Mathematically Looking at Critical Hit

When I first started playing the new steam version of ssl, it annoyed me that the critical hit skill tree was extremely vague. "Increased gun level" increased critical hit chance, but by how much? Without this information, one cannot know how valuable these skill points are. So, I decided to test it out my self.

I have upgraded 14 crit points so far (and one crit multiplier increase). I've heard people say each gun level increases crit hit chance by .1%, .5%, and even 1%. I decided to test .5% because it seemed to be the most likely.
To test, I shot 11ball at the computer opponent 50 times, and I did this 3 times.

• Test 1: 31/550 crit hits
• Test 2: 34/550 crit hits
• Test 3: 38/550 crit hits
• Total: 103/1650 crit hits = 6.2% chance

If the true value were .5% for each gun level, then you would expect a 7% chance (as I have 14 points). 6.2% seems very close to 7%, but you must be careful when dealing with these large sample sizes.
I decided to do a 1-Proportion Z-test. This test will tell you the probability of a difference in values occuring randomly. The result was a .113. This means there is only about an 11% chance that the results I got were due to chance if the real result were .5% per gun level. However, for all intents and purposes, we can say:

Each gun level increases crit-hit chance by .5%, and a maxed out skill tree will give you a crit-hit chance of 20%.


So how valuable is that? Well, lets compare a person with a maxed out crit tree to a person with none crit points at all.
For every 100 points a person with none gets, a person with max crit will get:
.8*100 + .2*(100*2) = 120 points

This means you can kill enemy tanks 20% faster. In an average game of 15 rounds, thats 3 turns faster.

In the end, I think crit is the best overall investment. Armor has more bang per buck (max armor you have a whopping 52% more health), but its usefullness is limited to high hp games (at low hp games its effectiveness is less than 20%). Also, crit is more usefull in multiplayer games as its damages can apply to all the opponents. As for luck and fuel, you can't really quantitatively argue against those. In my opinion, if you are a good shot, these are much less effective (aka you dont need to be right next to the guy to hit him).

Thoughts?

 

Mallard King has also brought out that it is best to buy the perks of it first. All the others are just increasing the chance.
I think though everyone will max out gun eventually.

 

Actually, I disagree. Lets look at the fourth lvl of the tree for example. If you only increase the non perk side, you will have:
(9 crit points *.5%) => .955(100) + .045(150) = 2.25% increase in damage
If you increase the perk side:
(2 crit points *.5%) => .99(100) + .01(165) = .65% increase in damage

For the last level of the tree:
(11 crit points *.5%) => .945(100) + .055(150) = 2.75% increase in damage
If you increase the perk side:
(4 crit points *.5%) => .98(100) + .02(175) = 1.5% increase in damage

So it would actually be better to upgrade the non-perk sides first.

 

v

very good job thank you for informations

 

Thank you for this, I was really curious.

 

1/5 chance? It seemed to occur like 1/3 to me, but anyways. Thanks for making this!

P.S. You should submit a guide to the community hub of the game.

 

I still pick armor. Sure, it doesn't help in low hp games, but most people play high hp games for weapon level-up anyways. The math you gave is correct, but it really isn't enough to sway my mind away from armor.
Nice thread, though. Gotta love the math-y threads.