In my experience Meteor strike+arrows+pots keep my team mostly alive against a 10er (I let heroes die during the end run). It can be really stressy though juggling potions.
Meteor strikes have no crossover matts with the staple Arrows/Cures nor with the advanced Tornadoes/Timestop, so I am able to build hundreds of meteors (I apparently have insane stockpiles due to being stingy on titans we have on farm, which probably colors me on this subject).
And yeah… a 10 star special or 11 star Titan? No idea how that works, but let’s tackle that when we get there. That 4 stars (perhaps Willy?) are a nono seems likely
Yes: here’s a mea cupla. We mostly use the term ‘tank’ to refer to the central defence position, and I was a fool to use it in the context of Titans without explanation. I did plan to explain and then I forgot, because I am an idiot.
When I talk about a ‘tank’ in an attacking context I mean some sort of status effect hero that has the same role as a defensive tank: they improve your team’s survivability. With Titans, they do this with their special, ideally by reducing the enemy’s attack or accuracy, increasing your team’s defence or defence against specials, or controlling the Titan’s mana. Omitting such a hero is fine (omitting any kind of hero is fine, depending on your playing style), but there’s a cost to it, as always - you’re much more likely to have your heroes killed if you leave the Titan’s attacks unhindered.
Perfectly fair burn, that, given my failure to explain what I meant. Suitable Titan ‘tanks’ would certainly not include Kashrek (the special is inverse to requirements) though Guin and Aegir might be pretty useful, depending on what heroes they were matched with. Picking from trainable examples, tanks might include Domitia, Justice, Magni, Khagan or even the much maligned Horghall, depending on the Titan’s colour.
This is wrong, for obvious reasons. First, we’ll look at those reasons. After that, though, let’s do something different - let’s pretend that you are right (you will be, for mid-game players), and measure Wu’s impact, compared to your original assertions.
Here’s why your assertion is silly. Using your proposed team construction (which problematically omits a tank, I note) and confining ourselves to trainable heroes, here’s your team against a blue Titan:
Debuffer - Isarnia
Healer/buffer - Melendor
Correct colour hitter 1 - Lianna
Correct colour hitter 2 - Elkanen
If we were to omit Wu, what hero would replace him? Despite using two trainable 5* heroes of the correct colour in our team, we still haven’t used Horghall or Kadilen (either of whom would significantly increase our team’s durability). And if a player does not have either of them? Then how about Joon, Leonidas, Justice, Sartana, Domitia, Obakan, Richard, Thorne or Magni? All these heroes have tile damage similar (usually better) than Wu, all have much, much higher survivabiity, and all have a special that either collects a significant chunk of damage or increases your team’s survivability.
So yes, the appropriate substitute for Wu will be a 5* hitter of the appropriate colour - there’s no shortage available from training camps. But if one wanted to be conservative and assume a player had not had a chance to run their training camps for long enough to generate a decent set of 5* heroes in every colour (I myself only have two green 5* heroes) then one would either replace Wu with a 5* hero of a neutral colour, or a 4* hitter of the best possible colour.
Now let’s measure the effect of substituting for Wu, using your (flawed - see above) assumption that a 5* hero is unlikely to be available.
What 4* hero would we use instead of Wu? There are two obvious choices: Boldtusk and Caedmon. Let’s consider the damage effect of both.
The Boldtusk calculation is relatively simple. Boldtusk is weak against blue (which is why we could not use him as our sole healer) so our base tile damage will be reduced somewhat:
So we would expect the Wu team to have about 8% higher base damage than the Boldtusk team. That difference does not apply to base special damage - it will be the same for both teams - but for the sake of the discussion, let’s pretend that the Wu team also scores 8% higher special damage.
Now what do the damage modifiers do?
