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League critical hits frequency?


Pelinor
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At my level you would think I already knew the answer to this, but I don't and it is driving me crazy. What is the point of even showing the Harmony stat when you can have a Harmony 10-60 points higher than your opponent and yet your opponent gets 4+ critical hits and you get zero or maybe one? This is happening even when the opponent has the same team (but at lower levels). So what is the point? How to you plan for what the battle sim says is a 1-2% shot? I meet the same players in Seasons and crush them every time, yet in the League I keep losing points (not battles). Seriously guys, this isn't a whine, it is a lack of understanding, I am missing something and it is annoying the crap out of me. So please, can I get a little help figuring this out?

While this isn't the best example of what I am talking about feel free to use the following in your explanation of how I am getting this wrong:

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All my stats are significatly higher. My girls are 100 levels higher, My club bonuses are 8 levels higher, yet I recieved an extremly poor result because of the critical hits in all three battles against Malkyo... ARGH!!!

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3 hours ago, Liliat said:

You're doing 300 fights per week, how is a 1-2% outcome surprising?

That in and of itself wouldn't be a huge surprize. What I am looking at seems to be the obtaining of the 1-2% result at roughly 4% of the time (almost double the expected rate). Honestly, if all I wanted was average results I would be fairly happy, but I want more! I want to get to @Rarum's "most powerful list" so I am looking for hints on how to get better than I am at the moment. To do that I need to understand why and how the damned critical hits happen (much more than my current understanding of the game).

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If it's the formulas you're looking for, they're all part of Slynia's Performance Handbook:

Regarding Harmony/Crit, it's 30%, shared by the two players, according to their harmony ratio. So, in your case, 84.6k vs 73.3k, it's almost equally shared:

84.6 / (84.6 + 73.3) = a ratio of 53.6% for you, 46.4% for your opponent.

You multiply that by the 30% crit chance for the harmony, and you get:

0.536 x 0.3 = 16.1% crit chance for you

0.464 x 0.3 = 13.9% crit chance for your opponent

Then you add the Physical bonus of your respective teams: 0 for you, 0 for your opponent. Assuming you both have 100 Orange girls in your harem, that's +7% each. So the total crit chance for each player:

16.1 + 7 = 23.1% chances of crit for you

13.9 + 7 = 20.9% chances of crit for your opponent

You need 6 rounds to defeat your opponent (Minus 1 per crit, so 5 on average), and he will crit once in 5 rounds (Again, on average). But he can technically crit up to 4 times. With a 20.7% chance of crit each round, doing 4 crits in a row has a probability of 0.2%.

Of course, considering how big the difference is, your opponent doesn't stand a chance: he needs 16 rounds to defeat you, or 8 if he crits non stop, but he only gets 5 chances if you never crit. So it's impossible for you to lose.

Some things to consider:

- You didn't include white girls in your team. Having an elemental bonus would help, with +20% crit chance. You would get a 43% crit chance each round, which is huge (A bit less actually, as you'd also lose a bit of harmony, but as we saw with the formula, harmony isn't significant when base values are close).

- Given the difference in power, you could consider including some blue girls in your team. With 80k damage per round (Or 160k+ if crit), healing 13% or 16% gives you +10.4/12.8/20,8/25,6k HP per round, when you take only 40k damage to begin with.

Of course, this are just general tips: tweaking your team for one specific opponent and checking what the script tells you is a lot more reliable, as it takes all available data into account (Including crit chances, crit damage and healing, which are "hidden stats").

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13 hours ago, Pelinor said:

Seriously guys, this isn't a whine, it is a lack of understanding, I am missing something and it is annoying the crap out of me. So please, can I get a little help figuring this out?

The calculation Liliat posted is of course correct... in theory. But meanwhile I'm pretty sure, there's some kind of defender-bonus in the leagues since the introduction of ''BDSM''.

