We’re on the ground in Rio covering the 2016 Summer Olympics. Check out all our coverage here.

Does Brazil have a home-field advantage in Rio?

Again and again, research has shown that home-field advantage is a constant in sports across the world. Basketball referees call more fouls on the visitors. Pitchers for the home team in baseball get a wider strike zone. Home teams in soccer receive fewer yellow cards.

To see whether the same is true in the Olympics, we analyzed medal counts since World War II by comparing a country’s results in the year it hosted the games to its results in the games four years earlier. In other words, we estimated Great Britain’s 2012 home-field advantage by comparing its 2012 performance to its results from 2008. This is an improvement over previous research, which analyzed home advantage by comparing hosts to non-hosts in the same year, which ignores the fact that the average host (like Great Britain or China) is much different than the average non-host (like Djibouti or Paraguay).

MEDALS WON BY HOST COUNTRY HOST COUNTRY YEAR PREVIOUS OLYMPICS HOST YEAR CHANGE Finland 1952 24 22 -2 Australia 1956 11 35 +24 Italy 1960 25 36 +11 Japan 1964 18 29 +11 Mexico 1968 1 9 +8 West Germany 1972 26 40 +14 Canada 1976 5 11 +6 Soviet Union 1980 125 195 +70 United States 1984 94 174 +80 South Korea 1988 19 33 +14 Spain 1992 4 22 +18 United States 1996 108 101 -7 Australia 2000 41 58 +17 Greece 2004 13 16 +3 China 2008 63 100 +37 Great Britain 2012 47 65 +18

The table above on the Summer Olympics shows that host countries tend to improve their medal count over their total in the previous games. On average, host nations of the Summer Olympics increase their overall medal count by 20.1 medals and their gold medal count by 10.9. It is worth noting that the biggest jumps occurred for the Soviet Union in 1980, when the United States and allies boycotted the Moscow Games, and for the United States in 1984, when the Soviet Union and allies boycotted the Los Angeles Games — both times removing a major competitor in the medal count for the host nation. Excluding the years affected by these boycotts brings the average increase in overall medal count to 12.2 and in gold medal count to 6.8.

ATHLETES FROM HOST COUNTRY PARTICIPATING HOST COUNTRY YEAR PREVIOUS OLYMPICS HOST YEAR CHANGE Finland 1952 129 258 +129 Australia 1956 81 294 +213 Italy 1960 135 280 +145 Japan 1964 162 328 +166 Mexico 1968 94 275 +181 West Germany 1972 275 423 +148 Canada 1976 208 385 +177 Soviet Union 1980 410 489 +79 United States 1984 396 522 +126 South Korea 1988 175 401 +226 Spain 1992 229 422 +193 United States 1996 545 647 +102 Australia 2000 417 617 +200 Greece 2004 140 426 +286 China 2008 384 599 +215 Great Britain 2012 304 530 +226

Why do host nations do so well? Research has pointed to referees or crowds as crucial to home advantage in other sports, but we found a unique factor driving the home advantage in the Olympics. The table above shows that the number of athletes that a country sends to the games jumps tremendously when it is the host. On average, there are 175.8 additional athletes representing the host country than represented it four years earlier.

The main explanation for this increase is that qualification standards are lower for athletes from the host country. Olympic hosts are guaranteed a spot in each team sport. For example, the Brazilian men’s field hockey team will participate in its first Olympics in Rio de Janeiro. Host-country athletes who compete in individual events also have an easier time qualifying for the games. In the triathalon, for example, hosts are guaranteed at least one competitor of each gender. While some of these “add-on” host country athletes aren’t good enough to contend for medals, elite athletes from the host may participate in more events than they otherwise would.

MEDALS WON PER ATHELETE PARTICIPATING BY HOST COUNTRY HOST COUNTRY YEAR PREVIOUS OLYMPICS HOST YEAR CHANGE Finland 1952 0.19 0.09 -0.10 Australia 1956 0.14 0.12 -0.02 Italy 1960 0.19 0.13 -0.06 Japan 1964 0.11 0.09 -0.02 Mexico 1968 0.01 0.03 +0.02 West Germany 1972 0.09 0.09 +0.00 Canada 1976 0.02 0.03 +0.00 Soviet Union 1980 0.30 0.40 +0.09 United States 1984 0.24 0.33 +0.10 South Korea 1988 0.11 0.08 -0.03 Spain 1992 0.02 0.05 +0.03 United States 1996 0.20 0.16 -0.04 Australia 2000 0.10 0.09 +0.00 Greece 2004 0.09 0.04 -0.06 China 2008 0.16 0.17 +0.00 Great Britain 2012 0.15 0.12 -0.03

To assess the impact that participation levels have on the medal count, we compared the ratio of medals to participants for host nations. The table above shows a much more mixed story about whether host country athletes are having more success at home. We find that, on average, Summer Olympics hosts win fewer medals per athlete, compared with their results just four years earlier (although this result is not statistically distinguishable from a difference of zero, which remains true even if we remove the games affected by the 1980s boycotts from the pool). This tells us that even though host countries tend to increase their aggregate medal count, the increase disappears when we account for the higher number of medal-winning opportunities. This is due in part to the host’s aforementioned automatic entry for team sports, which add a large number of athletes in one shot, and the fact that teams can win only one medal, while an individual athlete may enter multiple events.

So what do our findings mean for Brazil’s sporting performance in the coming weeks? The Brazilian team has 481 participants. That’s quite a jump from 2012 (248 participants) and 2008 (268). If Brazil’s medals-per-athlete rate were to stay about the same as in 2008 and 2012, it would be expected to win about 30 medals in Rio. And that would be the nation’s best Olympics showing ever (they won 17 in 2012).

Brazil has the goal of a top-10 finish in the medals table. Italy, tenth in the total medal count in 2012, won 28 medals in London. Coming into Tuesday, the fourth day of the games, Brazil had one gold in judo and one silver in shooting.

One gold medal that Brazil hopes to win is in men’s soccer, the country’s most popular sport. The men’s national team has won the World Cup five times but never Olympic gold. Beyond all the numbers, winning men’s soccer gold would make the games a success for many Brazilians.