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  #11  
Old 06-10-2015, 12:16 PM
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Quote:
Originally Posted by sillyface View Post
The slowest ever time for a particular puzzle cannot get faster over time.
I just came across one of your puzzle comments. You recorded the slowest time as 1315 seconds, but now I see it is 1195.

My guess is that the fastest time you see is actually the fastest, but the slowest is at the 90 percentile mark, or something like this.

If it really showed the slowest, then you would see times above 10,000 seconds (3 hours) all the time, since you can come back to a puzzle up to 24 hours later.

I've played logic-puzzles.org for a while, and theorized that the slowest times don't show up there, using the same reasoning. I'm glad you actually are recording this data, as it validates my theory!
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  #12  
Old 01-12-2017, 01:52 PM
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When I do these puzzles now, I just record my time, the fastest time, and the median time. So, I write something like this:
Code:
180, f=80, median=360
Once you have this, then you know what all 5 tick marks are on the chart. The first one is the fastest time (80s). The second one is half way between the fastest and the median (220s). The middle one is the median (360s). The 5th spot is either the median multiplied by 5 or your current time, whichever is larger (360 * 5 = 1800s). The 4th spot is half way between the 3rd spot and the 5th spot (1080s).

If you play a lot of puzzles, you'll see values that are not whole numbers some times. These can only appear in the 2nd or 4th spot of the graph. The number in the second spot of the graph will be xxxx.5 if fastest time + the median time is an odd number. The 4th spot of the graph is almost always an integer, but can be xxxx.5 if the median + your time is an odd number and your time is larger than the median time multiplied by 5.

Every size of puzzle has a maximum and minimum amount of points that you can score. I haven't experimented much to figure out the minimums, but the maximums are:

Code:
8 points for a 5x5
26 points for a 7x7
56 points for a 9x9
116 points for an 11x11
161 points for an 11x15
199 points for an 11x19
To figure out your score, your percentile must be calculated. This isn't a real percentile, because it's just based upon values: your time, the best time, and the median time. So, it's kind of a faked percentile, but I'll still call it a percentile because it's easiest to think of this way. Here's how it is calculated:

Code:
Your percentile = 1.00 if your time is better than the fastest time.
Your percentile = 0.50 if your time is the same as the median.
Your percentile = 0.00 if your time is worse than the median * 5
If your time (t) is between the fastest time (f) and the median time (m), then your percentile is:

Your percentile = 1 - 1/2 * (t - f) / (m - f)

If your time (t) is between the median time (m) and point 5 on the graph (m*5), then your percentile is approximately:

Your percentile = 1/2 - (((t - m) / m) - 1) / 8

I've noticed my calculations are a little off for the scenarios where I'm between (m) and (m*5), so the formula I listed above for your percentile in those cases may be off.

Now that you know your percentile, you can multiply it times the max points available for the puzzle. As long as this value is larger than the minimum number of points for the puzzle, this is what you will get. If it is lower than the minimum value for the puzzle, then you get the minimum value.

So, back to our example, where I recorded the following for an 11x11:
Code:
180, f=80, median=360
The median will be 1 - 1/2 * (180 - 80) / (360-80)

That comes out to be 1 - 0.5 * (100 / 480) = 0.8214

Now you multiply that by the maximum points for a puzzle of that size (116):

116 * 0.8214 = 95.29

Now you round that to the nearest integer (95), and that is the number of points you get!

Last edited by uigrad; 01-12-2017 at 01:54 PM. Reason: Small correction
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  #13  
Old 01-12-2017, 03:06 PM
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Quote:
Originally Posted by sillyface View Post
Trying to figure out the scoring system seems futile. From the same puzzle:
May 21st - 256s 213t 93p f133 s2230
May 25th- 149s 175t 113p f133 s2170
Using the scoring information from the previous post, I can show you that these work out.

I took the slowest times you listed (2230 and 2170), and divided them by 5 to get the medians: 446 and 434.

Then I used your times (256 and 149) along with the fastest times (133 and 133) and the medians (446 and 434) to get your percentiles: (.8035 and .9734)

From there, I use the max value for an 11x11 (116) and get your scores (93.21 and 112.92).

You recorded 93 and 113, which is exactly what I get after rounding.

Quote:
Originally Posted by sillyface View Post

Obviously the data is somehow corrupted. The slowest ever time for a particular puzzle cannot get faster over time. I've previously noticed that the 'slowest times' under the bell curve are rounded off to five second increments; I now wonder if they're even generated from player's times.
It turns out you were correct. Points 2, 4, and 5 on the graph are completely fabricated based on your score, the fastest score, and the median score.

Quote:
Originally Posted by sillyface View Post
Higher 'slow times' do seem to affect scores, so yeah, futile.
Higher 'slow times' just indicate higher medians, and yes they do affect score. But your original post (several years ago now) prompted me to figure this out myself, so it was certainly not futile, haha!
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  #14  
Old 01-19-2017, 09:30 AM
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the minimum for a 1119 is 20
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