Heat and archery competition scores: Qiu 2021 study

Two economists matched the qualification scores of every outdoor competition held in China between 2010 and 2016 against the weather of the day, to see how much heat weighs on performance and who pays for it. The material is 36,066 rows, reduced to 35,954 after discards, from 460 contests in 57 competitions held in 27 counties, covering 3,196 archers from 32 provinces; over 97% shot recurve. The mean score per arrow in the sample is 7.91 and 20.7% of arrows landed in the ten. Men made up 53.0% of the archers.

The relationship between heat and score has the shape of an inverted U, with its peak in the reference band between 18 and 22 degrees of heat index. At zero wind the mean score per arrow falls by 0.25 points in the 22-26 degree band, by 0.42 between 26 and 30, by 0.41 between 30 and 34, and drops by 1.07 points, or 13.5%, above 34 degrees. Wind, though, dampens moderate heat: fixing wind speed at the sample average of 2.35 metres per second, the losses between 22 and 34 degrees sit between 0.19 and 0.29 points, while above 34 degrees the loss stays large, 0.82 points, that is 10.4% of the mean score. Humidity on its own is never significant: what counts is the heat index, which combines it with temperature.

The central result is not the average but the spread. Above 34 degrees the gap between the best and the worst mean score in the same contest grows by 79.1% and the coefficient of variation by 105.2%. Heat, in other words, widens the field. Building an index of past performance for each archer, the authors show that those coming from better scores lose less above 30 degrees, and the advantage is greatest above 34; the top tenth of the sample handles extreme heat significantly better than the rest. Between men and women, by contrast, no difference emerges, with one barely significant exception in the 26-30 degree band on the percentage of tens.

The last part concerns adaptation, meaning getting used to heat with body and mind rather than with air conditioning. An experience index, built as the total number of arrows shot in competition before the current one, softens the damage: once past the first quartile of the distribution, above 34 degrees the score falls by 0.33 points less, about 40% of the effect. Exposure to heat over the preceding twelve months, on the other hand, does nothing: the coefficients at one, three and twelve months are almost all small and not significant. Where one lives does count: archers who train in southern China lose 0.296 points less than the others above 34 degrees, 24.6%, and those competing in their own province 0.348 points less, 29.8%. Adding experience to long-term acclimatisation, the authors conclude that together they offset over 70% of the effect of extreme heat.

A final exercise compares two climate scenarios that raise the mean heat index by the same amount: two degrees more for everybody, or a doubling of the days above 34 degrees. The second does more damage, with a reduction in the mean score about 20% larger and an increase in spread sometimes orders of magnitude greater.

The scores come from the archive of the Chinese archery association and cover every outdoor competition from 2010 to 2016. The authors use only the qualification rounds of individual competitions, and for a precise reason: in qualification the archers all shoot together without seeing anyone's scores, so each archer's performance does not depend on an opponent's, as it would in head-to-head matches. For each contest they collected the total score, name, sex and training location, plus the contest's characteristics: number of arrows, distance, bow type and the order of the contest within the competition. Archers are identified by the combination of Chinese name and sex.

There are three performance measures. The average score, the total divided by the arrows shot in that contest. The percentage of tens, which is the hard part of the task. And dropping out, which takes the value 1 when an archer's name appears in a contest but the total is missing.

The weather comes from two sources: the Chinese meteorological data sharing service, with temperatures, relative humidity, wind, precipitation and pressure for about 800 stations, and NOAA for visibility, used as an indicator of air pollution, from about 360 stations. The heat index is built from daily mean temperature and relative humidity using the formula of the US National Weather Service. For each county the daily values are obtained as a weighted average of the stations within 150 kilometres of the centroid, weighted by inverse distance, and then matched to the scores by county and date. For about 90% of the contests the exact date is known; for the rest the authors assume the qualification rounds were held in the first three days of the competition and use the three-day average weather.

