Soccer’s World Cup tournament starts in less than two weeks. Thirty-two national teams will vie for the title; some having a realistic chance of winning, while others are just happy to be there. As with any sporting event, there is gambling involved. Gambling involves odds, and odds involve numbers, so here we are.
The favorite is Brazil. The typical odds quoted for Brazil to win the tournament are +400. That’s in the format of a moneyline bet; what +400 means is that you risk 100 to win 400. Moneyline odds can be translated to an “implied probability”; that is, what are Brazil’s chance of winning? Turns out, it’s 20%, or 1 in 5.1For positive moneylines, the formula is 100 / (Moneyline + 100)
Let’s verify. Say there are five instances of the World Cup tournament, and you bet 100 on Brazil on each of them. If the 20% probability is correct, they will win one of those five. In that case, you win 400. Brazil lose each of the other four, so you’re down 100 each time. Your win puts you 400 up, your four losses put you 400 down, so you’re even. So the +400 betting line matches a 20% probability of winning.
Let’s look at the odds to win the World Cup for all 32 teams. I list the moneyline number, and the corresponding implied probability.
| Team | Moneyline Odds | Probability |
| Brazil | +400 | 20.00% |
| Argentina | +550 | 15.38% |
| France | +650 | 13.33% |
| England | +800 | 11.11% |
| Spain | +850 | 10.53% |
| Germany | +1000 | 9.09% |
| Netherlands | +1200 | 7.69% |
| Portugal | +1400 | 6.67% |
| Belgium | +1400 | 6.67% |
| Denmark | +2800 | 3.45% |
| Croatia | +5000 | 1.96% |
| Uruguay | +5000 | 1.96% |
| Serbia | +8000 | 1.23% |
| Senegal | +8000 | 1.23% |
| Switzerland | +8000 | 1.23% |
| Poland | +13000 | 0.76% |
| Wales | +13000 | 0.76% |
| Mexico | +13000 | 0.76% |
| USA | +13000 | 0.76% |
| Ecuador | +18000 | 0.55% |
| South Korea | +20000 | 0.50% |
| Ghana | +25000 | 0.40% |
| Japan | +25000 | 0.40% |
| Morocco | +25000 | 0.40% |
| Canada | +25000 | 0.40% |
| Australia | +25000 | 0.40% |
| Cameroon | +25000 | 0.40% |
| Qatar | +30000 | 0.33% |
| Tunisia | +30000 | 0.33% |
| Iran | +50000 | 0.20% |
| Costa Rica | +80000 | 0.12% |
| Saudi Arabia | +80000 | 0.12% |
One thing to notice is that odds drop precipitously as you go down the list. Outside of the top few elite teams, the oddsmakers say that the chances of winning the World Cup are slim. This matches history – very few countries have won the tournament. Since 1950 there have been 17 World Cups, and they all have been won by one of the top six teams on that list (Brazil, Argentina, France, England, Spain, Germany), with the exception of Italy who won in 1982 and 2006 but didn’t qualify this time around.
Another interesting thing is the the sum of all of the probabilities adds up to 119.15%. Why not 100%? Well, the simple reason is that sports books exist to make a profit. The fact that the probabilities sum up to greater than 100% reflects the vigorish, the baked-in mechanism that helps bookies make a profit. A profit is ensured by two things: 1) an appropriate distribution of bets, and 2) odds in the bookies favor. #2 is ensured by having the probabilities add up to something above 100%. Why?
Here’s one way to look at it. The probability of a team winning is in inverse relationship to their odds: the more likely they are to win, then lower their odds (and thus, the lower the payout if they win). As the win probability goes up, the payouts go down. This inverse relationship works for the sum of probabilities too. So, if the total probabilities are greater than 100%, then the total payouts will be, on average, less then 100%. And the sports books make a profit.
Another way to look at it is to take a simple example. A tiny tournament with four evenly matched teams. Each team has a 25% chance of winning. Without the vigorish, the moneyline for each team would be +300, which corresponds to a probability of 25%. Each better is risking 100 to win 300. If the bets were evenly distributed then the payouts will exactly match the bets, and the book doesn’t make any money. For example, let’s say 100 is bet on each team. The three losers each give their 100 to the winner, who pockets 300. The book acts as the middleman but doesn’t make any money.
So, to make a profit, the book adjusts the odds slightly, to +275. Now, if the bets are evenly distributed, each loser is out 100 (300 total), the winner gets 275, and the book takes remaining 25 in profit. That’s how vigorish works.
But, note that a +275 moneyline corresponds to win probability of 26.67%. If all four teams have a win probability of 26.67%, the sum is 106.68%. Which is, of course, greater than 100. The dictionary may define vigorish as “the percentage deducted from a gambler’s winnings by the organizers of a game”, but the way they actually do it is to adjust the odds so that the sum of implied win probabilities for all of the teams is greater than 100%.
