>>4471316 (lb)

This is a follow-up about statistics, elaborating on a specific detail that I've felt is important for anons to understand if they're looking for small numbers like 17 and 23. The topic is similar to the Texas sharpshooter's fallacy, but extended here to a discussion about the importance of considering the size of the "wall" being shot at.

When asking the question "what are the odds?", be skeptical of finding coincidences in situations where the range of possible outcomes is not that large.

I tend to ignore a lot of the "hey here's a 17" kind of evidence, because if you've got a seek space that generates numbers in (say) the 1-99 range, there will be random 17s all the time. 1-in-100, so if you look at 200 events (even if just checking to see "is there a 17 here?") you're bound to find one, by random chance. Finding small numbers is only significant if you've restricted the pool of "what counts as a hit" in some way.

For example, let's say that I had some reason to believe that a coin flip of "tails" meant something important. Let's imagine that I flip a coin 4 times, and one of those times it comes up tails. "I flipped a coin and it was tails, woo hoo!!!"

Um, no. The odds of getting tails on one of those four coin flips was 15/16 - very high, 94 percent. It's not a coincidence worth anything.

So simply FINDING a 17 or 23, by itself, means nothing.

Let's go to the Texas sharpshooter analogy. If your Texas sharpshooter wall is 100 bricks wide, and there are two special bricks, your odds of a "hit" with each random blindfolded shot are 2 percent. Take 100 shots at the wall blindfolded, and you'll make a direct hit. But what does that really mean? Not much.

There are small numbers everywhere. If the odds of a random hit are very small, say 1 in a million, then it's far less likely that you'll stumble into it by chance. But be skeptical about coincidences involving small numbers.

We're having this conversation because Q asks us to watch for "coincidences" that are not, with the catchphrase "what are the odds?" And sometimes Q points at events where small numbers (especially 17 and 23) are featured as the unlikely evidence.

Q speaks in riddles. By "what are the odds?" when talking about a series of apparently unconnected events, Q is really telling us "this was not a coincidence", or in plainer language, "we made this happen". It's a way of giving us information.

In mathematical contexts, like the delta between post times, Q is flirting with the edge of probability … intentionally not doing anything quite blatant enough to be totally incontrovertible, but unlikely enough to get anons' attention. So a lot of "coincidences" involving small numbers are perfect for Q's purposes (the odds stacking up, showing a repeating pattern of something only slightly unlikely). Usually the context is pretty limited - there are only so many posts in a day from Trump or Q, certain words can tie together particular posts so we're not looking at the universe of all post combinations, etc. It's a subtle game, and carefully constructed.

In statistical analysis,when thinking about the evidence for something being intentional (not coincidence), think about the odds that it COULD happen by random chance, which means

1) think about the size of the pool of events that you're looking at (how many shots at the wall you're evaluating)

2) think about the size of the target (the odds that each shot at the wall would count as a "hit")

It's good for anons to watch for "coincidences" that are more than that. I encourage digging in such directions, including the 17s and 23s that Q has signified are important (even if I tend to be skeptical for the reasons described here.)

But be aware that finding "coincidences" revolving around small numbers is shaky ground, and it takes a fair amount of care and caution to do it right. Most of the time, the special small numbers will just be scattered around everywhere by random chance.

I'd love it if Q did something that was REALLY unlikely involving these special small numbers, like arranging for two Trump tweets with timestamps separated by 152,881 seconds (17 * 17 * 23 * 23) = 42 hours, 28 minutes, and 1 second. But I wonder if any of us anons would pick up on a statistical signal that loud.

>>4471611

A follow-up that shows how even seemingly unlikely things can be … not so unlikely:

In my prior post about statistics, I used as an example if there were two Trump tweets separated by (17 * 17 * 23 * 23) seconds = 152,881 seconds, this would be a loud statistical signal.

But is it really?

Suppose Trump tweets 5 times a day. Over six months there would be 900 tweets. (Don't know how often he tweets, but this feels like a semi-realistic number for illustration.) We can look for a timing correlation between any pair of tweets - that's (900*899 / 2) combinations. (The divide by two is so we don't count a pair of tweets A and B twice as AB and BA.) That comes to 809,100 combinations.

Since we're comparing timestamp deltas, the "wall" being shot at is 6 months = 15.552 million seconds in width.

By looking at the deltas between every pair of tweets, during those six months, we take 809,100 shots at that wall. 15.552 million / 809,100 = about 19.

So the odds of finding a pair of tweets separated by EXACTLY some specific number of seconds (in this case, a "hit" is 152,881 seconds) would be only 1 in 19, if we're sitting back and watching over half a year.

That's unlikely, but really not that unlikely. Statistical significance is usually defined as more unlikely than 1-in-20 by random chance. This doesn't even hit that threshold.

So something that SEEMS unlikely may not be, in this case because (by looking for a hit in the timing between any pair of tweets) we're looking at so vast a pool that unlikely things are not unlikely to be in there somewhere.

When writing my original example, my intuition was that hitting 1 in 152,881 odds is much more significant than 1 in 17. But for that to be the scenario when comparing timestamp deltas, what we really want is a situation where we have some specific reason to look at THIS pair of tweets and no others. For example, if Trump made a specific typo in some rare word in both tweets, that would be an arrow saying "compare these tweets".

Even now, I may be making subtle statistical reasoning errors in calculating those odds. For example, I was supposing the deltas were randomly distributed in the 0 to 6 months range, but if there are defined start/stop times it's hard to get a pair at the extreme of 6 months, there are edge conditions to consider. Correct statistical reasoning is difficult and requires awareness of all kinds of implicit assumptions humans tend to make.

The first moral of the story is that it's good to really think about whether something that seems unlikely really is unlikely.

The second moral of the story is that it's good to watch for situations where two unlikely factors stack together. Like a rare word or a rare typo that's replicated in two places. Probabilities multiply with each other; stack two unlikely things together in the same place, and your evidence is MUCH stronger than if you have one unlikely thing happen. Like hitting the lottery twice. (And yes, that happens, but I don't know if it's random chance or rigged.)