The model is a regression on heat index bins, with the 18-22 degree band as the reference, plus the other weather variables and the contest characteristics. Identification comes from variations in heat index within the same archer over time, holding fixed the archer, the competition county, the year, seasonality and the yearly trends of each training province. The benchmark specification includes the interaction between heat index and wind speed. For the spread, the dependent variable becomes the difference between the highest and lowest score in the contest, or the coefficient of variation. Adaptation is estimated by adding interactions between the high heat bins and, depending on the case, the experience index, the days of heat experienced in the training city over the preceding one, three and twelve months, being from northern China, and competing in one's own province.

The heat in this study is not the heat of the shooting line. The heat index is built on the county's daily mean temperature and humidity, interpolated from stations up to 150 kilometres away: it is not the temperature of the hour when they were shooting, there is no direct sun, and there is no wind direction, only wind speed. For one contest in ten not even the exact date is known, and the weather is the average of the first three days of the competition.

The study is observational. The authors compare the same archer across different days, which removes many differences between people, but heat remains tied to season, place and calendar: which competitions are held when, and who enters which, is not assigned at random. Archers are identified by Chinese name and sex, so archers of the same sex sharing a name end up as the same person. Dropping out is defined as name present and total missing, a condition that can arise from many different things, a transcription error included.

The adaptation arithmetic should be read for what it is, coefficients from different regressions put together. The 40% attributed to experience comes from 0.33 divided by 0.82, where 0.82 is the effect of extreme heat estimated in the benchmark model at average wind; the 29.8% for the home province comes from 0.348 divided by 1.167, a different baseline effect taken from another specification. Adding the two percentages to reach "over 70%" assumes the two mechanisms add up without overlapping, which was not tested. It is also worth noting that only 5.6% of the observations involve archers competing in their own province, and that long-term acclimatisation is measured with a simple northern or southern China indicator.

The study measures no mechanism. There is nothing physiological, nothing on fatigue, nothing on equipment: the authors assume recurve bows are weatherproof and that any effect on equipment would be the same for everyone, so that all the difference between archers can be attributed to the person. The average scores come from different distances, held together by the controls on contest characteristics. And the aim of the work is not archery: the archers serve the authors as outdoor workers with a clean measure of productivity, and the questions are those of climate economics.

Finally the source. The document consulted is the working version deposited on SSRN, not the article published in the Southern Economic Journal: figures and tables may have changed in review, and the comparison with the final version remains to be made. The setting, moreover, is China between 2010 and 2016, with its climate and its competition calendar.

There is one number to remember. Above 34 degrees of heat index, at average wind, the mean score per arrow falls by 0.82 points relative to the 18-22 degree band: over a 72-arrow qualification that average amounts to some sixty points. Between 22 and 34 degrees the loss is far smaller, between 0.19 and 0.29 points per arrow, and wind softens it further. The step, then, is not gradual: it sits entirely in the highest band.

The second point concerns who pays. Extreme heat does not take points away from everyone equally: it widens the gap between first and last in the same qualification by 79.1% and doubles the coefficient of variation. Those coming from higher scores lose less, and the top tenth of the sample handles extreme heat significantly better than the rest. A qualification on a scorching day, then, is not only poorer in points: it is also more spread out, and it selects differently.

On getting used to heat the result is counter-intuitive and worth holding on to. The number of hot days experienced in the twelve months before a competition changes nothing measurable. What does change something is two more stable things: experience accumulated in competition, worth about 40% of the effect and already reached at the first quartile of the distribution, and where one lives and trains, with archers from southern China less affected than those from the north and those competing in their own province less affected than those who travel. The study tests no adaptation programme, so it does not say that exposing oneself to heat in training helps: it says that in those data the preceding months left no trace and the years did.

Between men and women no difference shows up, and that is an explicit result rather than an absence of data. Finally, a note on scope: no part of this work measures what happens in an archer's body or mind when it is hot. Heat enters as the county's meteorological record and shooting as a score in an archive, and what lies between the two stays outside the study.