Wu team: 1.08 x 1.85 x 0.65 = 1.3
Boldtusk team: 1 x 1.48 = 1.48
Shall we adjust for the duration of the special? I have noticed that players frequently neglect to do this, but it improves the Wu team’s position somewhat (Boldtusk’s special only lasts 4 turns while Wu’s lasts 5) so let’s do it. 0.48 x 0.8 = 0.384, 1 + 0.384 = 1.384
So even after adjusting for Wu’s better tile damage and longer special duration than Boldtusk, even assuming that the Wu team will have a higher base level of special damage, we would still expect the Boldtusk team to outperform the Wu team, 1.384 to 1.3.
Note that this is not a question of the Wu team sometimes crashing and underperforming. This suggests that the Wu team will generated lower expected damage over the long term than the Boldtusk team.
Huh. I didn’t expect that. Funny what happens when you actually run the numbers, isn’t it? That also saves us a step: we don’t need to bother calculating the frequency of Wu’s crashes, in this case, because we know that we wouldn’t rationally choose Wu - we’d always use Boldtusk instead.
(Note that Boldtusk is weak against Blue, which is why we wouldn’t rely on him as sole healer, but I think his weakness is more than mitigated by having two sources of healing on the team - him and Melendor.)
So how about if we substituted Caedmon for Wu, instead of Boldtusk for Wu?
The Wu team’s base tile damange is unchanged, while the Caedmon team gets a boost:
Wu team: 797 + 707 + 714 (x2) + 729 (x2) + 675 (x2) = 5740
Caedmon team: 797 + 635 (x2) + 729 (x2) + 675 (x2) = 6303
So we would expect the Caedmon team to have about 10% higher base damage than the Wu team. And we’re adding a new sniping special - a powerful one - to our existing three damage-dealing specials, so we’d expect our base special damage to increase by at least 33%, maybe more. Shall we be conservative and favour the Wu team? Let’s do that: let’s assume base special damage for the Caedmon team is only 20% higher than base special damage for the Wu team, and that this increases the Caedmon team’s total base damage advantage by only a couple of percent.
As before, let’s add our damage modifiers:
Wu team: 1 x 1.85 x 0.65 = 1.2
Caedmon team: 1.12 x 1 (unmodified) = 1.12
So we’d expect the Wu team to generate about 7% more damage than the Caedmon team, over the long term. (I’m ignoring the fact that Wu’s special won’t always be active. I want to give Wu the best possible chance.)
Not a big advantage even over the long term, is it? Again, I’m a little surprised: actually running the numbers is making it clear to me that Wu is not as powerful as I thought he was.
Now let’s quantify Wu’s chance of failure. Let’s pretend that non-Wu teams will always generate base damage 12% higher than Wu teams (it could be much higher than that, of course, because we are basing our calculation on the substitution of a bog-standard correct colour 4* hero for Wu, not a pimped out 5* or a correct colour modifying hero like Boldtusk or Kiril).
How frequently will a Wu team fail to improve its base score by the 12% necessary to beat the no-Wu team?
Well, we know that Wu’s special increases damage by 185%, and we expect it to succeed 65% of the time. If it succeeds less than 61% of the time in any particular battle, then damage will be less than what we would expect from a No-Wu team (because 1.85 x 0.61 = about 1.12).
Now we need to estimate the number of tiles that fall in a typical 90 second Titan fight. Between decision making and lengthy animations, a tile every second seems about right, so I’m going to guess 90 tiles.
The question we need to answer: if Wu’s special has a 65% of working for each tile that falls, how often would we expect it to work less than 61% of the time (that is, on 55 or fewer tiles)?
This is a simple binomial probability matter, answerable from binomial probability tables, which I am now retrieving from my shelf… and the tables tell me the answer is about 25%.
So about a quarter of the time, we’d expect our Wu team to underperform our Caedmon team on individual Titan battles.
The next step will be to estimate the frequency with which the Wu team will underperform the Caedmon team over Titans. This will be a bit more complicated than I first thought - I’ll need to build a distribution or rough it using quantiles, and I’ve run out of enthusiasm just now.
