What are the odds of this?

My latest calculation is that the odds of something happening 3 of 27 times that should only happen 1 of 216 times is
1 in 1079

Calculation:
1-(1-0.004)^(27)=0.102566789 This means there is a 10% chance of it happening 1 time in 27 tries, but for it to happen 3 times in 27 tries.....

.10256678 to the third power = 0.0010789971


odds of 1 of 1079

Of course I could be wrong.

Use the Excel Binomial Distribution function found in the Statistical Formulas section. Probability of 3 injuries in 27 rolls for a 1 injury player is 0.026 %. (That's a better calc than my use of Poisson).

Yes, Spider, you're right. Now apply this to 200 leagues running each week with 75 guys having a 1injury roll and playing regularly. You get 200 x 75 x .00026 which is 3.9 guys have this happen every week. It's not that uncommon,it just hurts like hell when it happens to you.

Use the Excel Binomial Distribution function found in the Statistical Formulas section. Probability of 3 injuries in 27 rolls for a 1 injury player is 0.026 %. (That's a better calc than my use of Poisson).

That is not what i get It is a 1 in 216 chance of occurring, but actually it is less than even that because 1-4 does not even get injured so it is (1 in 216 times .8 ) so one in 270 or .0037 chance of occurring in an at bat. Using binomial statistics you get .000138 chance of having 3 or more injuries occur in 27 rolls.1.38 in ten thousand. About 1/3 the chance of an individual being struck by lightning in their lifetime in the United States. Yes it happens, no it is not common.

Using binomial statistics you get .000138 chance of having 3 or more injuries occur in 27 rolls.1.38 in ten thousand. About 1/3 the chance of an individual being struck by lightning in their lifetime in the United States. Yes it happens, no it is not common.

LOVE IT.

Spider67,
Is this the formula parameters for the Excel Binominal Distribution?

=BINOM.DIST(3,27,1/216,TRUE) (I am using 216 for simplicity, although 270 might be more accurate as suggested earlier)

excel calc = 0.999992596 that Steven Drew won't get injured 3 times in 27 plate appearances.


(1 - .999992596) * 100 = 0.00074039999 percent probability of event (i.e., injured 3 times in 27 plate appearances) occurring

Odds = 1000000: 7.4
or, expressed another way....
Odds = 135100: 1

The odds of Stephen Drew getting injured in exactly 3 of 27 plate appearances as compared to the expected result of 1 of 216 plate appearances is 135,100: 1

So, if you fill University of Michigan football stadium and basketball arena with Strat-o-matic players and they all play three games per evening (assuming server is working and they all have the game on their laptop), after several weeks (allowing for player to return from injury), someone is expected to go, "What is going on? How could one of my players be injured three times in the last 27 games?"

Can I take you guys to the race track me ?

You can use: BINOM.DIST.RANGE(27,1/216,3) which yields .026%

The formula you show will yield .026% if you enter FALSE rather than TRUE. TRUE gives the cumulative probability of the result being 0, 1, 2, or 3.

gkhd - I hadn't factored in the "stays in game" or "out only for remainder of game" rolls - good point - changes to .014% (as you said)

rburgh's comment about this occurring frequently because of the large number of leagues and i-injury players at any given time is spot on.

Thanks, Spider. Great work!


Odds = 3846: 1


=BINOM.DIST.RANGE(27,1/216,3)

(I am using 216 for simplicity, although 270 is more accurate as suggested earlier)

excel calc = 0.000259656




.000259656 * 100 = 0.0259656 percent probability of event occurring

Odds = 10000: 2.6
or, expressed another way....
Odds = 3846: 1

Or to state this another way, if you fill McNeese State University's new basketball arena (capacity 3800) with Strat-o-matic players who play 3 games per evening, after a week or so, someone is expected to go "WTF? My player got injured three times in 27 plate appearances, instead of 1 in 216 plate appearances!"

If, as Rburgh says, we are assumed to have 75 regular players instead of 3846, then, depending on how many leagues per person we play per day (1 or 2?), it would be expected that one of us (nobody in particular) might experience this event once every 25-51 weeks (3846/75), instead of once every one or two weeks.

Lots of answers, only one correct one of course.