Feature branch drop balancing

[fizzix]

The last time we did a dedicated balancing effort with regards to drops was 3.4 I think. After that, some of the changes introduced in 4.0 broke stats generation. Over the past few days I've tracked down some of the bugs that would cause crashes after some tens of thousands of levels. (One memory leak, and two rare events), which means that we now can generate stats for the feature branch, and probably the current 4.1.x branch. I'll try to do some more detailed analysis in the coming days, but right off the bat I noticed one difference.

The standard metric I've used for general balance is to full clear every level once from 1 to 100. This, of course, doesn't really mimic how a regular player plays, but it is certainly useful for comparing across versions.

So here's what I noticed at first. 4.feature will provide you with about 59 artifacts per game (standard deviation about 2). 3.4 provides you with 51 (standard deviation also about 2). This means 3.4 is somewhat more generous with artifacts.

But, here's something that surprised me. 4.feature has, on average, far fewer monsters than 3.4. In fact at about level 40, the two branches diverge, with 4.feature having about 60% of the monsters per level than 3.4. There are a lot of possible reasons for this. But right now it's looking like 4.feature is probably being too generous with floor drops.

More analysis to come. Some things in stats are probably broken currently, (spell books for example) so I need to do some testing to make sure stuff is getting calculated correctly.

[Pete Mack]

That explains a lot about the 3.4 game I am playing. The deeper levels feel significantly more dangerous than 4.0 (and teleportation is too dangerous to use.) Add this to 15% fewer artifacts per 100 levels, and the ridiculous rate of high end ego items in 4.0, and there is a big difference in game difficulty.

[Nick]

Cool, I look forward to seeing more.

The lower monster rate is possibly related to changes in dungeon gen in 4.1.

[fizzix]

The lower monster rate is possibly related to changes in dungeon gen in 4.1.

Yup, both changes are probably related to dungeon gen. Some of this is probably a consequence of many more special rooms that are large but fairly weakly populated and have guaranteed items. The varied rooms are a general plus, but we might want to increase the monster generation rate in them.

The fact that they diverge after level 50 might be due to the former prevalence of pits/nests which used to spawn 1 or 2 per level and now spawn significantly less frequently.

As a next step I looked at stat potions, which I've used in the past as a good gauge of how generic non-artifact drops are behaving. I've split it into 3 graphs, total stat gain drops, drops from monsters, and drops from the floor (including vaults). I don't remember if Charisma was dropped in 3.4, but regardless it's not counted in the stat potion count. Augmentation counts as 5 stat potions.

There are some surprising takeaways from these figures.

The bulk of stat potions are dropped by monsters

Monsters are more likely to drop stat potions in 4.feature than 3.4, You get more potions dropped only in the later levels in 3.4 where the monster count is much higher. (I could make another plot of stat potions per monster if people want to see the actual numbers).

Not many of the stat potions are generated on the floor, yet this value is much higher in 4.feature than in 3.4, and increases very rapidly at high levels. It even increases more rapidly right at stat gain depth.

Monsters are much more likely to drop stat potions OoD (out of depth) in 4.feature. OoD drops appear to be zero until about level 20, yet you see the possibility of finding stat potions at surprisingly high probability rates in 4.feature. Rare drops should happen, but there's an indication here that we're being too generous with good early drops.

[Pete Mack]

Can you do a plot of "high end ego items?" I am not sure how to define it, but it is basically boots of speed+big 3 weapons with big 3 enchantments+crown of might. Maybe shield of preservation and higher dragon armor Dwarven.

[fizzix]

I'd have to modify the stat tracking program to get all of that. But I do track already all of Holy Avenger, defender, westernesse and gondolin. So hopefully that's good enough. I've plotted the drops of the sum of those 4 egos, and separately speed rings. (Jewelry is generated differently than weapons and unsurprisingly has different results)

Way more ego items are generated in 4.feature, both from monsters and vaults. For speed rings there's an increase in vault drops but surprisingly not much of an increase from monster drops.

