Tactical positioning behaviours in short-track speed skating: A static and dynamic sequence analysis

Figures & data

Table 1. Example analysis of winners tactical positioning behaviours ($n$ = 10) using discrete lap analysis and sequence analysis.

	Discrete Lap Analysis		Sequence Analysis
Race Id	Start Position	Lap 1 Rank	Race Sequence
1	1	3	(1, 3)
2	1	2	(1, 2)
3	1	2	(1, 2)
4	1	3	(1, 3)
5	1	1	(1, 1)
6	3	1	(3, 1)
7	2	1	(2, 1)
8	3	1	(3, 1)
9	3	1	(3, 1)
10	2	1	(2, 1)
Ranked 1^st	50%	60%	–
Mean Rank	1.8	1.6	–
Standard Deviation Rank	0.9	0.8	–

Note: Starting positions are coded from 1 (innermost track position) to $n$ (outermost track position). Lap 1 rankings are coded Lap 1 from 1 (leading athlete) to $n$ (last athlete).

Table 2. Most recurring group and winner tactical positioning behaviours in the 500 m, 1,000 m, and 1,500 m events.

		Group			Winner
Event	Race period	Sequence	$Sup$	$relSup$	Sequence	$Sup$	$relSup$
500 m	Start – Lap 5	(1,6)	250	12.4%	(1,6)	960	47.5%
	Lap 1–5	(1,5)	613	30.3%	(1,5)	1,356	67.1%
	Lap 2–5	(1,4)	777	38.5%	(1,4)	1,452	71.9%
	Lap 3–5	(1,3)	1,056	52.3%	(1,3)	1,621	80.2%
	Lap 4–5	(1,2)	1,463	72.4%	(1,2)	1,813	89.8%
	Lap 5	(1,1)	2,020	100%	(1,1)	2,020	100%
1,000 m	Start – Lap 9	–	–	–	(1,10)	126	8.1%
	Lap 1–9	(1,9)	53	3.4%	(1,9)	261	16.8%
	Lap 2–9	(1,8)	81	5.2%	(1,8)	344	22.2%
	Lap 3–9	(1,7)	144	9.3%	(1,7)	472	30.5%
	Lap 4–9	(1,6)	222	14.3%	(1,6)	614	39.6%
	Lap 5–9	(1,5)	336	21.7%	(1,5)	772	49.8%
	Lap 6–9	(1,4)	457	29.5%	(1,4)	946	61.1%
	Lap 7–9	(1,3)	683	44.1%	(1,3)	1,160	74.9%
	Lap 8–9	(1,2)	1,070	69.1%	(1,2)	1,380	89.1%
	Lap 9	(1,1)	1,549	100%	(1,1)	1,549	100%
1,500 m	Start – Lap 14	–	–	–	–	–	–
	Lap 1–14	–	–	–	–	–	–
	Lap 2–14	–	–	–	–	–	–
	Lap 3–14	–	–	–	–	–	–
	Lap 4–14	–	–	–	(1,11)	12	2.1%
	Lap 5–14	–	–	–	(1,10)	20	3.5%
	Lap 6–14	–	–	–	(1,9)	43	7.6%
	Lap 7–14	–	–	–	(1,8)	91	16.1%
	Lap 8–14	–	–	–	(1,7)	139	24.6%
	Lap 9–14	(.87,2) – (1,4)	18	3.2%	(1,6)	180	31.8%
	Lap 10–14	(.87,1) – (1,4)	29	5.1%	(1,5)	235	41.5%
	Lap 11–14	(1,4)	68	12.0%	(1,4)	307	54.2%
	Lap 12–14	(1,3)	135	23.9%	(1,3)	395	69.8%
	Lap 13–14	(1,2)	272	48.1%	(1,2)	487	86.0%
	Lap 14	(1,1)	566	100%	(1,1)	566	100%

Note: The group behaviour represents the similarity between all athletes’ intermediate and final rankings measured using Kendall’s Tau-b. The winner behaviour represents the rank of the winner. The state-permanence-sequence format provides each successive distinct state in the sequence with its duration. For example, a winner sequence of (1,6) in the 500 m indicates that the winner started and remained in first for the entirety of the race. $Sup$ = Absolute support; the number of times the sequence occurs in the sequence period. $relSup$ = Relative support; the proportion of races that the sequence occurs in the sequence period. Note, we only report sequences with a relative support ≥ 2%, i.e., a sequence that occurs 1 in every 50 races.

Figure 1. Static and dynamic race sequence formation. First, we extract the winner (denoted by the red circle) and group tactical positioning behaviours at the race start and end of each lap. Second, we form our static and dynamic sequences. The static sequence treats the whole race as a single unit of analysis. The dynamic sequences are nested race sequences with a constant endpoint (the final lap) but varying start points (e.g., Lap 1–5, Lap 2–5, Lap 3–5). Note that we represent all sequences using the state-permanence-sequence format, i.e., each successive distinct state in a sequence is given together with its duration. For example, we represent the static winning sequence: (4, 4, 1, 1, 1, 1), as (4, 2) – (1, 4).

Figure 2. The sequence duplication rate for group and winner tactical positioning behaviours in the 500 m, 1,000 m, and 1,500 m. A sequence duplication rate of 0% indicates that no sequences are identical, and a sequence duplication rate of 100% indicates that all sequences are identical. We report the number of unique sequences detected in the brackets.

Figure 3. Boxplots of sequence relative support for group and winner tactical positioning behaviours in the 500 m, 1,000 m, and 1,500 m. Frequently recurring sequences are identified as those greater or equal to the inner fence: $Q3+\left(1.5\ast Interquartilerange\right)$. Annotated sequences represent the most frequent sequence with a relative support ≥ 2%.