Sportsball: Series

I grew up playing soccer. I liked soccer because on any given day any team can beat another team. It only takes one goal. You only needed one good shot (this was particularly encouraging because our team was best described as "scrappy").

This is not the case in all games of sportsball (or sports-disc). Basketball for example is a game of averages, where each team takes hundreds of shots and the law of averages should prevail. The better team should win most games.

But there is another mechanism that sports use to ensure the best team wins: Series. Baseball has the World Series. Hockey has the Stanley Cup. The NBA has their championship series (honestly, not sure what it's called, but they play several games). Tennis has sets and matches. Football and futbol (soccer) are notable exceptions where it only takes one game to be the champion.

Why Play Series?

Let's take two examples of a championship game. First, let's assume the teams are even. There is a 50/50 chance either team will win. In a one game match, it is anybody's guess who will win. Second, let's assume we have an underdog with only a 10% chance of winning. Most of the time the favorite will win, but once a decade, we can expect the underdog to prevail.

Now let's think about a best of 7 series. In the first case, each team still has a 50/50 chance at each game, and it's still a coin toss who will win. However, now the team that has a 10% chance of winning on any given day, has to win 4 times in a row. Mathematically, that is 10% * 10% *10% *10% = 0.01% chance of winning. Series stack the deck against the underdog.

Now let's consider a 1, 3, 5, 7, and 9 game series, give each team a probability of winning one game and see how they would fair on average in a series:

Not surprisingly, the 1 game series is a straight line. Also, unsurprisingly, at 50% chance of winning, all series have a 50% chance of going either way.

More surprisingly, let's look at the 30% probability of winning a single game. In just a 5 game series the probability of winning goes to16%, lowering the chance of winning for this team by nearly 50%. In a 9 game series the probability of winning drops to 10%.

Effects on Gambling

Now with perfectly set gambling odds, this really has no effect. This isn't news for Vegas odds-makers, but it might be important for fans who bet with emotions over practicality.

Let's say you always bet on the Yankees. If you believe they are an above average team (which due to payroll only makes sense), they are a good bet. Even if they have only a slightly better than 50% chance of winning any game, the chance of winning a 7 game series is significantly increased by this slight edge. Conversely, betting on a baseball team that is slightly below average is unlikely to pay off. They may have a harder time winning 4 out of 7 games, but they are perfectly capable of winning 1 out of 1.

Or let's say you love Brazil in the World Cup. Not a bad bet, but in the elimination stages anything can happen. They only have one chance. This makes them a riskier bet then if they had a series to show off their skill.

Final Thoughts on Sportsball Series

Series are fun. They bring people together for a whole week. They ensure the better team has the best chance at winning. They reward consistent performance.

However, I am not sure they are as interesting. It ensures the favorites and top teams win, but this boxes out the underdogs. I'm a fan of the day of the dog. March Madness is interesting because in one game, anything can happen. There is no waiting for the next game that "really matters." A top seed can be knocked out by an underdog. In soccer, Iceland could have won the World Cup. A series of fortunate events can propel an underdog to be the champion if it is only one game, one chance, one goal, that separates two teams from the title.