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1. A Newbie with a Newbie Math Question

Hi, all, I'm new to the site but I'm excited to get to know you. Thanks for taking the time to read this.

Here's my question: let's assume a hockey player averages a goal every 20 minutes of ice time. Let's further assume he'll get 20 minutes of ice time tonight. What's the percentage chance that he'll score tonight?

All I can figure out is that it must be less than 50%, because SOMETIMES he must score multiple times in 20 minute stretches, which would then require more than an equal amount of empty 20 minute stretches to get him to his average, but I can't get my brain around what the proper discount below 50% should be.

2. I would assume a Poisson distribution (not a perfect fit, but close). Excel has a function to compute the probability. For 0 goals given an average of 1.0, =POISSON.DIST(0,1,0) returns 0.367879441. So the chance that he'll score is 1-0.367879441, about 63%.

3. Originally Posted by Bsims
I would assume a Poisson distribution (not a perfect fit, but close). Excel has a function to compute the probability. For 0 goals given an average of 1.0, =POISSON.DIST(0,1,0) returns 0.367879441. So the chance that he'll score is 1-0.367879441, about 63%.

Thanks. If you'll keep my secret, I'll admit to you I have no idea what a Poisson distribution is, but would its answer be a 36.8% chance he's score tonight? (The only thing I'm reasonably sure about this question is that the answer must be a number below 50%).

4. you should probably try to estimate his chances of scoring greater than or equal to 1 goal, not the probability of exactly one goal being scored

whoops

So the chance that he'll score is 1-0.367879441, about 63%.

he calculated the chances of scoring 0 goals, then subtracted that from 1 to find the probability of everything but 0 goals

5. Originally Posted by PerfectGrape
you should probably try to estimate his chances of scoring greater than or equal to 1 goal, not the probability of exactly one goal being scored

whoops

So the chance that he'll score is 1-0.367879441, about 63%.

he calculated the chances of scoring 0 goals, then subtracted that from 1 to find the probability of everything but 0 goals

OK, so what we're saying then is our hockey player's chance of scoring 1 or more goals tonight is 37%-ish?

So the true line of his 'score a goal tonight?' prop would be about Yes +172 / No -172?

Thanks for your help. I definitely need to brush up on my probabilities math.

6. Originally Posted by MeanPeopleSuck
OK, so what we're saying then is our hockey player's chance of scoring 1 or more goals tonight is 37%-ish?

So the true line of his 'score a goal tonight?' prop would be about Yes +172 / No -172?

Thanks for your help. I definitely need to brush up on my probabilities math.
No. 37% is the chance he won't score. 63% is the chance he will score.

7. Originally Posted by MeanPeopleSuck
All I can figure out is that it must be less than 50%, because SOMETIMES he must score multiple times in 20 minute stretches, which would then require more than an equal amount of empty 20 minute stretches to get him to his average, but I can't get my brain around what the proper discount below 50% should be.