[Help Thread] Number of solves trimmed at each side: 5%

[patricKING]

I've been using csTimer for a short amount of time now and it is one thing that I can't understand. I was doing a couple of solves but then I saw that even though I did a very good solve, my average didn't change. I then looked in the settings and saw the one setting which is in the title. You can find it in 'settings' and then 'statistics'. I need help with understanding what it is, and what option I should choose.

 

[DGCubes]

In cubing, average has a very specific definition that's different from the arithmetic mean. For small averages (like averages of 5 or 12), the best and worst time are removed, and the result is the mean of the middle ones. This way, if one of your solves is a DNF, you won't have a DNF average. (Similarly, if one of your solves is insanely good compared to your usual average, it won't have a huge influence on your average of 5.)

For bigger averages (like averages of 100 or 1000), the top 5% and bottom 5% are removed before calculating. Essentially, in an average of 100, you have room for 5 awful solves (or DNFs) before they start counting. You should almost certainly keep the setting at 5% where it is; since cubers around the globe define averages in this way, if you change this setting, you wouldn't exactly be on an even playing field if you want to compare your averages to those of another cuber.

Another reason your averages might not change is because averages are "rolling"; that means that, for example, your average of 5 will only improve if your next solve is better than your time exactly 5 solves ago. As an example, say a cuber has done the following 5 solves:
1) 12.00
2) 22.00
3) 19.00
4) 20.00
5) 23.00

Their current average is (22.00+19.00+20.00)/3 = 20.33. It's pretty clear that this solver averages around 20 seconds, but say they get an awesome 14.00 on the next solve. Their new average of 5 will be the same, since their counting solves will still be the 22, 19, and 20. In fact, if you calculate the mean instead of the average in this case, the result will actually be worse, even though 14.00 is a very good time for this solver. The 12.00 that they got 5 solves ago is just too hard to beat.

 

[patricKING]

Where is the difference between small averages and big averages? Where is the line drawn?
How does 5% apply to small averages? Is csTimer counting for this? Do they only remove one solve when it's a small average and apply the removal of 5% of the solves when it's big?

Thank you for the previous answer, it cleared up a lot of things.

 

[DGCubes]

Happy to help! I actually intentionally left in some ambiguity between small and big averages because I wasn't quite sure how the calculation worked. I just checked and learned something new!

The rule for calculating an Average of X (where X > 2) is to remove exactly \[ \lceil 0.05 * X \rceil \] solves from the top and the bottom (the cut-off brackets represent the ceiling function). In layman's terms, this means that you take 5% of the number X, and round it up to the nearest whole number. This actually works for both "small" and "big" averages; here are some examples:

Average of 5: 5% of 5 = 0.25, which rounds up to 1. Drop 1 solve on each side.
Average of 20: 5% of 20 = 1, which cannot be rounded up further. Drop 1 solve on each side.
Average of 21: 5% of 21 = 1.05, which rounds up to 2. Drop 2 solves on each side (?!?!?!)

It might be surprising that you actually end up dropping over 19% of solves in an average of 21 instead of the ideal 10% for big averages, but this is actually how csTimer calculates an ao21! You can check yourself by going to Settings -> Statistics -> Statistical indicators -> Custom, and then typing in ao21. If you input 21 times and click on the time for your average of 21, you'll see 4 times in parentheses. (Putting a time in parentheses is the standard way to show it doesn't count in an average.)

Keep in mind, this particular edge case (for weird things like average of 21) might be slightly less standardized - I'm not sure if every timer uses the ceiling function in the same way csTimer does. The only one I've actually checked is csTimer, but seeing as it's kind of the gold standard for timers nowadays, I'd guess that most other timers follow a similar rule. It is pretty straightforward too, since it doesn't require distinguishing between big and small averages. Maybe some older cubers who know more about where this standard originated can comment.