Home Articles The Gambler’s Toolbox: Using Poisson Distributions in Betting

# The Gambler’s Toolbox: Using Poisson Distributions in Betting

As a gambler, my number one skill isn’t that I pick games. It isn’t that I price props. It isn’t that I have a crystal ball, or a secure safe full of cash and coins, or a vault like Scrooge McDuck (although that would be both awesome, and not nearly has hard to swim in as he makes it look).

As a gambler, my number one skill is a willingness to learn. I’m always trying to find new edges, and I’m always willing to cast off old ways of thinking if I find they aren’t successful. “Oh, this doesn’t really work? Time for the next thing.” It’s easy to be stubborn and think the laws of the universe are conspiring against you. It’s easy to think your processes are ironclad and it’s everything else around you that’s going wrong. Constant re-evaluation and improvement (tweaking, if you will) will lead to much more success, though. Keeping an open mind helps a lot too. As Alan Boston, noted college basketball degenerate, once said, “you get better at something by eliminating mistakes, not by being a genius. How many genius things do you really do in the course of your life?”

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One way to eliminate mistakes is to figure out the best way to solve a problem. Any gambling situation, prop or otherwise, is something I choose to consider a problem, and then I try to figure out how to solve it. Roulette? That’s not solvable. On to the next problem.

In sports, some of the problems can be solved using a tool called a Poisson distribution, which predicts the probability of a certain type of event occurring. Many sites offer a Poisson calculator that will do the work for you as long as you have a number you trust to run in it. Although it can be important to know the ins-and-outs of the formula itself, the variables, the exact way the math is calculated, that’s just never really been my bag. If the world of math and statistics tells me that’s what this formula is for, I’m using it. Leap of faith? Maybe. But it’s also math, so that’s basically a contradiction.

The criteria which you use to decide whether Poisson is applicable is the most important thing. Many have tried and failed to equate it with certain props, only to lead themselves unknowingly down the path to ruin (or just heavy losses). The common example people use is a coin flip. If you use Poisson to price a coin flip, you get a price so obviously outrageous (Heads +154/Tails -154) that you can see what I mean.

–Does the thing you are pricing occur in a fixed time and space? For sports betting, this one is fairly easy, and almost always comes up yes.
–The number of trials you are looking at needs to be pretty big. Several things I’ve read list 20 or more as a guideline. So for example, if you were trying to calculate the # of sacks in an NFL game? There are definitely more than 20 dropbacks-to-pass in an NFL game. That’s an opportunity for the event to occur.
–Does the thing you are pricing occur rarely? A standard metric is, in every trial, a 10 percent chance or less of occurrence. You will immediately rule out many things based on this. Heads on a single coin-flip, for example (which also fails the first criteria).
–Does the thing you are pricing go up in increments of 1? This will rule out other things – scoring in football and basketball for example (which goes up by 2,3, and 7), although not necessarily the number of a certain type of score (like field goals).
–Is the event “memoryless”? Or, put another way, if the event occurs (a sack happens), does that increase or decrease the likelihood of it occurring again in the same game? If it does, then Poisson does not apply. You need to be able to trust the distribution of results you’ve observed going backwards, that you are using to come up with your numbers, and that those will continue to apply. This is a hang-up that has led many people I’ve seen to question whether NHL goals are applicable, because scoring increases sharply in the last 2 minutes of many games (when the other team pulls their goalie down by 1). If teams wouldn’t adopt this strategy, I think we’d have a winner. Now? I’m not so sure.

And that uncertainty is also something I want to hammer here. The applications here are up to you to decide. Take this for a spin, and try it out. There are things that I know this works for, especially in football. The likelihood of a team recording a safety, for example. Or the number of sacks they’ll record in a game. The likelihood of a game during bowl season, or the NCAA tournament, going to overtime (which, if you follow me on Twitter, was something I have brought up before). In these cases, the prop fits the criteria, and you can use research and past history to come up with a number that’s pretty solid to enter into the formula. The number can be trusted.

Folks have tried to argue that NBA rebounds and assists are successfully predicted using this formula as well, but I’m not totally convinced, since there are so many variables during an NBA season (resting starters, playing teams with faster pace) that I’m not sure previous data can be trusted to price current games.

The important thing with this type of tool is to figure out what problems it best solves, and use it there. Keep an open mind. Eliminate mistakes. Be willing to learn.

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