Last week I talked about building better skill build analysis tools. Shortly after finishing that post, I decided to grab some new samples and build a working prototype. Instead of doing it with Ursa though, I decided to go with Crystal Maiden.
A big part of this is that I expected Crystal Maiden builds to be a bit all over the place, and she did not disappoint. The other part is I had just read a conversation about the value of Brilliance Aura and whether it was worth skilling early, and it occurred to me that I didn’t know. Sure, I had inclinations, but on reflection I wasn’t really that set in them. I also didn’t have a clue how to value the change in 6.76 that doubled the personal benefit of the aura. In an ideal world I would have pre-patch and post-patch samples and could do a direct comparison, but the Ability Usage section in the API is far too recent to manage that. It is however an interesting idea to keep in mind for the major changes of future balance patches, but I digress.
Sample creation was pretty simple, if a bit disappointing. For the moment I can only get 500 samples a day per skill bracket, and the samples are not randomized for time. Hopefully this will change in the near future. In the meanwhile, I could only grab a sample of 3000 matches in each of the skill brackets (normal, high, very high). After filtering out useless and broken matches I was left with ~2500 Normal matches and most of the high and very high intact. At some point in the next few days I may go back and expand the sample. By the end of the week, another ~7000 matches should be available.
The first step was to divide the matches by the skill build categories that I outlined last week. If you want to read about them in depth go to the link, but for now, here’s the short version.
Single-Skill: Strongly prioritizes a single skill. Example builds include 4/2/0/1 and 4/1/1/1. Comes in Q, W, and E variants.
Double-Skill: Splits attention primarily between two skills. Example builds include 4/3/0/0 and 3/1/3/1
Split-Skill: Spreads attention fairly evenly among all 3 non-ult skills.
If you want to know the rules I’m currently using to make these divisions, here’s a flowchart describing the process.
Update: By popular request, here’s a quick write up of what Q, W, and E actually are.
Q – Crystal Nova: AoE Nuke and Attack/Movespeed Slow
Scaling — Duration, Damage, and Mana Cost
W – Frostbite: Single Target semi-Stun and DoT
Scaling — Duration, Damage (non-linearly), and Mana Cost
E – Arcane Aura: Passive Mana Regen Aura
Scaling — Mana Regeneration Rate
Future versions will hopefully be a bit more thought out. In the meanwhile check out http://www.dota2wiki.com/wiki/Crystal_Maiden for more detailed information.
Using this method, I created a table of usage and win rates for each build strategy in all 3 brackets.
Usage is pretty unsurprising. Q heavy builds get more popular the higher you go up. Split builds get less popular. What is surprising is the win rate chart. Builds that prioritize W and E seem to do significantly better in the higher skill brackets. I wasn’t expecting this, and so I made some extra tests to check and see whether I did something wrong.
Before moving on, I’d like to note a couple of things
- Average win rate of Crystal Maiden on Dotabuff over the 6 days of the sample was 51.51%. Weighted average of my sample (using .8, .15, .05) was 51.42%.
- Early Stats is insanely unpopular, and almost certainly a dumb idea.
- Late Stats win rate is, like the asterisk note says, unreliable. Don’t use it for anything. I’ll probably regret even including it. Damn you symmetry.
- Ult Skipping (not taking Ult at 6) gets significantly more popular in the higher brackets.
- I include the 8 and Over Win Rate because most of my tests only include samples where CM hits at least 8. This is the majority of the samples, but it’s still for the best to use the 8 and Over Win Rate as the comparison point.
What I tried next was to just group the builds by how many points they have in each ability by level 8. This would hopefully establish some trends in how valuable each point in an ability tends to be worth.
This appeared to confirm the initial findings. Brilliance Aura, Crystal Maiden’s E, has the strongest positive slope in all 3 brackets. Crystal Nova, Crystal Maiden’s Q, has the most negative slope. I don’t know whether I like this method much, but as a relatively independent confirmation it seems to work.
Finally, I tried a new method out not related to the skill build groupings. Instead, this one creates a skill cluster at a certain level while ignoring build order entirely. For the purpose of this sample I chose level 5. Larger samples in the future might allow me to be a bit more aggressive in choosing a later level or different combinations, but for now I’m trying to stay conservative in order to maintain sufficiently large sample sizes for each sub-category.
This shows the use and win rates of the top 6 level 5 clusters in each skill bracket. Once again, W and E heavy builds tend to perform the best. Also of note, builds that leave any of CM’s non-ult skills at 0 are very unpopular in all brackets.
Are W and E Crystal Maiden’s strongest early skills? It’s possible that this analysis is incomplete. Maybe the sample is too small. Maybe the sample is biased towards the build patterns of a small selection of people who play regularly around the sample gathering times. Maybe there’s just a bug I haven’t caught yet.
On the other hand, my findings seem to match Dotabuff’s Crystal Maiden Skill Build Page, and they almost certainly do not have issues with sample size or sample bias.
Another possibility is that Q builds under-perform because they’re so popular. Negative correlations between popularity and win rates are certainly not unheard of.
Finally, maybe W and E really are her strongest early skills. E is significantly better than it was a couple months ago, and we tend to drastically underestimate the value of global auras. The Q to W comparison might also not be that bad if you think about it. Both abilities give you an extra half a second of their respective CC, and an extra half second of W’s semi-root thing is likely more valuable than an extra half second of a 30% slow in an early fight. In a single target scenario the damage per rank between the two abilities is actually relatively even: 150 for three ranks of Q, possibly 140 for three ranks of W? W does 70 damage per second so I’m not sure if each rank is worth a flat 35 damage (for 105 total) or if you only get 70 at each new second, which gives you +70 at 2 ranks, 0 at 3 ranks, and +70 at 4 ranks. playdota doesn’t explain how the scaling works, but losing 45 damage in the worst case scenario might be worth extending your stronger CC.
In any case, I’m not going to commit to saying that 1/4/4/0 is the strongest CM build, particularly because it seems to be only average in Normal level games, but I do intend to keep this in mind for the next time I play her. W and E focused builds are at the very least worth experimenting with.
But moving beyond Crystal Maiden, during this analysis I’ve attempted to make the tools I’ve created generalizable for all heroes (with the exception of Invoker). Sample creation still has some issues, but theoretically all of this can be used on any hero, so if there’s anyone in particular that you’d like to see get this treatment feel free to bring them up in the comment section or through e-mail.