Celtic Heroes

Hello,

While waiting last night for the reset that never came, I engaged in one of my favorite pasttimes, conducting experiments of the game's mechanics. This time around, I sought to explore critical hits, and perhaps gain insight into the effectiveness of the ability. The conclusions were... disappointing.

The experiment was simple: for three different crit abilities, I auto hit a training dummy many times, recording each regular hit as a 0, and each crit hit as a 1. This is known as a binomial distribution. From the data, we can determine confidence intervals (the range of values that the true average is likely within) to see how the rate differs between different levels of the ability.

The results follow:

Critical Strike Ability: 1172
# of Trials: 600, Crits: 50
95% Confidence Interval: [.061 to .106] (avg: .083)

Critical Strike Ability: 2265
# of Trials: 600, Crits: 49
95% Confidence Interval: [.060 to .104] (avg: .082)

Critical Strike Ability: 2968
# of Trials: 600, Crits: 48
95% Confidence Interval: [.058 to .102] (avg: .080)

Critical Skills Ability: 2230
# of Trials: 600, Crits: 50
95% Confidence Interval: [.061 to .106] (avg: .083)
[It seems Crit Skills and Crit Strike follow the same crit rates, as expected]

Now, to put these results into words, there is no discernable difference between a level 1172 crit strike ability and a level 2968 crit strike ability (p-value = .833, using 2-Prop Z-Test).

Why? Is this a mistake on OTM's end? Did an intern forget to look back at the "TODO: Replace .08 with the Crit Strike Formula"? Is it intentional that there is no statistical difference between my level 110 alt's ability to crit and an endgame player's?

It does seem rather odd that maxing such a valued ability, or using high-end fishing rings, results in non-existent gain. What do you think?

First, thank you Regenleif for doing the numbers, I've wanted to know the specifics of these stats for a while.
Second, I would definitely like to hear a comment/explanation from the developer's end of things.
Third, if this is truly the case, I am going to start ignoring a lot of potential time-wasting on the fishing rings/leveling these abilities.

(This is a further pointless idea: how impractical would it be to run the tests with the dragon stat boosts?)

I believed this was the case without having the numbers to back it up.

I know it’s much harder to find, but I believe the same is for Scholar and Lucky Treasure.

I don’t agree with your numbers or your statement. I just got a lvl 6 dragon. So my crit stands at 3250/3250. I crit about 50% more often then the rest of my clan. No one else has a lvl 6 in server yet. I did some testing myself. (On actual mobs and not a dummy) I have some crit strike rings so I tried them out as well. Put crit strike up to 4250. I do believe it has a max or plateau. There was no difference between 3750 and 4250. But a huge difference between 2250 and 3750.

Everyone has been like “Damn Songz, those crits!”

+1 to the great work by OP.

Did some unscientific tests on dummy before (non-comparison type). Just gut feel here sorry. I think Storm Touch seems to have a lower base crit rate compared to all other skills (I'm not even sure if skill-specific base crit rate exists), but to not crit once out of 30 attempts even after gaining significant ability.... I seem to crit more against non-dummies.

I'm also wondering if there's a hidden 'Critical resistance %' property for all entities - players and mobs, all along. We applaud the efforts of guys who done great work discovering the sqrt-like damage curves, but I don't think they could get many data points easily from the community when it comes to crit chance. (Tell me if I'm wrong about this). Now back to this possible 'Crit resistance'. Did it scroo up when it comes to dummy? Did the dummy adjust its crit resistance wrongly if it tried to scale up with the player's level or ability?

Sorry for so many if and buts, consider the fact we're shrouded in darkness.

I don’t agree with your numbers or your statement.
[...]
Everyone has been like “Damn Songz, those crits!”

3250 is only about 10% more than my highest test (2968), so I highly doubt you are actually getting 50% more crits overall...

I encourage you to test this for yourself though: follow the method I did, recording each crit as a 1 and each non-crit as a 0, until you have at least 30 crits... should be about 400 trials, then find the average. I recommend using google sheets, librecalc, or excel to record the data, and “=average(Column)” to get the average. Do post your results

It is definitely possible that at bosses you crit more, but that is more likely (95% likely, lol) from normal variation: random distributions are more likely non-uniform than uniform! Even in my tests, I often had clumps of 4-6 crits in near-series; right after I finished testing (at the 600 mark) I crit three times in a row! Shame I couldn’t count them.

I'm also wondering if there's a hidden 'Critical resistance %' property for all entities - players and mobs, all along. [...] I don't think they could get many data points easily from the community when it comes to crit chance. (Tell me if I'm wrong about this). Now back to this possible 'Crit resistance'. Did it scroo up when it comes to dummy? Did the dummy adjust its crit resistance wrongly if it tried to scale up with the player's level or ability?

