@Riot: 10% Crit chance is actually 8%
Work swamped me, 55% will be finished tonight and 50% as well as one crit rune will be run shortly. I also should have a spell counter program up and running for public use in a few days (It counts when you use spells and how many of each type).
With another test and an additional 3000+ points performing the same test, the combined total is 8.4% critical chance from a Zeal. I conclude that their crit chance algorithm is incorrect. Additional pictures are included on PAGE 11 and the excel files can be provided upon request (Since I cannot upload them here).
I will be testing 4% and 50% soon, as well as whether buying new items resets the critical algorithm.
2/1/13 Update: With the server down at 2 AM this morning (About when I got home) I was unable to run additional tests. I have two more runs planned tonight (bringing the aggregate total close to 6000 data points). Those three runs will be evaluated as individuals, as well as with an additional combined analysis. I hope to finish the last two sets on Saturday night, so that all five will be completed before Sunday. I will then move to check 4% crit, or 50%, as well as looking into time of game vs. number of attacks.
Firstly, let me say for all those who just want the meat and potatoes, that there is a TL;DR version at the bottom. Look at the pretty pictures and read it.
For all the rest of you, here we go!
A Rioter said a few days ago, when talking about 1% crit chance...
So, in regards to 1%, it should be 1%, with a little bit of roughness. I decided to test what 10% critical chance actually meant: After many auto-attacks, are we truly hovering around a 10% chance of a critical? Or is it more or less, depending on how far into a game we are, and how many attacks have been made?
Using Sikuli, I created the following script, the text file attached below. Now, while the pictures you obviously cannot see at the moment, you can get the gist of the code. It imports a library for viewing, sets the scan/test rate, and reduces the region to that above my target's head. She attacks, stops attacking, checks the crit, waits to ensure it's recorded, then repeats.
Then I create a text file, and for every crit, the line "Critical Elapsed: xx seconds" is written. For every non-crit, the line "Normal Elapsed: xx seconds" is created.
All of this is timed so that I perform no more than 1 auto attack per second, and the entire scan, identify, repeat process takes on average, 1.8 seconds. Granted, it could be faster, but I have not yet optimized it for max data acquired compared to speed. Rather, I wanted accuracy.
Mundo is my tank, for the added hp regen benefits from his passive. His build was wholly damage mitigation and regen.
Sivir was the free week adc, who was given a zeal for 10% crit chance, and her lvl 18 attack speed is 1.2.
Attached as a .txt is the raw data acquired from a 58 minute run (Dominion ends at roughly 97 minutes, so the first 40 minutes the program isn't run while tank mundo builds up his hp regen and resists).
For this initial run, I have nearly 2000 data points, corresponding to a time of 3500 seconds. That is an average collection rate of 1 point every 1.8 seconds, which fits with my code. Ok, check seen and approved.
For every critical, I replaced the value with "1" and every normal as "0." What this does is allow me to equate the data to real values and perform various standard tests on it. Now, for 1900 points, at a 10% crit rate, the average should equal 190 for the true total. However, as you can in the provided word document with the graph and 1 variable analysis, the sum was only 157.
You can also see on the graph, that barring for a region from ~150 to 400 attacks, we are always below .1%, and as time goes on, we are below by a rather large margin. The final value is .0816, or 8.16%.
What does this mean?
For the duration of my test, 10% crit chance seems to actually be around 8%. However, as you and I both see, there is a region noted above that in the data. What does that mean for this test? It means I need to run it several times again, to test whether Riot's random algorithm is inflated for either the # of attacks, or the time in the game.
If the algorithm is modified so that the number of attacks has an effect on crit chance, it would make sense that it's artificially high to start and lower afterwards (forcing the ADC to break towers and push before their crit chance decreases, thereby reducing their damage and making bruisers and AP more valuable with steady skill related damage). It could also be a function of time. As I said earlier, it took almost 40 minutes to make tank Mundo into a champion able to stand and take the auto-attacks without fear of dying.
I will re-test 10% crit chance under the same conditions several times, to see if the same general trend of "Earlier more, later less" applies, as well as the overall timing of it. I would also like to test out 1, 2, 5 and maybe 50% to see what kind of spectrum this has. Perhaps with enough data, someone more math driven than me can actually discover the overall crit algorithm.
10% crit chance is 8%. Will test more to ensure it is the same from multiple games. Look, pretty documents/pictures!
Any questions, concerns, ideas?
Riot: You have known too much.....
Cool analysis, I'd recommend doing more trials though. 2000 data points is nice, but people will doubt the numbers until you get more. Also, you should try other crit rates, like 1 red crit rune (0.93%, i think). This one's especially important as people commonly run it for the random crits that could win a lane.
bump for math
isnt it easier to test it with 100% then? should be 80% but easy to test if just one hit doesnt crit
This is a very interesting test, and I look forward to the other tests.
thanks dude. you're cool
It's possible Zeal is bugged. Would other items giving 10% (or adding to 10%) give the same result?
Try an avarice blade.
Actually I have a request.
Would you mind if you repeat the test with 0%crit chance?
Because one time I had a crit with 0% crit chance and I swear that was a crit.
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