All Forums > SimLeague Baseball > SimLeague Baseball > How Billy Beane are we really ? - how it ended up
3/7/2013 3:18 AM
All right, I really want to get a handle on this and am NOT being pedantic.  If you create a program to spit out the letter H 28% of the time and the letter O 72% of the time and run it an infinite number of times (OK, you can't do that; say 100 trillion times) it will produce H 28% of the time - not 30%, not 25%.  Now, if you look at any given series within those 100 trillion, there may be (and probably will be) an instance where H was produced twenty times in a row.  Therefore, the rest of the times the production of H is less than 28%, because it was 100% for that stretch.

Or am I confusing analysis of past events with prediction of future results - as in the sex-of-my-second-child scenario (if I introduce you to my daughter and say my wife is expecting our second child, there's a 50-50 chance the next child will be a boy, whereas if I introduce you to my daughter and tell you her only sibling is visiting my parents, there is a 2-1 chance it's a boy)?
3/7/2013 5:05 AM
 pinotfan, I  do  think these explanations are missing a point:

You run the program a million or a hundred trillion times or whatever for H to come up 28% of the time. But you keep going and that "equilibrium" is temporary.

This is also true of the vaunted equilibrium that economists worship as their deity. If it happens at all in real life, it happens once, or at most for a short period and then some deviation starts up again. 

As to the second example, I think I am the one missing something. Why is there a 2-1 chance it is a boy if you say her sibling is visiting your parents ? 

It seems to me that even here these things are only relative: Schroedinger's cat takes over doesn't it ? There is a 50-50 chance of a fetus being a boy or girl but this is another way of saying it is uncertain which it is and so it is determined by its birth, after which, the wave function having been collapsed, it is a 100% chance of being one and 0% of the other - no ? 
3/7/2013 5:12 AM
To use a simpler example: you flip a coin. Despite their being a 50-50 chance of it being heads or tails each time (this is the "program") you might, after 100, 1000, 5000 flips get results like: 

heads  55 tails 45, heads 560, tails 440, heads 2800, tails 2200. After  a billion flips you might end up with exactly 500 million heads and the same tails. But flip the coin one more time and you no longer have it 50-50. 

True, the standard deviations should gradually, asymptotically grow smaller with large numbers of coin flips, but even with even numbers of flips there is rarely going to be exactly 50-50 results. 

In economics, supply and demand may actually, in the real world, be in equilibrium for like 15 minutes once every few years, or millennia, but they will deviate from each other with the very next purchase, logistical tardiness (we should have those on Thursday) etc. Marx, in Capital vol. 3 shows that the same is true of value and prices - they MAY actually coincide every once in a while in the real world, but that is rare and almost coincidental. 

This explains why every time I like a TV series it gets cancelled within a season or so. 
3/7/2013 11:34 AM
In the child example, predicting the future event is unaffected by the past event: the fact I have a girl has no influence on the sex of the child my wife is carrying (throwing out biological factors; this is a probability question).  However, if I have two children already, there are four possible outcomes:
     
First child G, Second B
First child G, Second G
First child B, Second B
First child B, Second G

If I tell you one of my children is a Girl, that eliminates the two boys option.  Two of the other three options are Boy/Girl and only one is Girl/Girl, so the odds are 2-1 the second child is a boy.  The difference between the two scenarios is that the first is predicting a future outcome (the 50-50 chance, unaffected by the past - like the Sim having no memory) whereas the second is analyzing an existing data set.
3/7/2013 1:25 PM
It's not unlike the Monty Hall paradox; always take the curtain, there's a 2/3 chance it's the winner.
3/7/2013 1:46 PM
In the sim, each plate appearance is a completely separate event. The confusion comes when you start putting multiple events together. To use your example, there is a 50% chance that child #1 is a boy. That event has now happened, is complete, and has no bearing on anything else. In another separate event, child 2 comes along. There is once again a 50% chance this child is a boy. If there's 9 boys, the chance of child 10 being a boy is still 50%. Now, if you were to take the whole of 10 children as one event, what are the chances of all 10 being a boy? Very low.

The same with plate appearances in the sim. Each plate appearance is a totally separate event. A .300 OBP hitter has a 30% chance of getting a on base every PA. If he's been on base 9 times in a row, the next PA still gives him a 30% chance. To take the whole 10 PA as a single group and say "what are the chances he'll go 10-10?", this also would be very unlikely.

In other words, the way the sim works, the group size is always 1 - a yes or no. We tend to want to look at a group - what did this guy do last game? What did he do all season? and make our predictions based upon that. The sim shows us the combined results of a bunch of individual events, but they are still all independent of each other.

Not sure if I've cleared anything up or just repeated the same thing, but that's how I look at it.

