Pythagorean Expectation

Football betting with the numerator

About 1,500 years ago in ancient Greece a mathematician named Pythagoras is said to have discovered a method to calculate the length of the sides of a right angled triangle which would prove to be the bane of many school children for centuries. Fast forward some 1,470 years to when a baseball historian and statistician named Bill James made his own discovery which would revolutionize the way the ability of many teams across a number of sports were assessed.

In this article we take a closer look at one of the most powerful predictive and analytic tools available to sports bettors, pythagorean expectation.

What is Pythagorean Expectation?

Understanding pythagorean expectation is vitally important for all sports bettors, especially those who bet or trade on futures markets.

Put simply, pythagorean expectation takes the key component of winning a sport (in baseball for example the scoring and conceding of runs), and uses those statistics to predict the number of games a team will be expected to win in a given season.

Pythagorean expectation is not just a predictive tool though, it also can be used in real time to see if a team is meeting, exceeding or under-performing expectations.

So where do triangles come in?

Luckily for use there isn’t any 7th grade geometry involved. Pythagorean expectation gained its name as the formula used resembles that of the famous triangle calculation.

For baseball, the formula used to calculate winning percentage is:

Win Percentage = Runs Scoredˆ1.81 / (Runs Scored ˆ1.81 + Runs Allowed ˆ1.81)

To then work out the amount of expected wins for a season, the winning percentage is times by the amount of matches in the season.

Using Pythagorean Expectation in betting

The most obvious application for pythagorean expectation is simply betting on season win totals for an individual team, or in betting on the overall winner of a competition.

However it can also be used as a powerful tool for judging form, and analysing whether a team may be “unlucky”, or is over-performing their true ability.

Teams with a winning percentage over their expected win percentage using pythagorean expectation are thought to be “lucky”, and perhaps winning matches they should not be. This may be because of a soft draw, or they have simply been getting the rub of the green. The opposite is also true, teams under-performing their expectation may be playing stronger opposition or have been unlucky in some of their matches.

For most sports- particularly one like baseball’s MLB where teams play a large amount of matches- it would be expected that over the course of a season teams will finish closer to their expected winning percentage.

So those over-performing teams will soon run out of luck, while the under-performing teams would be expected to begin winning more matches.

Applying Pythagorean Expectation to other sports

While pythagorean expectation is very much an accepted statistic in baseball, it has also been modified and applied to a host of other sports very successfully.

In its most basic form the formula:

Win Percentage = Points Scoredˆk / (Points Scored ˆk + Point Conceded ˆk)

Can easily be adapted for different sports through the use of a different “k” value.

An online search can help to find a host of different k values for a range of sports, while often they are modified as sports and their scoring evolves over time. In some sports different statisticians also have differing opinions on what are the most accurate k values.

Some k values applied to different sports include:

  • Baseball- 1.81
  • Basketball- 13.91
  • American Football- 2.37
  • English Premier League- 1.3
  • Ice Hockey- 2.15
  • Australian Rules Football- 3.87
  • Rugby League- 1.89

The ability to easily implement such an accurate and powerful predictive tool makes pythagorean expectation a must for all sports bettors.

Through the use of a simple excel spreadsheet with minimal updating you can at a glance tell how well a team is performing, as well as how they will be expected to perform over the course of a season. Whether or not you use pythagorean expectation as a stand alone betting system, or to compliment your existing handicapping make sure it’s something you add to your punting toolkit.

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