Yes, improbable results happen more often than most people think (who usually have a very poor grasp of probabilities**). And if you've played millions of Poker hands, thousands of Yahtzee games and a lot of other luck based games like me, you've seen it all. ;)

That said - the frequency with which bad results happen in league fights seems way too high. I'm with you. I once even took a closer look at this phenomenon (for 2 weeks I watched every league fight from beginning to end) and found that I lost points in the three-digit range every season just because of ''bad luck''. But even if I hadn't done that, just watching my opponents starting a fight with a critical hit many times in a row (while I don't) or how often I get a 0-3/0-4 against players with very low harmony compared to the amount of fights where I get really lucky... well, you get the gist.

The thing is, even if I'm right, it doesn't matter and I don't care. It might be frustrating from time to time, but if it's real it definitely happens to everyone. Otherwise I wouldn't stand a chance in the leagues. And if there really is some kind of hidden harmony boost for the defending player, it could even benefit weaker players a little bit and prevent the strongest players from getting almost perfect scores too easily. Maybe that was the intention?

 

**(Sid Meier has a funny little anecdote about this in his autobiography. Long story short: In the end he had to adjust the probabilities in Civilization Revolution because players were constantly angry and didn't understand how they could lose a fight with something like a 75% winning chance. ''75 is a higher number than 25!!! The §$#&% computer is cheating!!!'' ... so he taught his game how to cheat - in favor of the player, so that the probabilities felt right)

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When it comes to probabilities, "feeling" is a strong factor, but also a very misleading one. It's even worse when you take a small sample out of a long series, because we know that on the long run, bad luck happens (so does good luck, but we tend to accept it much more easily :) )

For example, a 0.2% chance in a series of 300 fights actually has a total chance of 45% of happening once. So it will happen once every other week, on average (It might also happen two or three times in a week if you're unlucky, or might not happen at all for a couple of months if you're lucky).

Since we're doing so many fights (300/week), bad luck is bound to happen.

Il y a 2 heures, Moonlynx a dit :

The calculation Liliat posted is of course correct... in theory. But meanwhile I'm pretty sure, there's some kind of defender-bonus in the leagues since the introduction of ''BDSM''.

Could be. But unless we get large, unbiased data samples (with detailed league fights, round by round, from many players, for each individual league fight), this is really just an empty claim. I'm not tracking my league fights (Heck, I don't even use the script, and I skip all fights), so I can't say if the formulas are accurate or not. If they aren't, they can be fixed - assuming we get enough data. But the amount of data and level of detail required makes it impossible to collect manually. So, unless data collection is directly integrated to the script, I don't imagine this happening.

Il y a 2 heures, Moonlynx a dit :

**(Sid Meier has a funny little anecdote about this in his autobiography. Long story short: In the end he had to adjust the probabilities in Civilization Revolution because players were constantly angry and didn't understand how they could lose a fight with something like a 75% winning chance. ''75 is a higher number than 25!!! The §$#&% computer is cheating!!!'' ... so he taught his game how to cheat - in favor of the player, so that the probabilities felt right)

This is actually a scary thought. Biased probabilities are worse than no probabilities at all.

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I've been gathering data on how well I do in leagues in comparison to what would be the calculated expected score. I have data before 16th of June as well, but it's less reliable due to me having to rely on my own calculations because of an in-game bug that affected HH++'s expected average calculations. (Actually for 16th of June as well, I do believe, but the two methods agreed to such an extent that it's probably good enough)

 

7th of July:

My score: 7472 (100.072% of the score with completely average luck)
Expected score: 7466.6

30th of June:

My score: 7474 (100.137% of the score with completely average luck)
Expected score: 7463.8

23rd of June:

My score: 7543 (99.878% of the score with completely average luck)
Expected score: 7552.2

16th of June:

My score: 7616 (100.211% of the score with completely average luck)
Expected score: 7600

 

Totals:

My score: 30105 (100.0745% of the score with completely average luck)

Expected score: 30082.6

 

There are some other people who also have been tracking their expected scores, but I've not heard about any "systematic bad luck problem" from them.

