Archetypal Ballers and Ternary Plots

M. Edward (Ed) Borasky (@znmeb_dfs)

February 9, 2017

Archetypal Analysis (Eugster and Leisch 2009)

Goal:
- Dimensionality reduction
- Reduce a dataset with 17 box score metrics to three archetypes
- Represent players’ skills in terms of the archetypes
Inputs:
- Player box scores for the season (2016-17 to date)
- About 450 players
Outputs:
- Archetype table
- Player table

The Three Archetypes

Weighted box score metrics
Each archetype represents a skill set
- Front: skills for a frontcourt player (Center, Power Forward, Small Forward)
  - dominated by rebounds
- Back: skills for a backcourt player (Point Guard, Shooting Guard)
  - dominated by three-point shots
- Bench: the “bad” archetype - players with low overall skills

The Player Table

For each player, the percentage of a player’s skill in each archetype
Total of Front, Back and Bench for each player is 1.0
Sum of Front and Back represents Overall skill
The archetypal player is the one with the largest value for the archetype
So who are the archetypal players?

Top Twelve Backcourt

Player	Position	Team	Back	Front	Overall
James Harden	PG	Houston	1.0000	0.0000	1.0000
Russell Westbrook	PG	Oklahoma City	0.9997	0.0000	0.9997
Stephen Curry	PG	Golden State	0.9991	0.0000	0.9991
Kyle Lowry	PG	Toronto	0.9991	0.0000	0.9991
Isaiah Thomas	PG	Boston	0.9991	0.0000	0.9991
Damian Lillard	PG	Portland	0.9988	0.0000	0.9988
Kemba Walker	PG	Charlotte	0.9921	0.0000	0.9921
John Wall	PG	Washington	0.9461	0.0528	0.9989
CJ McCollum	SG	Portland	0.9311	0.0677	0.9988
Eric Bledsoe	PG	Phoenix	0.8910	0.1080	0.9989
Kyrie Irving	PG	Cleveland	0.8875	0.0000	0.8875
Devin Booker	SG	Phoenix	0.8787	0.0753	0.9539

Top Twelve Frontcourt

Player	Position	Team	Back	Front	Overall
Rudy Gobert	C	Utah	0.0000	1.0000	1.0000
Andre Drummond	C	Detroit	0.0000	0.9998	0.9998
DeAndre Jordan	C	LA Clippers	0.0000	0.9998	0.9998
Hassan Whiteside	C	Miami	0.0000	0.9998	0.9998
Dwight Howard	C	Atlanta	0.0000	0.9996	0.9996
Marcin Gortat	C	Washington	0.0000	0.9995	0.9995
Jonas Valanciunas	C	Toronto	0.0000	0.9808	0.9808
Tristan Thompson	C	Cleveland	0.0000	0.9633	0.9633
Steven Adams	C	Oklahoma City	0.0416	0.9578	0.9994
Gorgui Dieng	PF	Minnesota	0.0552	0.8975	0.9527
Mason Plumlee	C	Portland	0.1205	0.8789	0.9994
Robin Lopez	C	Chicago	0.0000	0.8743	0.8743

Top Twelve Overall #BallIsLife

Player	Position	Team	Back	Front	Overall
James Harden	PG	Houston	1.0000	0.0000	1.0000
Rudy Gobert	C	Utah	0.0000	1.0000	1.0000
Andre Drummond	C	Detroit	0.0000	0.9998	0.9998
DeAndre Jordan	C	LA Clippers	0.0000	0.9998	0.9998
Anthony Davis	PF	New Orleans	0.2836	0.7162	0.9998
Hassan Whiteside	C	Miami	0.0000	0.9998	0.9998
Karl-Anthony Towns	C	Minnesota	0.3116	0.6882	0.9998
Russell Westbrook	PG	Oklahoma City	0.9997	0.0000	0.9997
Dwight Howard	C	Atlanta	0.0000	0.9996	0.9996
DeMarcus Cousins	C	Sacramento	0.7031	0.2965	0.9996
Marcin Gortat	C	Washington	0.0000	0.9995	0.9995
Giannis Antetokounmpo	SG	Milwaukee	0.4682	0.5314	0.9995

Ternary Plots (Hamilton 2016)

“A ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle.” - https://en.wikipedia.org/wiki/Ternary_plot

But that’s exactly what each entry in the player table is!
- Three variables - Front, Back and Bench - that sum to a constant 1.0.
So we can plot players as points on a ternary plot.

Top Twelve Backcourt

Top Twelve Frontcourt

Top Twelve Overall #ThisIsWhyWePlay

Portland Trail Blazers #RipCity

Player	Position	Team	Back	Front	Overall
Mason Plumlee	C	Portland	0.1205	0.8789	0.9994
CJ McCollum	SG	Portland	0.9311	0.0677	0.9988
Damian Lillard	PG	Portland	0.9988	0.0000	0.9988
Maurice Harkless	SF	Portland	0.2623	0.4577	0.7201
Evan Turner	SG	Portland	0.3288	0.2489	0.5778
Allen Crabbe	SG	Portland	0.4594	0.0967	0.5560
Al-Farouq Aminu	SF	Portland	0.1738	0.3157	0.4895
Ed Davis	PF	Portland	0.0000	0.4419	0.4419
Noah Vonleh	PF	Portland	0.0000	0.3359	0.3359
Meyers Leonard	PF	Portland	0.1669	0.1677	0.3346
Shabazz Napier	PG	Portland	0.0540	0.0000	0.0540

Portland Trail Blazers

Pop Quiz!

Who is the archetypal backcourt player?
Who is the archetypal frontcourt player?
Who are the three best Trail Blazers?

References

Eugster, Manuel J. A., and Friedrich Leisch. 2009. “From Spider-Man to Hero – Archetypal Analsis in R.” Journal of Statistical Software 30 (8): 1–23. http://www.jstatsoft.org/v30/i08/.

Hamilton, Nicholas. 2016. Ggtern: An Extension to ’Ggplot2’, for the Creation of Ternary Diagrams. https://CRAN.R-project.org/package=ggtern.

Oliver, D. 2004. Basketball on Paper: Rules and Tools for Performance Analysis. Brassey’s, Incorporated.

Shea, S.M. 2014. Basketball Analytics: Spatial Tracking. CreateSpace Independent Publishing Platform.

Shea, S.M., and C.E. Baker. 2013. Basketball Analytics: Objective and Efficient Strategies for Understanding How Teams Win. Createspace Independent Pub.