3/7/2013 2:59 PM
The monte hall effect deals with one outcome and requires knowledge of which possibilities to to remove.   Each individual event is independent in the SIM.   I don't think it works here.
3/8/2013 2:50 AM
We got to Monty Hall in a convoluted way; I conceded that I was probably confusing prediction with analysis of existing data, and it sort of wandered from there.  Monty Hall most definitely does not apply.
3/8/2013 2:56 AM
Posted by mattedesa on 3/7/2013 1:48:00 PM (view original):
In the sim, each plate appearance is a completely separate event. The confusion comes when you start putting multiple events together. To use your example, there is a 50% chance that child #1 is a boy. That event has now happened, is complete, and has no bearing on anything else. In another separate event, child 2 comes along. There is once again a 50% chance this child is a boy. If there's 9 boys, the chance of child 10 being a boy is still 50%. Now, if you were to take the whole of 10 children as one event, what are the chances of all 10 being a boy? Very low.

The same with plate appearances in the sim. Each plate appearance is a totally separate event. A .300 OBP hitter has a 30% chance of getting a on base every PA. If he's been on base 9 times in a row, the next PA still gives him a 30% chance. To take the whole 10 PA as a single group and say "what are the chances he'll go 10-10?", this also would be very unlikely.

In other words, the way the sim works, the group size is always 1 - a yes or no. We tend to want to look at a group - what did this guy do last game? What did he do all season? and make our predictions based upon that. The sim shows us the combined results of a bunch of individual events, but they are still all independent of each other.

Not sure if I've cleared anything up or just repeated the same thing, but that's how I look at it.

Yes, Event One has no bearing on Event Two: the birth of the girl does not affect the chances of future child two being a boy or girl.  But, if I tell you I have two children and one is a girl, that's a different situation: the odds are 2-1 the second child is a boy, for the reasons given above.

As for the rest, yes; I was looking at the results of running a simulation multiple times as opposed to predicting future events.  Unlike many, I do not retreat behind "we'll have to agree to disagree"; I stand corrected.
3/9/2013 6:16 PM
Here is an update: 

Graney, Jack 1919 L 40 139 17 38 8 3 0 13 25 9 0 0 1 .273 .382 .374 .756 2 5
Wolf, Chicken 1889 R 37 138 18 47 4 1 0 18 11 12 0 2 1 .341 .389 .384 .773 6 6
3/9/2013 6:20 PM
As to the admittedly interesting paradox above and the admittedly lucid explanation you give pinotfan, I wonder if this is a "This is not a Pipe" kind of problem: Is it really a 2-1 chance the other child is a boy ? Or just 2-1 that I will think it is a boy ? Since the actual second child can still, as a separate event, not just their past birth, but their present existence, can only be either a boy or a girl and therefore the odds remain 1-1 no ? 
3/10/2013 5:21 AM
No; again, it's the difference between predicting a future event (in which case it's 50-50) versus analyzing a pre-determined data set.  If I have two children there are four possible combinations as stated above (listed in birth order): GG, GB, BG, BB.  If I tell you one outcome is G, that leaves only GG, BG, and GB as possibilities; therefore 2/3 of the time the second result (not chronologically) will be B.  The difference is if I were to tell you my FIRST (or second) child is F; then there is no impact on the sex of the second child; I'm only telling you one of the children absent birth order is F.
3/10/2013 5:05 PM
http://mathforum.org/dr.math/faq/faq.boy.girl.html
3/13/2013 6:02 PM
Latest Update - the team is 26-27 so far, performing a little below where I would expect but not out of it yet. Graney has scored 22 runs and Wolf 25. I thought these a little low, given their respective OBPs - Graney .371 and Wolf .385. So I have moved Holliday from 4th in the lineup to 3rd, moving King Kelly back to 4th where he might drive in Holliday who hopefully will produce more runs, as both he and Kelly's RBI totals did not seem overwhelming. 


Jack Graney '19 (L) 100 230 178 0 18 0 .253 .371 .348 3.96M 
Chicken Wolf '89 (R) 100 200 185 0 22 2 .335 .385 .378 3.92M 
Bug Holliday '89 (R) 100 235 206 5 41 11 .335 .413 .481 5.86M 
King Kelly '89 (R) 100 237 211 8 40 26 .265 .329 .436 5.37M 
Baby Doll Jacobson '19 (R) 99 207 199 2 38 5 .317 .343 .462 4.24M 
Wally Pipp '19 (L) 100 166 156 1 23 0 .295 .331 .423 4.73M 
Deacon White '89 (L) 100 105 97 0 9 0 .227 .286 .278 1.21M 
Shorty Fuller '89 (R) 100 194 177 0 13 4 .232 .275 .277 3.41M 
3/20/2013 8:28 PM
Here's what I see as the fault in your logic, pinotfan:  I already know that one child is a girl, but that doesn't matter, it could be a boy.  All I know about the other child is that it is either a girl or a boy, a population of two, either g or b.  odds are 50-50 either way.  If the child is a girl , the possible  combinations are not gb,bg, gg, they are gb, gg. 
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