June 30, 2006

Championship draws: a statistical analysis

With every contest, every band takes a close look at the order-of-play for the event. Playing as close as possible to the end of the contest is generally considered an advantage. Playing at the beginning, or, heaven forbid, first is generally considered a disadvantage.

Also important is the competition playing before or after you. If you’re a band looking for recognition because you think you’re rating with the usual prize-winners, playing right beside an odds-on favourite can help get you into the list. Conversely, if you’re a favourite that might be having an off-year, playing next to a band in top form can be a problem.

The Scottish Championship, the first major of the UK year, has already happened, and the British Championship will be on June 24 in Pitlochry. A few readers alerted us to the draws for each Grade 1 contest, and we picked up on a few similarities. Considering that draws are random, we wondered about the statistical probabilities of a few of the parallels.

Because we’re not statisticians, we contacted a few people who know about these things for their mathematical assessments, and they follow below.

First, the order-of-plays for each major:

Scottish Championship
1 ScottishPower
2 Boghall & Bathgate
3 Field Marshal Montgomery
4 House of Edgar-Shotts & Dykehead
5 Dysart & Dundonald
6 Bleary & District
7 Strathclyde Police
8 Ballycoan
9 Ballinderry Bridge
10 Lothian & Borders Police
11 Robert Wiseman-Vale of Atholl
12 Clan Gregor

British Championship
1 ScottishPower
2 Lothian & Borders Police
3 Ballycoan
4 Boghall & Bathgate
5 Dysart & Dundonald
6 St. Laurence O’Toole
7 Field Marshal Montgomery
8 House of Edgar-Shotts & Dykehead
9 Simon Fraser University
10 Strathclyde Police
11 Bleary & District
12 Robert Wiseman-Vale of Atholl
13 Clan Gregor

Here are the statistical probabilities of some of the coincidences between the two random draws, according to our experts.

The odds of ScottishPower being drawn first in both contests and Clan Gregor being drawn last in both are approximately 1:156.

The odds of Field Marshal Montgomery playing immediately before Shotts at both contests are approximately 1:132.

What are the odds that at both contests ScottishPower is drawn first, Clan Gregor drawn last, Vale of Atholl drawn immediately before Clan Gregor, and Field Marshal is drawn immediately before Shotts?

Approximately 1:12,500.

Every pipe band association makes the draw for contests without prejudice, of course. But it is interesting to consider the statistical likelihood of the random coincidences in the order-of-plays at each of these UK major championships.

We’d also like to do a statistical analysis of MSRs or Medleys drawn from the hat at the starting line at competitions. We all know that in a submit-two event the probability is 50/50. But doesn’t it sometimes seem that some bands always draw the #1 medley or set? Go figure.

Draws: always a great discussion point.


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