A Newbie with a Newbie Math Question

[MeanPeopleSuck]

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.

Thanks in advance for any help you might be able to provide!

[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%.

[MeanPeopleSuck]

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%).

Thanks again for the reply!

[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

[MeanPeopleSuck]

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.

[Bsims]

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.

[gdon44]

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.

Thanks in advance for any help you might be able to provide!

The player you are talking about averages 82 goals a season in this scenario. I bolded the part that might be causing you confusion. You seem to have ruled out that tonight's game is not going to be one that he scores multiple times. Bsims poisson distribution (there's lots of good info on how to use it for sports gambling...worth a look into at least the theory behind it) would suggest more than 50% because it's taking into account that this might be one of those nights he gets 3 goals. If he's a goal a game guy then you have to figure there's a good probability he'll score not a weaker probability.

I'm no expert but that's my take on reading this thread. If I'm wrong I'll give my apologies and bow out.

[MeanPeopleSuck]

Bsims and gdon44, oh, right, duh. No, you're completely right. Thanks very much for your help.

Heh, I think it's amusing that the only conclusion I thought I could draw from my hypothetical -- that it must be less than 50% -- was dead on wrong. It probably won't come as a shock to anyone here that I wasn't a math major in college!

Thanks to you guys and to everyone on the thread for helping set me straight. To quote Family Guy's Brian Griffin: "math, you dick."