TL;DR - the damage advantage of Wu teams over non-Wu teams is much less than I first thought - nearer 10% than 20%, even ignoring the durability and special effects benefits of alternate heroes. Not only is he not OP, he might actually be overrated.
To do: quantify frequency with which our Wu team is likely to underperform our Caedmon team over whole Titans.
Edit: Difficulty in believing in how bad these results make Wu look led to me reviewing them and finding an obvious error that will improve his expected performance. Credit for finding the error goes to the drink that helped me. Unfortunately that drink has also convinced me not to fix it up today, but to instead seek more drinks, and to review all this over the weekend - or next week, if the hangover is bad enough.
I have not neglected it: you will see that in the second substitution, neither team has an attack buff, which for the purpose of calculating effectiveness is the same as both teams having attack buffs.
Edit: Although I note also that it is pretty high risk to include both fragile little Wu and fragile little Boldtusk or Kiril in a team. You’d expect hero deaths to wear away some of the the expected damage benefits of those pairs.
Who are you calling fragile? 700+ defense on BT does not seem fragile to me.
Yes, you have a team where neither has an attack buff. But that in no way demonstrates the damage that could be achieved with +185% +48% and -32% accuracy. That results in an average buff of x * (1+1.85 + 0.48)*0.68 = 2.26x, or +126% tile damage. Also, if you are worried about too many healers, use Little John instead of Melendor.
That’s the wrong comparison, unless you live in a world where you are only permitted to use Boldtusk if Wu is on the team too. The right way to assess Wu is to compare a team with Wu to a team without Wu, leaving the other members constant.
So using you own example, your team with Wu and Boldtusk would achieve expected damage of 2.26 x base damage. What damage would the team without Wu achieve? Depends who is substituted for him, right? How about a nice debuffer, like Isarnia?
Our modifier damage expectation for that team would be 1.48/0.56 = 2.64 x base damage, so substituting Isarnia for Wu would result in improved expected tile (and special) damage.
And don’t forget: this completely ignores the improvement in tile damage you’ll get by using a hero that has a higher attack stat, and the potential benefit of using a hero of the right colour instead of Wu.
I spotted it as well, it’s a mistake that’s really easy to make. Wu doesn’t raise your offense to 185% but to 285%. Hence the gain after misses is not 20% but 82.5%, which makes a Wu team about 30% more effective than BT
I make mistakes like those almost every day, your calculation is still valuable.
I do hope your drink is not 100% though
And see, I proof it immediately, there is my mistake:
I don’t think that’s true due to the multiplier effect. Wu and BT multiply, which makes the gap even bigger than from baseline. It’s a reason why shieldbreaker/wu/buffer all need a spot before adding hitters. Luckily you can usually color match some of those roles.
They don’t multiply facepalm. Ares does multiply with Wu/BT, but Wu BT add up. So you are correct on this one.
Also, but Kiril’s buff peters out really fast, which makes keeping it active significantly harder. This is noticable in scaling; BT has 33% longer effect than Kiril, whereas WU has just 25% longer duration than BT. Keeping Wu active is easier, but keeping BT active is pretty doable. Kiril? A lot harder.
About the tank role, got it, I use Meteor strikes+arrows, so cheating here
It’s best I don’t try to post anything analytical in my current state, but it is worth acknowledging your point that the relatively short duration of Kiril’s buff (and, to a lesser extent, BT’s buff) are disadvantages, compared to Wu’s long duration special. You are right.
This can be managed with mana pots, of course, just as you choose to use projectiles to increase your team’s durability instead of a tank, but all items come at a cost. When assessing the effectiveness of a team (or hero) it’s not okay to assume one can compensate for shortcomings with items: nothing is free in the game.
Let’s use the following formula to calculate the damage per tile for each lineup:
I’ll omit the denominator, the common factor of 100, and the random parameter since it will be the same in all of the cases.
