On Tanking and Competitive Balance

By Aleksandr M. Kazachkov and Shai Vardi

February 2020

This project contains the code for a simulator of an NBA season aimed at understanding tanking behavior.

Requirements

For general requirements, check the "compat" section under Project.toml. If PyPlot is available, the figures in the paper can be plotted using do_plotting=true in the commands below.

On a Mac, for plotting, one needs to install XQuartz.

Gurobi is needed. To install, you need to use Pkg.build("Gurobi") in a shell in which the GUROBI_HOME variable is defined or Gurobi can be found on the PATH. E.g., on Mac, GUROBI_HOME is set to /Library/<gurobiversion>/mac64.

Before running the code, you should instatiate the environment. It is further strongly recommended to create a sysimage, the steps for which should be automatically performed if you type make from the main project directory on a Linux or Mac.

Running the code

To run a simulation, parse NBA data, and reproduce data regarding noisiness of the reverse order ranking, first change directories to the julia subdirectory, then start julia, type ] to enter pkg mode, and type activate ./ to activate the tanking environment. Type instantiate to get the required packages. Afterwards, pressing backspace will return you to the normal prompt. You can also run julia --project to avoid the activate step above.

The code can be run with the following commands:

	using Tanking
	Tanking.main_simulate(do_simulation=1, num_replications=100000, do_plotting=false, mode=Tanking.STRICT, math_elim_mode=-2, gamma=0.71425) 
	Tanking.main_parse(do_plotting=false, mode=Tanking.STRICT)
	Tanking.rankings_are_noisy(do_simulation=true, num_replications=100000, do_plotting=false, mode=Tanking.STRICT)

Options

1. Option mode repesents the base true ranking.

    mode = STRICT: true ranking is strict. 1 > 2 > ... > 30
    mode = TIES: true ranking has ties. [1,5] > [6,10] > ... > [26,30]
    mode = BT_DISTR: each team gets a strength score based on random distribution (either Beta(1,1) = uniform, or Beta(2,5)), and game winners are determined by (Zermelo-)Bradley-Terry model
    mode = BT_EXPONENTIAL: same as mode = 3, except winners are determined with exponential version of the Bradley-Terry model
    mode = BT_ESTIMATED: each team gets a strength score (calibrated using an MLE on NBA data) and game winners are determined by (Zermelo-)Bradley-Terry model
   

2. Number of teams can be changed in the code (num_teams).

3. There are other plotting mechanisms implemented, but not all have been tested thoroughly.

4. math_elim_mode: how an eliminated team is identified, and how this will be used to determine tanking

   0: use effective elimination 1: use mathematical elimination, but calculated by heuristics only 2: use math elim, binary MIP, team-wise formulation 3: use math elim, general integer MIP, team-wise formulation 4: use math elim, binary MIP, cutoff formulation 5: use math elim, general integer MIP, cutoff formulation <0: use effective elimination for tanking, but calculate mathematical elimination

Assumptions

1. No simulataneous games
2. No conference / division play
3. True ranking is static
4. No home/away advantage
5. Ties broken between two teams with the same win percentage is by head-to-head record, and afterwards uniformly at random

To create a sysimage

1. Create pre-compilation statements (running from project directory)

    mkdir -p results/tmp
    julia --trace-compile="precompile.jl" --project="Tanking" scripts/test_script.jl 1
   

2. Create the sysimage (from the Tanking directory)

    julia> using PackageCompiler
    julia> PackageCompiler.create_sysimage([:Combinatorics, :DelimitedFiles, :Distributions, :Gurobi, :JuMP, :LaTeXStrings, :MathOptFormat, :Plots, :Printf, :PyCall, :Random, :StatsPlots, :Tanking], project=".", sysimage_path="JuliaTanking.so", precompile_statements_file="precompile.jl")
   

3. Run the script

    julia --sysimage=Tanking/JuliaTanking.so --project="Tanking" scripts/run_script.jl