Olympic medals in host countries
Fractional medal count in Olympic summer games from 1995 to 2012 for the last 7 host countries, plus Brasil, host in 2016. The fractional medal count is the number of medals a team has gathered divided by the total number of medals available. This scaling is necessary because the number of Olympic events increased significantly over this timespan. For the current games, the numbers are calculated after 200 of 302 events.
The goal of making this figure was to find out whether there is evidence that the current success of the GBR team is in any way unprecedented or unexpected, as it is sometimes implied in the media. The figure is held deliberately simply because additional scalings to quantify the 'host effect', as they are sometimes done in the literature, are difficult to justify. In general, it's not possible to compare the 'host effect' (i.e. the fractional increase in the medal count for the host nation), because the participating nations vary with time. Medals are a limited resource, i.e. the addition or subtraction of one team affects all other teams. That's the reason why pre-1996 numbers are not plotted here, the disappearance of the Soviet Union, East Germany, and Yugoslavia causes strong changes in all other numbers, which makes it difficult to isolate the host effect. The only teams that can realistically be compared with GBR are China and Greece. The USA is plotted here only for completeness; the generally high medal count and the fact that the USA hosted two events in the recent past (1984 and 1996) makes it impossible to compare it with other teams.
The analysis yields three robust results:
1) The host effect exists - all countries documented here show the highest fractional medal count in the year in which they hosted the games. Of course, this result is not new.
2) The magnitude of the host effect is difficult to quantify (see above). Using the average fractional medal count in the years before the event was hosted by a given nation as a base line, the relative increase is a factor of 1.6 (GRE), 1.7 (CHI) and 2.4 (GBR). The absolute increase is 0.06 (GRE), 0.05 (CHI), 0.05 (GBR). The values for GRB are entirely consistent with previous events. Thus, the success of team GRB is not unexpected.
3) All host nations show a 'pre-host effect', i.e. a significant increase in the fractional medal count 4 years before they host the event. The 'pre-host effect' is typically around 30-50% of the entire host effect, with large scatter. Note that the selection of the host nation is typically made 7 years prior to a given event. This basically rules out that the host effect can be explained only by referee bias or crowd effects; the dominant factor are long-term decisions, e.g., a systematic increase in the funding prior to the event.
4) Almost all host nations show a 'post-host effect', i.e. a sustained high level compared with pre-host numbers after they hosted the event. The only exception here is GRE, which fell back to pre-host levels within 4 years. Spain (ESP) has sustained higher-than-normal numbers for at least 4 events, South Korea (KOR) for at least 6 events. The case of KOR is particularly interesting because this team had practically zero medals before they hosted the games, peaked in 1988, and were able to sustain high levels for several decades. CHI may be the first case managing to top their host numbers 4 years later. Again, the existence of this 'afterglow' demonstrates that long-term decisions are the dominant cause for the host effect.
5) Based on the non-existence of a pre-host effect for Brasil, it is fairly easy to predict that we will not see a particularly strong host effect in 2016 - expected is an increase by maybe 50%, i.e. a fractional medal count in the range of 0.02 to 0.04, which corresponds to 18-36 medals. For comparison, they are currently projected to finish with 12 medals in the London games.
In summary, the host effect is a well-established phenomenon and the currently observed success of the home team GBR is not unexpected. Parts of the effect can be seen 4 years in advance and 0-24 years after the hosted event, which indicates that it's not a 'hometown bias', but due to long-term decisions.