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4 hours ago, Liliat said:

This is actually a scary thought. Biased probabilities are worse than no probabilities at all.

Mmh, depends. As we all know, a lot of game AIs cheat because they would otherwise be no match for human players (especially in strategy games). Less common but not unheard-of is the mentioned Sid-Meier-approach to cheat in the favor of the player. I tend to be pretty harsh on any kind of cheating, especially if it is to the advantage of me or my team. But I try to be forgiving if it is for the sake of a better game experience. If Calvinball taught us anything, it's: fun > rules. ;)

 

And thanks @Rarum- this is of course much better than my little 2-week-experiment and some rudimentary tracking of my fight results after that. But now I really want to know if my impressions (and my few numbers) are so far from reality. I'm still not fully convinced, because tracking your expected score could be misleading when you're dominating most of your opponents like you do. Even I get full points against some players despite having bad luck. So this doesn't say much about how many crits you and your opponents did.

Starting tomorrow I'll try to watch all my fights in full length again (urgh!) to record all the critical hits and compare them to the expected ones. At least it's just tedious, not overly complicated.

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6 hours ago, Moonlynx said:

As we all know, a lot of game AIs cheat because they would otherwise be no match for human players (especially in strategy games). Less common but not unheard-of is the mentioned Sid-Meier-approach to cheat in the favor of the player.

Both things are VERY common. Many games are biased in favor of whoever is losing, for example. It depends on the game but this is specially true of racing games.

On HH, there's something else. If you have a 40% of getting 25 points and 1% of getting 20 points, when you are very unlucky it's very visual: you're getting 20 points and that's outrageous. But you don't really notice when you're very lucky because it's thrown together with many other battles with slightly above average luck, with 25 points.
On CxH, I'm noticing as many "very lucky" scores as "very unlucky points". There I can have a 0.1% of getting 25 points and, guess what, I get one of those once in a while.

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7 hours ago, Kenrae said:

Both things are VERY common. Many games are biased in favor of whoever is losing, for example. It depends on the game but this is specially true of racing games.

Okay, yes - rubberband AI is a third category, I guess. Didn't include that because this isn't really cheating for a predetermined player. And probably already a little bit too sophisticated for a game like Hentai Heroes.

 

Quote

On HH, there's something else. If you have a 40% of getting 25 points and 1% of getting 20 points, when you are very unlucky it's very visual: you're getting 20 points and that's outrageous. But you don't really notice when you're very lucky because it's thrown together with many other battles with slightly above average luck, with 25 points.

We are not really in disagreement here. This is how it usually works. At least for players on top of the food chain. A lucky victory can be way more visual than an unlucky loss of points when you have a weaker battle team. We should consider that.

The other thing is... my brain tends to jump at ''unfair'' advantages for me way faster than at disadvantages**. This is why I could tell you roughly how many times I got lucky during the last few months while I completely forgot about any outrageous bad luck. Or why I have a sense for streaks of good luck that aren't very visible. Like when I get 10x25 points while it should have been only 8 or 9. And, yes, that's the opposite of what brains usually (and for good reasons) do. I repeat - we are not in disagreement about the general concept of ''noticing and remembering bad stuff better than good stuff''. ;)

Doesn't mean I'm right in this specific case. Far from it. And if I'd have to choose, I'd always trust Rarum's numbers more than my mostly casual impressions that are based on what might have been just a short but very unlucky streak last year. I see several ways in which those impressions could have been twisted besides the usual emotional reactions. But I noticed funny results in league fights (that are maybe not very visible to the top dogs) for quite a long time now and this thread is reason enough for me to take a closer look again. That's all.

