Re: Stats Gone Wild! Plus Triple-Play Bonus

M C Hamster wrote:
> Mike Kruger wrote:
>>
>> I simulated 2000 sequences of 108 years (1901 to 2008) and in 8 
>> of
>> them there's a gap as long as from 1927 to 1968. [boring details
>> below]
>>
>
> Oh cool, I love simulations of baseball statistics.
>
>> Baseball expansion hits in 1962 (?)
>
> It was in 1961.
>
>> with the move from 8 to 10 teams
>> (Mets, Astros ...)
>>
>> Base stealing hits about the same time as expansion with Maury 
>> Wills
>> stealing 104 in 1962. However, this is NOT break Ty Cobb's record 
>> of
>> 96 stolen bases because the number of games in the season had 
>> gone
>> from 154 to 162, and Wills' 97th stolen base occurred after the
>> 154th game.
>>
>> Lou Brock then took up the mantle. Brock was traded from Cubs to 
>> the
>> Cardinals in 1964 in one of the great trades of all time 
>> [snicker],
>> and went on to steal 118 bases in 1974 -- breaking both Cobb's 
>> and
>> Wills' records.
>>
>> Brock went on to market the Brockabrella:
>> http://www.yardbarker.com/author/user_photo/9971
>
> Wait.  Where are the "boring details below"?  I LOVE boring 
> baseball
> simulation details.

The boring details were below my sig line. I'll repeat them here:

Boring details:  I ignored baseball expansion [which creates more 
games in a season] and treated each year
as an entity.  Based on the fact that there are 14 occurrances in 
108 years, I estimated a poisson mean of .129 per year. Then each 
year can have 0, 1, 2, etc. triple plays based on that poisson mean.
Once 108 years are simulated, it's a simple matter to count the 
largest string of zero years (which can be any set of years, not 
just 1928-1967).

I did this 2,000 times, which is enough to get the idea that this is 
rare but not terribly impossible under random cir***stances.

> Without seeing your simulations, though, if you
> had to simulate 2000 seasons [actually 2000 sets of 108 seasons] 
> to produce just 8 examples of a 41-year
> gap, that's highly improbable to have occurred by chance, only a 
> 0.4%
> probability.

Right. I characterized it as "rare but not terribly impossible", 
which is in the same ballpark.

Not as rare as a Cubs World Series win, evidently.  ;)

> Then you have to add in the 24-year gap that followed
> 1968... it's the two consecutive gaps that is especially amazing. 
> In
> how many of the 2000 simulated seasons did you have no more than 1
> occurrence in a 65-year period?  I'm going to guess no more than 
> 1.

I could look at that, but that sort of thing gets dicey. For 
example, we can look at a 41 year gap followed by a 24 year gap, but 
really that's no more unlikely than a 40 year gap followed by a 25 
year gap, or a 39 year gap followed by a 26 year gap.  You can see 
where this is heading -- it's hard to determine exactly what set of 
events are comparable.

An example of a similar problem is names.  It would be unusual to 
find a girl with a first name of "Delight" -- I've only heard of 
one.  But it's not unusual to find a girl with a name you have never 
heard of before, so the exact class of events is hard to define.