Wednesday March 17th 2010 (3pm Newcastle)
Abstracts
Phil Scarf (Salford)
Decision problems in sport: Naismith's rule and route choice in
adventure racing.
The adventure racer, when competing in mountain navigation
events, is often faced with an over-or-around route choice. Is
it quicker to go over or around a hill when trying to get from
a point A, on one side, to a point B, on the other? Route
choice aesthetics are of no interest. The competitor wishes to
get from A to B as efficiently as possible. Naismith's rule
can be used in these circumstances. This rule relates climb to
distance, and implies that, in terms of time taken, 1 unit of
distance vertically is equivalent to N units of distance
horizontally. Naismith in his original paper in 1892 implied
that N=7.92. Now, if a route (from A to B) comprises a
horizontal distance component of x units and a vertical
distance component of y units, then x+Ny is the equivalent
distance of the route. Given a choice between routes, the
competitor should then ceteris paribus choose that route with
minimum equivalent distance. This talk will consider a number
of questions in this context: What are the origins of
Naismith's rule? What is the connection between the rule, the
treadmill crane at Harwich, and the Scottish Mathematician
MacLaurin? Can N be estimated from data? Does N vary with age,
that is, do veteran runners find ascent relatively more
difficult, and therefore should they be more inclined to go
around? If the over and around routes between points on
opposites sides of a simply shaped hill are equivalent, is
there a quicker route in between? What is the shape of an
isochronic hill? Is the rule applicable to cycling?
Frank Duckworth
The D/L method in one-day cricket: 13 years on
The Duckworth/Lewis method for resetting targets in rain-interrupted one-day cricket matches has now been in use for thirteen years and has been employed in every country of the world where cricket is played.
The talk will explain what was wrong with previous rain rules and why a mathematical method was needed. The story of how Duckworth and Lewis came together and produced a method which gained world-wide acceptance will be related.
How the method works and how easy it is to understand will be illustrated with examples covering all types of match interruption and the audience will be invited to participate in performing some simple Duckworth/Lewis calculations!
Some of the experiences with the method~s operation in over 1000
matches will be related, and it will be shown how the method
has undergone small modifications to accommodate changes in
the way the game is played.
Dr Frank Duckworth is one of the two English mathematicians who formulated the Duckworth/Lewis method.
He graduated in physics at the University of Liverpool and spent his entire career as a mathematical scientist in the UK~s nuclear power generation industry. One of the things he worked on was the quantification of risks from nuclear power and this led to his gaining some renown in recent years as inventor of a ~riskometer~ for comparing risks of differing kinds.
He took early retirement in 1992 and since then has been honorary editor of RSS NEWS, the monthly news magazine of the Royal Statistical Society. His time during retirement has been largely divided between this activity and his cricket work.