Prior analysis and scheduling of the 2011 Rugby Union ITM Cup in New Zealand

Abstract

This paper describes work done for the New Zealand Rugby Union (NZRU) in preparation for their most important wholly domestic competition in 2011. This competition had to be played during a shorter timescale than usual because of the 2011 Rugby Union World Cup, and the NZRU were keen to ensure that they could incorporate the format they wanted into this timescale without unfortunate consequences. In addition, they wanted to introduce a novel feature into this tournament. Thus some detailed prior experimental, or ‘what-if’, analysis was necessary. This paper describes this analysis and its results. As a result of this analysis, the NZRU was persuaded to abandon one of its design ideas, but was able to proceed with others, enabling them to announce the detailed format of the competition in the confidence that it would work well in practice. Subsequent scheduling of the competition in this format proved successful, and the resulting schedule is shown together with detailed analysis of its notional costs. The paper demonstrates how important it can be for schedulers to be closely involved in tournament design in advance of the actual scheduling.

Appendices

Appendix A

Notional costs

The notional cost relating to each requirement and preference is shown below for the schedule detailed in Table 1. The number in brackets is the penalty cost for any incidence of non-observation. These costs were determined according to the perceived relative importance of each requirement and preference and modified according to the actual outcomes achieved, but there was inevitably a great deal of arbitrariness about the precise numbers.

Where a requirement or preference was not met by more than one unit, the general rule, unless otherwise stated, was that the penalty was multiplied by the square of the amount by which the number was missed. Thus, for example, for R3, a midweek round with only one match would have incurred a cost of 4 × 80=320.

Requirements

R1 (50)—every team should have a home match in one of the first three rounds—fully met—cost 0.

R2 (50)—every team should have a home match in one of the last three rounds—fully met—cost 0.

R3 (80 for too few, 20 for too many)—every midweek round should have either three or four matches—fully met—cost 0.

R4 (180 for too few, 60 for too many)—every team should have either three or four weekend home matches—fully met—cost 0.

R5 (15)—no team should at any stage have played two more matches than another team—fully met—cost 0.

R6 (200)—no team should have more than three matches in a row without a bye—fully met—cost 0.

General preferences

G1 (3)—No team should have a run of three consecutive weekend homes—fully met—cost 0.

G2 (42)—No team should have a run of three home matches in consecutive rounds—not met for Bay of Plenty—cost 42.

G3 (34 if four, 2 if three, 6 if the same team has three twice)—No team should have a run of four rounds without a home match—ideally no team should have a run of three rounds without a home match—34 for three teams, 6 for two teams, 2 for eight teams—total cost 130.

G4 (9 if the last three weekends, 1 otherwise)—No team should have a run of three weekend rounds without a home match—9 for Northland, 1 for Auckland—total cost 10.

G5 (5)—No team should have a bye in each of two consecutive midweek rounds—not met for Southland and Hawke's Bay—cost 10.

G6 (2)—No team should have three consecutive crossover matches—not met for four teams—total cost 8.

G7 (1)—No team should have a pattern of home-away-home at any stage—not met for five teams—cost 5.

G8 (1)—No team should have a pattern of away-home-away at any stage—not met for six teams—cost 6.

G9 (16)—There should be no more than one crossover match in each of rounds 1, 11 and 13—met for rounds 1 and 11, but not met for round 13—cost 16.

G10 (20)—Each midweek round should involve at least two teams from each division—not met for rounds 4, 8 and 10—cost 60.

G11 (3 multiplied by matrix entries (see Appendix C)—no cost if to or from a bye)—Travel should be minimised—total cost 456.

G12 (350 if none, 7 if one)—Each weekend round apart from the first should contain at least one ‘backwards flexible’ match, preferably two—always at least one backward flexible match, but only one for rounds 3, 7 and 13—cost 21.

G13 (350 if none, 7 if one)—Each weekend round apart from the last should contain at least one ‘forwards flexible’ match, preferably two—always at least one forwards flexible match, but only one for rounds 1, 5 and 11—cost 21.

Specific preferences

S1 (80)—Canterbury not to be at home in round 7—met—cost 0.

S2 (200)—Canterbury not to be at home in round 12—met—cost 0.

S3 (200)—Canterbury not to be at home in round 13—met—cost 0.

S4 (200)—Auckland not to be at home in round 7—met—cost 0.

S5 (200)—Auckland not to be at home in round 12—met—cost 0.

S6 (200)—Auckland not to be at home in round 13—met—cost 0.

S7 (200)—Wellington not to be at home in round 5—met—cost 0.

S8 (200)—Wellington not to be at home in round 12—met—cost 0.

S9 (200)—Wellington not to be at home in round 13—met—cost 0.

S10 (100)—Taranaki not to be at home in round 3—met—cost 0.

S11 (20)—Taranaki not to be at home in round 13—not met—cost 20.

S12 (200)—Bay of Plenty to be at home in round 3—met—cost 0.

S13 (120)—Bay of Plenty to play against Wellington in round 3—not met—cost 120.

S14 (120)—Bay of Plenty not to be at home in round 7—met—cost 0.

S15 (20)—Bay of Plenty not to be at home in round 13—met—cost 0.

S16 (20)—Southland not to be at home in round 13—not met—cost 20.

S17 (20)—North Harbour not to be at home in round 13—not met—cost 20.

S18 (40)—Tasman to have only one home match in the first five rounds—met—cost 0.

S19 (200)—Manawatu to be at home in round 1—met—cost 0.

S20 (120)—Manawatu to play against Hawke's Bay in round 1—met—cost 0.

S21 (160)—Otago to have two home matches in the final four rounds—met—cost 0.

Appendix B

Crossover matches

The automatic crossover matches pre-determined by seeding were:

Otago versus Canterbury (14 versus 1)

Manawatu versus Waikato (13 versus 2)

Tasman versus Auckland (12 versus 3)

North Harbour versus Wellington (11 versus 4)

Northland versus Taranaki (10 versus 5)

Counties Manukau versus Bay of Plenty (9 versus 6)

Hawke's Bay versus Southland (8 versus 7)

The numbers in brackets indicate the seeding positions. Thus, for example, Otago was Seed 14 and Canterbury Seed 1. The seeding positions were determined by the finishing order in the 2010 competition.

For Pick 1, Championship teams (playing at home) selected a Premiership opponent in reverse seeding order (14 to 8):

Otago versus Southland

Manawatu versus Taranaki

Tasman versus Canterbury

North Harbour versus Auckland

Northland versus Bay of Plenty

Counties Manukau versus Waikato

Hawke’s Bay versus Wellington

For Pick 2, Premiership teams (playing at home) selected a Championship opponent in seeding order (1 to 7):

Canterbury versus Northland

Waikato versus Otago

Auckland versus Counties Manukau

Wellington versus Manawatu

Taranaki versus Tasman

Bay of Plenty versus Hawke’s Bay

Southland versus North Harbour

For Pick 3, Championship teams (playing away) selected a Premiership opponent in seeding order (8 to 14):

Taranaki versus Hawke’s Bay

Southland versus Counties Manukau

Wellington versus Northland

Bay of Plenty versus North Harbour

Waikato versus Tasman

Canterbury versus Manawatu

Auckland versus Otago

Appendix C

Travel cost matrix used

The notional travel costs pertaining to journeys undertaken by teams were taken from the matrix below. Note that these are not very closely related to actual distances, but more to convenience of travel. Thus journeys to and from locations close to major airports tend to have a lower notional cost than other journeys.

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