paradina	Toronto	1
08-Eriq Jenkins	Western	1
13-Julian Walker	Western	1
20-Nikola Farkic	Western	1
08-Chris Poloniato	Windsor	1
11-Telloy Simon	Windsor	1
14-Thomas Kennedy	Windsor	1
20-Lucas Orlita	Windsor	1
02-Chevon Brown	York	1
05-DeAndrae Pierre	York	1
11-Johneil Simpson	Brock	2
10-Kadre Gray	Laurentian	2
06-Ali Sow	Laurier	2
12-Omar Shiddo	Western	2
10-Michael Vos Otin	Brock	3
03-Marcus Anderson	Carleton	3
10-Yasiin Joseph	Carleton	3
05-Aaron Nugent	Guelph	3
21-Davarius Wright	Lakehead	3
22-Josis Mikia-Thomas	Laurentian	3
24-Litha Ncanisa	Laurentian	3
32-Gaetan Chamand	Laurentian	3
23-Sefa Otchere	McMaster	3
32-Jordan Henry	McMaster	3
05-Marvin Ngonadi	Nipissing	3
08-Jordan Roberts	Nipissing	3
12-Quintin Ashitei	Nipissing	3
04-Harry Range	Queen’s	3
05-Yusuf Ali	Ryerson	3
10-Filip Vujadinovic	Ryerson	3
14-Keevon Small	Ryerson	3
04-Simon Petrov	Waterloo	3
05-Colin Connors	Waterloo	3
07-Jeff Baradziej	Waterloo	3
15-David Ramon Prados	Waterloo	3
23-Justin Malnerich	Waterloo	3
09-Marko Kovac	Western	3
10-Anthony Zrvnar	Windsor	3
04-Prince Kamunga	York	3
08-Gianmarco Luciani	York	3
10-Gene Spagnuolo	York	3
06-Nathan Riley	Algoma	4
35-Cassidy Ryan	Brock	4
15-Malcolm Glanville	Guelph	4
32-Tommy Yanchus	Guelph	4
40-Banky Alade	Guelph	4
01-Isaiah Traylor	Lakehead	4
11-Connor Gilmore	McMaster	4
21-David McCulloch	McMaster	4
13-Marcus Lewis	Nipissing	4
12-Gage Sabean	Ottawa	4
41-Guillaume Pepin	Ottawa	4
03-Jaz Bains	Queen’s	4
12-Tanner Graham	Queen’s	4
07-Myles Charvis	Ryerson	4
08-JV Mukama	Ryerson	4
42-Nedim Hodzic	Waterloo	4

3.5 Conclusion

Unsupervised learning used on basketball data can be very helpful. It can be used to categorize players and to see what their style of play is. It can also be used for match-ups and for predicting important players. For instance, if you find that a player was in the same cluster as the catch and shoot players, a coach can assign an appropriate defender. Knowing the style of play for your opponents is very useful for defensive purposes. In my opinion the higher the number of clusters assigned, the better because it would distinguish the type of player more.