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Pythagorean Formula and Basketball Betting

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Updated February 08, 2013

Pythagorean Formula and Basketball Betting

Using mathematics to help predict the outcome of a sporting event is something that has been done for years. That's what statistical handicapping is all about.

In recent years, there has been a tendency to use the Pythagorean Formula to determine how many games a team should have won in any years based on its scoring, both for and against. It is frequently used for baseball and the general premise is that "Expected wins = runs scored(2)/runs scored(2)+ runs allowed(2)."

Later, the exponent was changed from 2.0 to 1.83. The theory behind the method is that teams who won fewer or more games than expected could be good wagers to see a reversal the following year.

The method has been altered for nearly all sports, which use the same premise, but use different numbers. Many times the method is referred to as the Pythagorean Expectation.

There is another use of the Pythagorean Formula that was first mentioned in Sports Betting: A Winner's Handbook, a classic in the handicapping field that you have seen me refer to on occasion. The method presented by Jerry Patterson and John Painter was for the NBA and we'll look at that, as well as a formula for using it in college basketball.

Pythagorean Formula in the NBA

What Patterson and Painter did was to break NBA point spread results into three different categories: home and away; home and away against .500 or opponents and home and away against below .500 opponents; and home or away against division or non-division opponents.

For each team playing, you would need its spread results for each of those three categories and you would then total them up.

Using a game between Philadelphia and Boston at Boston for an example, let's assume the 76ers are 7-9 against the spread on the road; 4-4 on the road against .500 or better opponents; and 5-4 on the road against divisional opponents. When you total the 76ers' spread record:
On the road: 7-9
On road vs. 500+: 4-4
On road vs. division: 5-4
You will get 16-17.

For Boston, we'll use the following:
At home: 10-6
At home vs. 500-: 6-5
At home vs. division: 6-4
When you total Boston's spread records you will get 22-15

The first step is to take the road team's spread wins (in this case 16) and add them to the home team's losses, which is 15, to get a total of 31. Next, take the home team's spread wins (22) and add them to the road team's losses, which total 17, to get a total of 39.

The next step is to square both numbers, hence the Pythagorean Formula name, and 31*31=961 and 39*39=1521.

Because the home team is classified as A-squared, we will calculate the home's teams percentage of covering the spread. The Pythagorean Formula has you divide A-squared by A-squared + B-squared, so our formula for this game will read "1521/1521+961 or 1521/2482=.613 or 61.3%, meaning Boston has a 61.3% chance of covering the point spread.

Patterson and Painter said to look for favorites with a greater than 70% chance of covering the spread or underdogs with a greater than 58% chance of covering.

Pythagorean Formula in the NCAA

The formula is the same for college basketball in that you divide A-squared by A-squared + B-squared, but the difference is the categories used. For the NCAA, I would use: home and away; favorite or underdog; and conference or non-conference.

Using the Thursday, Feb. 7, 2013, game between Washington and UCLA in Los Angeles, lets assign the following for Washington:
Away: 6-3
Underdog: 6-3
Conference: 7-2
When you total Washington's record you get 19-8.

For UCLA, we'll assign the following:
Home: 6-7
Favorite: 6-13
Conference: 4-5
When you total UCLA's record you get 16-25.

Adding Washington's wins to UCLA's losses gives a total of 44 and adding UCLA's wins to Washington's losses gives a total of 24.

When both numbers are squared, we get 44*44=1936 and 24*24=576. Now the formula will read 576/576+1936 or 576/2512=.229, meaning UCLA has a 22.9% chance of covering the spread, so the play would be on Washington. UCLA won 59-57 as 7.5-point favorites.

Like many other articles, this is one of those that I am throwing out there for you to examine and play around with. I wouldn't blindly wager on its games, but do some tinkering and see if it still holds any value.

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