A recent article in BMJ offers a nice illustration of logistic and Poisson
regression applied to a practical problem. I want to write an article about
this for Chance News. Here is a first draft. There is a strong belief that
athletes who live and train at high altitudes have an unfair advantage over
those athletes visiting from lower altitudes. In response,
football's governing body, the Federation of International Football
Associations (FIFA), banned international matches from being played at more
than 2500 m above sea level.
There is a plausible mechanistic explanation for this concern.
At high altitude hypoxia, cold, and dehydration can lead to
breathlessness, headaches, nausea, dizziness, and fatigue, and possibly
altitude illness including syndromes such as acute mountain sickness, high
altitude pulmonary oedema, and cerebral oedema. Activities such as football
can exacerbate symptoms, preventing players from performing at full
capacity.
What would the data say. An ideal database exists to explore whether high
altitude has a detrimental effect on athletes visiting from lower altitudes.
In South America, which has three large cities at high altitude (Bogota,
Columbia, Quito, Ecuador, and La Paz, Bolivia), there are records of 1460
football matches played over a 100 year period at a wide range of altitudes.
This data set included four variables:
(i) the probability of a win, (ii) the number of goals scored, (iii) the
number of goals conceded, and (iv) the altitude difference between the home
venue of a specific team and that of the opposition.
as well as indicators for individual countries. This study used a logistic
regression model to predict the probability of a win, and two Poisson
regression models to predict number of goals scores and number of goals
conceded. The graph of the predicted equations appears below. These graphs
show clearly that a two thousand meter difference in altitude between the
home team and the opposition produces a large change in the probability of a
win for the home team, the expected number of goals scored by the home team,
and the expected number of goals allowed by the home team.
Questions:
1. There are many variables that were not considered in this analysis. List
some of the more important variables that were not included. Consider whether
these variables are easy to measure or hard to measure.
2. Is there an alternate explanation other than change in altitude that
could account for the differential in home team win probability, goals scored
by the home team, and goals allowed by the home team?
3. Should international football matches be allowed in high altitude
locations?
Effect of altitude on physiological performance: a statistical analysis
using results of international football games. Patrick E McSharry. BMJ
2007;335:1278-1281 (22 December), doi:10.1136/bmj.39393.451516.AD. [Full
text] [PDF].
This webpage was written
Steve Simon on2008-01-05
and was last modified on
2008-07-08. Category: Wiki pages
