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].
