Well Isnt That Speshal..

[tfriede2]

Sorry for being short earlier. This is difficult to explain, but I’ll try:

From a scientific and probabilistic standpoint, changing the Blues from 11th to 9th creates a different initial state, which means you are no longer analyzing the same event. You are analyzing a counterfactual — an alternate timeline.

The actual lottery result is the product of:

1. the exact teams occupying each slot,
2. the probability combinations assigned to those slots,
3. and the random draw itself.

Once you alter one of those variables — replacing San Jose with St. Louis in the 9th slot — you have changed the system being evaluated. In probability theory, you cannot hold the outcome constant while simultaneously changing the inputs to the random experiment.

In other words:

* The real-world lottery outcome only applies to the real-world configuration of teams and odds.
* A different standings outcome requires a new realization of the random process.

Scientifically, this is similar to rerunning an experiment with altered initial conditions:

* If you change the starting conditions, you do not assume the same random outcome will occur. Instead, you must perform a new trial.

So the correct conclusion is not:

“The Blues would have gotten the #2 pick.”

The correct conclusion is:

“If the Blues had finished 9th, they would have entered a different lottery configuration in which they had approximately a 5% probability of obtaining the #2 pick.”

[Aesa]

Excellent and accurate analysis. Well done!