Regarding mobs having crit %s: I considered this, but it seems too complicated... Regardless, I’ll test this tonight

Regarding crits via player level: This also seems too complicated, but also worth testing!

Regarding skills: also a bit too complicated, but worth testing. Cooldowns will be a huge pain haha.

The community can definitely contribute to crit tests, but I often just use my clannies when I test mechanics haha... I do not believe crit tests are a worthy subject to get the whole forum community involved in (as we did with skill formulas), it’d be much nicer to get an response from Muldar or a dev.

If anyone does want to test their crit rates on various mobs/levels/skills, just respond with the number of trials (attacks, preferably 500+) and number of crits. Be sure to be completely accurate and unbiased! Set a trial amount, stop at that trial; don’t wait to get more crits, make sure to count every non-crit too, and note that sometimes autohit animations don’t actually do anything (only record if a number shows). Beyond that, a cruel knife + haste gloves are an easy way to meet the 1100 minimum attack delay.

A good place to run tests like this, providing it's quiet enough, is in the arena with a ranger. The aggro range of the gladiators, once attacked, is a bit less than the range of a rangers auto attack. You hit the gladiator, it's outside it's aggro range, so immediately resets and its health is instantly restored.
So sit yourself outside the range of the least popular gladiator hit auto and count. No hassle of ruined dummies and waiting to respawn or running to another dummy.

Yea too much work. Hints from the dev better. What if the dummy is only a mechanism to test damage numbers only, such that crits against it are simply in fixed %ages, hence it has fixed hp and no level to speak of. (We also have 100% hit chance on it right?) All work done on it will be wasted.

I don’t agree with your numbers or your statement.
[...]
Everyone has been like “Damn Songz, those crits!”

3250 is only about 10% more than my highest test (2968), so I highly doubt you are actually getting 50% more crits overall...

I encourage you to test this for yourself though: follow the method I did, recording each crit as a 1 and each non-crit as a 0, until you have at least 30 crits... should be about 400 trials, then find the average. I recommend using google sheets, librecalc, or excel to record the data, and “=average(Column)” to get the average. Do post your results

It is definitely possible that at bosses you crit more, but that is more likely (95% likely, lol) from normal variation: random distributions are more likely non-uniform than uniform! Even in my tests, I often had clumps of 4-6 crits in near-series; right after I finished testing (at the 600 mark) I crit three times in a row! Shame I couldn’t count them.

I'm also wondering if there's a hidden 'Critical resistance %' property for all entities - players and mobs, all along. [...] I don't think they could get many data points easily from the community when it comes to crit chance. (Tell me if I'm wrong about this). Now back to this possible 'Crit resistance'. Did it scroo up when it comes to dummy? Did the dummy adjust its crit resistance wrongly if it tried to scale up with the player's level or ability?

Regarding mobs having crit %s: I considered this, but it seems too complicated... Regardless, I’ll test this tonight

Regarding crits via player level: This also seems too complicated, but also worth testing!

Regarding skills: also a bit too complicated, but worth testing. Cooldowns will be a huge pain haha.

The community can definitely contribute to crit tests, but I often just use my clannies when I test mechanics haha... I do not believe crit tests are a worthy subject to get the whole forum community involved in (as we did with skill formulas), it’d be much nicer to get an response from Muldar or a dev.

If anyone does want to test their crit rates on various mobs/levels/skills, just respond with the number of trials (attacks, preferably 500+) and number of crits. Be sure to be completely accurate and unbiased! Set a trial amount, stop at that trial; don’t wait to get more crits, make sure to count every non-crit too, and note that sometimes autohit animations don’t actually do anything (only record if a number shows). Beyond that, a cruel knife + haste gloves are an easy way to meet the 1100 minimum attack delay.

Muldar has confirmed that each mob has a specific "critical resistance" based on its level. Assuming a dummies are the lowest possible critical resist (not 0 otherwise all hits would be crit), that means that those rates you are getting are not just average rates, theyre the effective maximum crit rates due to plateau in ability effectiveness, which is embarassingly sad, but would also explain why your numbers are essentially equal across the board.. i reccomended a fix in feedback and suggestions a few weeks ago ( http://celtic-heroes.com/forum/viewtopi ... 61#p736461 ) asking for 1% static crit chance for every 500 critical auto and 2% static for every 500 skills ability that you have more than your targets resist that i think could help remedy the murderous plateau

I noticed this as well when i tested it back when i got some crit rings, basically from what i can tell once your crit abilites equal that of the boss more crit ability makes little difference.

^+1 to the static crit chance