There is a special category of Prop Bet that you should know about, and those are the prop bets that can be analyzed using the Poisson Distribution.  (Poisson was a French statistician and the concept is named for him.)  Simply put, Poisson looks at the probability of the number of times an event will occur.  That event, however, must meet two criteria:

• The events must happen one at a time
• There must be a known average rate for the occurrence of these events. 

For example, the Cleveland Browns are averaging 3.6 (known average rate) turnovers (event occurring one at a time)  per game.  This fits the model for a Poisson distribution.  Whereas the Cleveland Browns are averaging 22.4 points per game does not.  While the rate is known, points are not accrued one at a time in NFL football. (NHL totals on the other hand...)

Lets say you were offered the following prop bet:

• Cleveland will commit 3.5 turnovers during their next game:
• Over -115
• Under -115 

Is there value here?  To know we must find the probability that Cleveland will commit 0, 1, 2, or 3 turnovers.  Then we need to compare that to the betting line being offered.  Fortunately there is a Poisson calculator built into MS EXCEL.

To use it, open a spreadsheet and select a cell, then press the function button (fx).  This opens the function dialogue box.

Select "STATISTICAL" from the category drop down menu.  In the function list box select "POISSON" and click "OK".

This opens the POISSON Distribution Function Arguments Box.

Now we just need to enter the arguments (which in fancy math speak means the details of our particular problem).  X = the number of events we are interested in.  I have entered 3, because we want to know the probability of 3 or fewer turnovers.  MEAN = 3.6, the average turnover rate.  CUMULATIVE is asking us whether or not we want to know the total of the probabilities from 0 - 3, or if we just want to know the probability of exactly 3 turnovers.  We want to know the total of 0 - 3, so CUMULATIVE = true.  If you wanted to know the probability of exactly 3 turnovers, you would enter false.

At this point MS EXCEL calculates the Poisson Distribution for us.  The formula result is listed as 0.51521661.  If you really want that on a spreadsheet, you can click "OK" and the Function Arguments box will close and the formula result will be in the selected cell on the spreadsheet. 

For our purposes, we can round or truncate the result to 3 digits.  Therefore the probability of 3 or fewer turnovers by Cleveland is 0.515.  This means the probability of 4 or more turnovers is 1 - 0.515 or 0.485.

Back to our prop bet.  We need to compare the break even odds for our known probabilities against the offered terms of the bet.  A simple trick for this is to make a ratio of the losses to wins and multiply by 100.  (Whenever that ratio is less than 1, you invert it and multiply by -100) If we bet the UNDER we lose with a probability of .485 and win with a probability of 0.515. As (0.485/0.515) gives a losses to wins ratio of less than 1, we invert the ratio and multiply by -100.  (0.515/0.485)*(-100)= -106.  We would need to bet the under at better than -106 to expect to make a profit.  As it is being offered at -115, we should NOT take this bet.

Turns out that the offer on the OVER is even worse.  Given that our loss probability is 0.515 on the over, we would need to get this at better than +106 to expect a profit on Cleveland making over 3.5 turnovers.  We should not take this bet as offered, either.  There is no value in the line being offered on this bet, and using a bit of analysis with the Poisson Distribution we can prove it.

You can find a wide selection of poisson distribution prop bets at SportsInteraction.  Read our SportsInteraction sportsbook bonus review.