 

**(ah, the innumerable groans of teammates, when I told the referee why we really, really shouldn't get this penalty/free kick/whatever 😅)

Edited by Moonlynx
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Battle cycles that drive me nuts are the extremes. For example: 1st round I get multiple crits and my opponent gets none which count*, 2nd round it is the exact opposite, and the 3rd round neither of us get a crit. The results look like this: 25-19-23 when the expected score is 23.6

Is the Orange (Physical) element worth it when you get no crits and the player without the element gets 3 in a row! That disparity in expected reslults drives me nuts.

*for it to count as a crit, imho, it has to happen before the battle reaches the point where regular damage is sufficient to defeat the other player.

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1 hour ago, Pelinor said:

That disparity in expected reslults drives me nuts.

The expected result for a roll of a six-sided die is a 3.5 - but I've never rolled a 3.5! :P

Not very helpful, sorry. What I want to say is: Don't get mad, extremes happen, everyone experiences it to approximately the same degree. Especially the last thought helps me a lot when I get really bad results. This guy I desperately try to keep behind me in the league? He gets those ugly results, too! Another hopefully helpful thought: When the expected score is close to 25, the real results can swing down way more than they can go up. So there's a lot of ''bad beat'' potential but no result that could be considered extremely lucky.

Yeah, I know you know all that. That's not the point. But somehow you have to get this information from your prefrontal cortex to the more primitive regions of your brain and... feel it. The only other option is to keep being frustrated by such vanities. In my book this isn't worth it.

If it's any consolation - just a few minutes ago I fought an opponent with exactly half of my harmony stat (85.6k vs 42.8k). First round: 3-0 critical hits. Second round: 0-5. Happens. If you throw 5 dice, sometimes all of them just show 1s and 2s. Even when they aren't biased. This isn't too spectacular (don't walk into the same trap as the mentioned Civilization players). For the number fetishist in me it's even mildly amusing. ;)

Things it isn't: serious. Something personal. Something that affects my league performance in the long run.

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51 minutes ago, Moonlynx said:

Yeah, I know you know all that. That's not the point. But somehow you have to get this information from your prefrontal cortex to the more primitive regions of your brain and... feel it. The only other option is to keep being frustrated by such vanities. In my book this isn't worth it.

I agree, it isn't worth getting mad about (unlike a few times I've been seriously mad at a human DM who cheats). Still, there must be some method of minimizing the down skews in the results. Random is random, we don't control that aspect, but using girls that increase your crit probabilities really should pay off in the long run, right?

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EDIT: (my former calculation was total bs... I definitely need more sleep than 4 hours per day, sorry)

Yes, in the long run it should make a significant difference. I guess that's all there is to say. ;)

Edited by Moonlynx
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5 hours ago, Pelinor said:

I agree, it isn't worth getting mad about (unlike a few times I've been seriously mad at a human DM who cheats). Still, there must be some method of minimizing the down skews in the results. Random is random, we don't control that aspect, but using girls that increase your crit probabilities really should pay off in the long run, right?

It pays off.

Using blue and dark girls even more.

But if your expected result is close to 25, you'll only have "bad" unexpected results, because it can't be better than 25.

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Randomness (including computer generated pseudo randomness) often triggers our biases, the only way to get around it is recording the results to confirm the expected averages in the long run if you are of the OCD type ... or taking things easy and not minding too much when you get a bad result or streak if you are of the easygoing type.

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@Pelinor

O~kay... so I did my little experiment last week, watched every fight (312 in total) from beginning to end and took notes. And even calculated right this time.

There weren't many extreme results - boo! And no ''10 consecutive critical hits in the first round for the opponent'' either. That's what's usually driving me crazy because it isn't as rare as it should be.
No, it was all pretty average and I even had the impression that I got lucky more often than not.

In the end I had 534 critical hits. The expected value was 535.4 - spot-on.
My opponents had 415 critical hits with an expected value of 388.8.
That's slightly unlucky but not suspicous. My amount of ''unnecessary'' critical hits in the last round (except when the additional healing lets me win one extra point) was disproportionately high, but - as far as I can tell from the very low sample size - not significantly high.