Will post the ring info in the next post (can only attach 5 files at once)

[fizzix]

Here's the info for the speed rings.

[Pete Mack]

Actually, I was thinking of +attacks rather than Westernesse, which actually do have a maximum depth under DL 100. (It's a problem for artifactless mages.) But this graph is pretty much what I expected: essentially every big 3 weapon in a vault is good enough to use.

[fizzix]

One other big difference. I also track the first time you find an item with a given ability.

In 3.4, on average you find an item with free action (could be anything including amulet of inertia) by level 22 (stdev about 2). in 4.feature that is down to level 13 (with stdev also about 2).

You have about a 42% chance to find an item with free action by level 20 in 3.4 That's up to 90% in 4.feature.

Telepathy also has a similar disparity.

in 3.4 you will on average find an item with telepathy by dungeon level 52 (stdev about 4). in 4.feature that's down to level 38 (stdev 3.5)

4.feature appears to be way more generous across the board.

[fizzix]

I could have included extra blows weapons too (I track them). From spot checking numbers by eye they don't look any different from Westernesse or Holy avenger.

[Pete Mack]

The speed ring stats are a real problem: it means that you probably will find an OOD speed ring in 4.0, but you probably won't in 3.4. The difference at or above native depth isn't a big deal--it means about a +1 bias in the best ring you find.

It is the latter kind of statistics that are more critical: at what depth do you find an endgame weapon/speed ring/dragon armor etc? Or are the odds of finding one significantly less than 1? (Just as is the case for first-found FA, speed ring, damage ring, resistance armor, etc.)

I am actually enjoying 3.4 more than 4.0, despite the annoyance of ID and bad squelching.

[Derakon]

I don't have a problem with SI/FA showing up "early", since they're so critical to being able to play the game at all. Other abilities though should definitely have a period where you're trying to push forward despite not having them; this is especially true of speed and ESP.

[Philip]

In the recent O competition my character didn't find any ESP or +speed (or a couple other handy utilities) before dying horribly of not having ESP or +speed. The character died at dlvl 86 after spending a significant amount of time between dlvl 70 and 86. I'm not going to claim the process was fun the whole way through, but it was definitely an interesting experience, and trying to push through (because it was a comp) despite the significant difficulty spike (enhanced by O monsters and O monster drop generation) when I largely stopped being able to kill things at-depth. It brought on a feeling of dread and fear of the unknown (with no ESP on a warrior whose staffs of detection kept getting fried). This is a sort of feeling that Nick has mentioned before as being the goal of the later levels of the game. Making powerful abilities harder to get early on (in O, you can find shoes and hats of telepathy reasonably early, but they are rare) really ratchets up the pressure and can make a win more satisfying, and a death more impactful. It can feel a bit unfair, but sometimes that's a feeling you want to generate.

Of course, instituting full O difficulty would be undesirable in V, since there is only so much you can do before you start turning off new players. On the other hand, I feel like the creation of the foreboding and unfair feeling of later levels is part of what enables player retention, since it makes getting past those a much more satisfying accomplishment than dying 5 times in the early levels, twice to some unexpected mechanic later on, and then winning the game.

[Pete Mack]

I agree about SI being pretty much a necessity after DL 30. Dreads (and later, Ethereal dragons) are just too dangerous to mess with. But going without FA between DL 20 and 30 is fun, in the same way that do8ng without ESP after DL 50 is. At the same time, I agree with Philip: there are only so many levels you can survive at low HP, without speed or ESP. But better to be forced to push the envelope than to always get OK speed by dl 50.

[fizzix]

Luckily these issues are pretty easy to fix. They're just tweaks in various constants. It was my intention to do these sort of balancing fixes after every version. Unfortunately the overhaul to dungeon creation had introduced some bugs that caused crashes and I wasn't able to find them.

We should probably regularly do these balances with the knowledge that if we're going to depart in one direction or another in drop rates, it should be for good reasons.