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)?

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 ?

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.

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.

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.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.

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.

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 |