Gotta repeat this and collect some more data. Especially on the last round hits. For now I didn't find anything scandalously wrong with the RNG. At least no recognizable pattern whatsoever. And I've watched almost 4000 fighting rounds. Because I'm really that stupid. ;)

But for the next two weeks I'm definitely out. I need the meager remains of my concentration for RL stuff.

Edited by Moonlynx
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17 hours ago, Moonlynx said:

Gotta repeat this and collect some more data. Especially on the last round hits.

I find myself morbidly curious, in the sense that I am going to try to collect data next week (provided RL doesn't whack me up side the head like it did this week). I'm still debating with myself on the best way to format the spreadsheet.

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On 7/11/2022 at 6:47 AM, Pelinor said:

Is the Orange (Physical) element worth it when you get no crits and the player without the element gets 3 in a row! That disparity in expected results drives me nuts.

*for it to count as a crit, imho, it has to happen before the battle reaches the point where regular damage is sufficient to defeat the other player.

I questioned this 2 weeks ago, and came to the conclusion, that using blessed girls, instead of physical girls was the better choice, since the physical girl bonus increased the overall crit chance very little, compared to the giant stat boost from blessed girls.  Harmony played a larger role than I previously thought.

As stated in that thread, a visual representation of the actual critical hit chance % would be appreciated.  Instead of having to do harmony mental gymnastics (0.3*your harmony)/(your harmony + opponent's harmony), plus passive physical crit chance, plus elemental crit chance.

17 hours ago, Moonlynx said:

In the end I had 534 critical hits. The expected value was 535.4 - spot-on.
My opponents had 415 critical hits with an expected value of 388.8.

How do you estimate the expected critical hits, by looking at a range of scores w/ probabilities?  After observing 312 fights, you noticed a certain score equaled a certain # of crits per player?

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21 hours ago, Pelinor said:

I'm still debating with myself on the best way to format the spreadsheet.

There are probably better ways but basically I had ''my harmony | opponent's harmony | number of my fighting rounds | number of opponent's fighting rounds (usually one less) | my bonuses (2% * physical girls in the team + 7% for having over 100 in my harem) | opponent's bonuses (physical girls + estimated bonus for physical girls in the harem) | my expected criticals | opponent's expected criticals | my critical hits | opponent's critical hits''.

Except for the values in the ''expected'' columns - and maybe the number of opponent's fighting rounds -  I've had to type in everything manually. So as Ravi-Sama said, that's super tedious (but I was guarding a pigeon's nest all week long so I didn't have much else to do ;)). Tell me when you find a method that is a little bit more timesaving. But I advise against the whole plan to collect data yourself. Except when you tend to have fun with trivial numbers. Lots of them. Which... isn't as bad as it may sound. I think.

Btw - as soon as I stopped counting, the RNG pressed the doom button again. He does this on purpose, I swear. 🤨

Edited by Moonlynx
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On 7/19/2022 at 10:05 AM, Ravi-Sama said:

I questioned this 2 weeks ago, and came to the conclusion, that using blessed girls, instead of physical girls was the better choice, since the physical girl bonus increased the overall crit chance very little, compared to the giant stat boost from blessed girls.  Harmony played a larger role than I previously thought.

That's not from harmony, that's having a team with 40.000 more power, the difference in attack, defense and ego from that is huge. No crit% from physical girls is going to give you better chances. Harmony plays a small role there.
FWIW, you girls power gives attack, defense and ego, NOT harmony. You had more harmony with that team because you had 4 voyeur girls.

 

On 7/19/2022 at 11:06 AM, Liliat said:

Crit% x Number of rounds?

No. That gives you 100% after 4 rounds with 25% crit :) .

It's 1 - (1-Crit%) ^ Number of rounds 

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