2016년 2월 11일 목요일

Educated Guess on SWGOH's Squad Arena Critical Hit Rate




I. Preface

So tharos_mt, a fellow redditor has given me datamined critical rate formula, and it was the following:
(Critical Chance) = (Critical Rating)/(Critical Rating Divider) + (Level Difference)x(Level Difference Multiplier) + (Base Critical Chance)
Luckily, this formula is linear! And, since level difference can easily be set to 0, I knew this was going to be rather easy task.
However, I knew that EA/CG could have set different Base Critical Chance for different game modes, as they did with animation speed, and since I had absolutely no clue about what level enemy heroes were, I could not conduct research.
However, recent update unveiled enemy heroes' levels! Now I could finally analyze how critical ratings worked. I conducted over 30 battles, recording around 400 hits to come to following conclusion. But, before going in to the results, I need to assume several things.

II. Assumptions

1) Above datamined critical chance formula is correct
2) I have not made human error in documenting critical hits
3) The game has not made an error in displaying enemy level or critical hits
4) The game has not made an error in generating random numbers
5) Critical Rating Divider (CRD) is equal for all heroes
6) Critical Rating Divider is equal for both Physical and Special Damage
7) Base Critical Chance (BCC) is equal for all heroes
8) Developers have not changed neither the Divider nor Base Chance while I was recording critical hits

III. Methods

Since I know the formula is a linear one, I conducted linear regression to get coefficient 1/CRD and y-intercept BCC. My R-Squared reached 96.9%, and I decided to stop conducting, because crystals are scarce, and quite a decent portion of my data started to settle as my observations neared 400.
My work(Google Spreadsheet) can be viewed here
My linear regression result showed that CRD is 1736.41 and BCC is 0.045. Now I thought that EA/CG would not have chosen such random numbers, and must have chosen 1750 for CRD and BCC for 0.05. This is purely my speculation, but one I can stand by.
Thus, my conclusion is that :
(Critical Chance for Same Level) = (Critical Rating)/1750 + 0.05
You will see that my guesstimation has minimal impact on the overall predictability of my regression result. 

IV. Conclusion

Now I know what Critical Rating means! This work was important for my upcoming Role-Adjusted Tier List, which will be epic in proportion.
One interesting thing about this chart is that, special CC is lower than physical CC for ALL CHARACTERS.


NamePhy CRSpec CRPhy CCSpec CC
Ahsoka Tano725046.43%5.00%
Darth Maul695044.71%5.00%
Stormtrooper-1604039.51%5.00%
IG-885581036.89%5.57%
Nute Gunray554036.66%5.00%
Luke Skywalker5501036.43%5.57%
Princess Leia539035.80%5.00%
Greedo5291035.23%5.57%
IG-86 Sentinel Droid5162034.49%6.14%
Cad Bane507033.97%5.00%
Geonosian Soldier494033.23%5.00%
Resistance Trooper4914033.06%7.29%
Ewok Scout4872032.83%6.14%
First Order TIE Pilot4871032.83%5.57%
Dathcha475032.14%5.00%
Ewok Elder473032.03%5.00%
Asajj Ventress4701531.86%5.86%
Rey468031.74%5.00%
Biggs Darklighter465031.57%5.00%
Darth Sidious4642031.51%6.14%
Resistance Pilot462031.40%5.00%
Aayla Secura458031.17%5.00%
Coruscant Underworld Police453030.89%5.00%
Lando Calrissian4502530.71%6.43%
Jedi Knight Anakin449030.66%5.00%
Clone Sergeant - Phase 1423029.17%5.00%
Tusken Raider4174028.83%7.29%
Luminara Unduli4121528.54%5.86%
First Order Officer4091028.37%5.57%
Stormtrooper Han4072028.26%6.14%
Snowtrooper401027.91%5.00%
Captain Phasma3981027.74%5.57%
Boba Fett3941027.51%5.57%
Poe Dameron3921027.40%5.57%
Hoth Rebel Scout3782526.60%6.43%
Kylo Ren3771026.54%5.57%
Savage Opress3742026.37%6.14%
Ima-Gun Di3692526.09%6.43%
Kit Fisto365025.86%5.00%
Nightsister Initiate358025.46%5.00%
Count Dooku3401024.43%5.57%
Jedi Consular3296023.80%8.43%
Clone Wars Chewbacca3252023.57%6.14%
Teebo3141022.94%5.57%
General Veers3131522.89%5.86%
Darth Vader3084522.60%7.57%
Finn3072022.54%6.14%
Barriss Offee2992022.09%6.14%
CT-5555 Fives2931021.74%5.57%
Hoth Rebel Soldier2908021.57%9.57%
Obi-Wan Kenobi (Old Ben)2841021.23%5.57%
HK-472813021.06%6.71%
Grand Moff Tarkin2592519.80%6.43%
URoRRuR'R'R2586019.74%8.43%
Jawa2552519.57%6.43%
Jedi Knight Guardian2553519.57%7.00%
Mob Enforcer2526019.40%8.43%
Royal Guard2481019.17%5.57%
Talia2414518.77%7.57%
Poggle the Lesser2378518.54%9.86%
Eeth Koth2364018.49%7.29%
Nightsister Acolyte2236017.74%8.43%
Ugnaught2224517.69%7.57%
Admiral Ackbar2212517.63%6.43%
Old Daka2211517.63%5.86%
Lobot2188017.46%9.57%
First Order Stormtrooper2161017.34%5.57%
Qui-Gon Jinn2043016.66%6.71%
Mace Windu2025516.54%8.14%
Plo Koon2023516.54%7.00%
IG-100 MagnaGuard2002016.43%6.14%
Grand Master Yoda5.00%5.00%