Wu - Kiril - Isarnia - Lianna - Little John
Full buff to use: (1 + 1.85 + 0.3)/0.56 = 5.625
Yellow tiles fully buffed: (707 * 5.625)^1.35 = 72340 * y
Blue tiles fully buffed: ((656+797) * 5.625)^1.35 = 191303 * b
Green tiles fully buffed: 2 * ((741+729) * 5.625)^1.35 = 388663 * g
Board damage = (72340 * y + 191303 * b + 388663 * g) * 0.68
Average damage rating per tile = (72340 * y + 191303 * b + 388663 * g) * 0.68/5 = 88713.6
Isarnia - Caedmon - Melendor - Lianna - Elkanen:
Full buff to use: 1/0.56 = 1.786
Blue tiles fully buffed: (797 * 1.786)^1.35 = 18072
Green tiles fully buffed: 2 * ((635+729+714+675) * 1.786)^1.35 = 192667
Board damage = 18072 * b + 192667 * g
Average damage rating per tile = (18072 + 192667)/5 = 42147.8
Wu - Boldtusk - Isarnia - Lianna - Little John
Full buff to use: (1 + 1.85 + 0.48)/0.56 = 5.946
Yellow tiles fully buffed: (707 * 5.946)^1.35 = 77968
Red tiles fully buffed: 0.5 * (588 * 5.946)^1.35 = 30397
Blue tiles fully buffed: (797 * 5.946)^1.35 = 91658
Green tiles fully buffed: 2 * ((741+729) * 5.946)^1.35 = 418901
Board damage = (77968 * y + 30397 * r + 91658 * b + 418901 * g) * 0.68
Average damage rating per tile = (77968 + 30397 + 91658 + 418901) * 0.68/5 = 84173
Wu - Isarnia - Melendor - Lianna - Elkanen:
Full buff: (1+1.85)/0.56 = 5.089
Yellow tiles: (707 * 5.089)^1.35 = 63193
Blue tiles: (797 * 5.089)^1.35 = 74288
Green tiles: 2*((714+729+675) * 5.089)^1.35 = 555883
Board Damage = (63193 * y + 74288 * b + 555883 * g) * 0.68
Average damage rating per tile: (63193 + 74288 + 555883) * 0.68/5 = 94297
Boldtusk - Isarnia - Lianna - Elkanen - Melendor:
Full buff to use: (1.48)/0.56 = 2.64
Red tiles : 0.5 * (588 * 2.64)^1.35 = 10157
Blue tiles: (797 * 2.64)^1.35 = 30629
Green tiles: 2 * ((714+729+675) * 2.64)^1.35 = 229189
Board damage = 10157 * r + 30629 * b + 229189 * g
Average damage rating per tile: (10157 + 30629 + 229189)/5 = 53995
Every team with Wu is superior. The surprising result to me was that the stacked buff does not quite make it to the damage that an extra strong color provides, so on that, @Brobb was right for a blue titan. I’d want to do this for other colors since this is Boldtusk’s weak color. If I was allowed a Season 2 hero to test, it would be Gadeirus, since it is green and buffs neighboring heroes’ attack (Tarlak does not play nice with Wu and this discussion is about Wu). The team without Wu or any attack buff fared the worst. Using Caedmon instead of an attack buff is not a worthwhile exercise, according to this method of assessing titan damage.
TL;DR: Ranking of blue titan teams considered when they are fully buffed: 1) Wu - Isarnia - Melendor - Lianna - Elkanen ( 94297 ) 2) Wu - Kiril - Isarnia - Lianna - Little John ( 88713 ) 3) Wu - Boldtusk - Isarnia - Lianna - Little John ( 84173 ) 4) Boldtusk - Isarnia - Lianna - Elkanen - Melendor ( 53995 ) 5) Isarnia - Caedmon - Melendor - Lianna - Elkanen ( 42147.8 )
I thought I could make a worthwhile criticism of your calculations now, but upon further review I just don’t think my brain is functioning well enough yet. Suffice to say they are good and worthwhile calculations to make, I applaud you for making them, and I’ll try to give them the attention they deserve when my head stops hurting.