Yeah. There are a lot of useful ways to look at it, honestly. But after doing that work on the Burst Time metric, I've basically come to the conclusion that there's definitely no "one number" that can really cover it.

I like your hit-chains-to-EH thing above. Note, though, that I'd suggest you express it in terms of frequency or probability instead of doing a simulation (your iterative loop? Otherwise your math is way off). It definitely does not take a simulation to calculate the likelihood or frequency of these things.

Code:

1.84% 5+hit chains 5.03% 5+miss chains
2.26% 4-hit chains 4.12% 4-miss chains
5.01% 3-hit chains 7.49% 3-miss chains
11.14% 2-hit chains 13.61% 2-miss chains
24.75% 1-hit chains 24.75% 1-miss chains

Code:

1m49s 5+hit chains 39.76s 5+miss chains
88.50s 4-hit chains 48.54s 4-miss chains
39.92s 3-hit chains 26.70s 3-miss chains
17.95s 2-hit chains 14.70s 2-miss chains
8.08s 1-hit chains 8.08s 1-miss chains

The probability of a n-hit chain with avoidance a is (a)(1-a)^n. The probability of an n-miss chain is (1-a)(a)^n. The probability of an n+hit chain is (1-a)^n. The probability of an n+miss chain is a^n. The frequency of an event with probability p on a stream with interval t is t/p. (i.e. 2.0s/0.0501 for 3-hit.) The 5+miss chains are more frequent than the 4-miss chains because the probability of getting 5 or more misses in a row is greater than the probability of getting exactly 4 misses in a row.

So--the math is not hard at all, but the probabilities involved are such that for a simulation, you'd have to do a lot more samples to get the probabilities correct. Let's compare your hit numbers to the probable hit numbers from the probabilities I've given:

Code:

Your numbers Probability
---------------- ------------------
0 4-hit chains 13.6 4-hit chains
4 3-hit chains 30.0 3-hit chains
41 2-hit chains 66.9 2-hit chains
174 1-hit chains 148.5 1-hit chains
================ ==================
270 hits total 270.0 hits total

That's far enough off that I'm really not sure what you were doing to get your numbers.

Anyway: What it comes down to is, I think that some sort of "distribution"-based information (like showing the frequency of various numbers of hits in a row) combined with EH is best. Trying to distill things to one number was too much. Good luck.

## Bookmarks