New mathematical models for team formation of sports clubs before the match

Abstract

Coaches of sports clubs aim to form the team that optimally determines the roles of positions before the match. These types of decisions are referred to as the team formation problem, and they are critical for the sports industry in the financial sense. Finding the optimal solution to the team formation problem is more difficult without the use of systematical approaches, as the number of players and their past performance records have increased substantially in recent years. In this paper, we discuss previous studies on the team formation problems of sports clubs and outline the deficiencies of their results in real-life decision processes. Then, we propose two new formulations that address coaches’ preferences in the decision-making process. A real-life application of the proposed models is displayed for a volleyball team that participates in the first division of the Turkish Volleyball League.

Appendices

Appendix 1: Weights of positions $(MS_j)$ (Budak et al. 2017)

Positions	S	L	MB 1	MB 2	SP 1	SP 2	OP
Weights	0.26	0.07	0.12	0.12	0.13	0.13	0.18

Weights of skills for each position $(SM_{yj})$ (Budak et al. 2017)

Skills/positions	S	L	MB 1	MB 2	SP 1	SP 2	OP
SE	0.21	0.00	0.27	0.27	0.21	0.21	0.27
R	0.00	1.00	0.00	0.00	0.44	0.44	0.00
B	0.16	0.00	0.54	0.54	0.12	0.12	0.22
A	0.00	0.00	0.18	0.18	0.22	0.22	0.51
P	0.63	0.00	0.00	0.00	0.00	0.00	0.00

Appendix 2: Forecasts of player skill performances $(SS_{iy})$

Player/skills	SE	R	B	A	P
Player #1	50.0	0.0	33.3	25.0	0.0
Player #2	50.0	16.7	8.3	58.3	42.8
Player #3	0.0	66.8	0.0	0.0	0.0
Player #4	52.4	33.3	11.0	90.3	0.0
Player #5	31.3	33.3	33.3	65.2	0.0
Player #6	23.6	30.3	24.3	74.2	0.0
Player #7	42.6	33.3	37.7	72.2	0.0
Player #8	41.2	0.0	33.0	72.7	0.0
Player #9	40.4	60.3	35.3	69.5	0.0
Player #10	46.5	0.0	35.7	79.0	0.0
Player #11	50.3	0.0	55.7	87.3	0.0
Player #12	16.7	0.0	11.0	26.7	0.0
Player #13	0.0	16.7	0.0	4.2	0.0
Player #14	45.0	0.0	20.0	0.0	48.0

Appendix 3: Possible position that players are able to play $(PM_{ij})$

Player/positions	S	L	MB 1	MB 2	SP 1	SP 2	OP
Player #1	0	0	1	1	0	0	0
Player #2	1	0	0	0	0	0	0
Player #3	0	1	0	0	0	0	0
Player #4	0	0	1	1	0	0	0
Player #5	0	0	0	0	1	1	1
Player #6	0	0	0	0	1	1	0
Player #7	0	0	1	1	0	0	0
Player #8	0	0	0	0	0	0	1
Player #9	0	0	0	0	1	1	0
Player #10	0	0	1	1	0	0	1
Player #11	0	0	1	1	0	0	0
Player #12	0	0	0	0	1	1	1
Player #13	0	1	0	0	0	0	0
Player #14	1	0	0	0	0	0	0

Thresholds for each position’s skill $(TH_{jy})$:

$\hbox {Position}\backslash \hbox {skill}$	S	L	MB 1	MB 2	SP 1	SP 2	OP
SE	35	0	20	20	20	20	20
R	0	10	0	0	20	20	0
B	10	0	20	20	20	20	20
A	0	0	25	25	20	20	40
P	40	0	0	0	0	0	0

Appendix 4: Higher thresholds for each position’s skill $(TH_{jy})$

$\hbox {Position}\backslash \hbox {skill}$	S	L	MB 1	MB 2	SP 1	SP 2	OP
SE	40	0	30	30	30	30	30
R	0	30	0	0	30	30	0
B	25	0	30	30	30	30	30
A	0	0	35	35	30	30	50
P	50	0	0	0	0	0	0