Panzers vs. Horsemen - the verdict

Panzers vs. Horsemen - the verdict

Postby popo » Sat Jul 12, 2014 11:04 pm

I've run the numbers and under the following assumptions, Horsemen and Panzers have the same expected damage output (assume for simplicity that the horseman's team is mono-element).

1) H-team has 6.5K total attack (a bit generous?).
2) The probability of rolling the correct element in a cell is independent of other cells, with probability 1/6 that a given cell will contain the correct element (this is almost certainly not how DE is coded, but gives an expected value consistent with testing).

Under these assumptions, the probability of success on, say, line 1 is roughly 7.3% when horseman is activated. If 21 lines are rolled over two turns, this gives an expected value of roughly 35,200 damage.

Some comments:
1) The standard deviation on this estimate is roughly 11K if one assumes that the lines are independent. Since they are in fact highly dependent, the true standard deviation is much higher.
2) If a team has multiple horsemen, this value does not increase, since it is calculated within the window of activation.
3) This equality of expectation only holds if both attack the same number of targets. Since a huge portion of the horseman's value comes from very high numbers, this is a realistic assumption.
4) The only circumstance under which H-team has a clear edge (in expectation) is in the presence of, e.g., Lilith. Whether this is a clear advantage in reality is highly debatable, as the horseman's attack is over two turns and is quite unreliable.

In conclusion, one must say that panzers are indeed far stronger than horsemen, and the only circumstance I can envisage in which H-team would have a commanding superiority would be in combination with Lilith against a raid boss with 5 million HP or so (not guild war). Claims that they are equal in the case of, say, guild wars is completely unsubstantiated, given both the generous assumptions needed to have equal expectation, and the diminishing returns of the GW-curve.

That said, those who claim that they have the same expected damage output are certainly not wrong, though perhaps that assertion should be qualified.
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Re: Panzers vs. Horsemen - the verdict

Postby mattyb79 » Sun Jul 13, 2014 7:35 am

While your math is most certainly correct and I appreciate the time you put into the statistics, I think there are way too many variables to compare these two cards head to head mathematically. Almost anyone who is going to play a horseman in a mono team is going to be using one (if not two) Oath leaders. This makes your assumption of 6.5K attack extremely low. A panzer alone in a GW without supporting cards (i.e. Oath/Reaper or double Reaper) will net you far less points over the course of the GW than a mono team with a horseman. Comparing the two is futile IMO as they are very different cards. Panzers provide a consistent, large amount of damage that can be controlled by the player, while horsemen have the POTENTIAL to do unbelievably massive damage...... or none at all.
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Re: Panzers vs. Horsemen - the verdict

Postby Slikknick » Sun Jul 13, 2014 8:13 am

Let the naysayers stay ignorant and when horseman are discontinued revel in the fact that you have a 5/5 8 star horseman in your team.

Dark horseman + Cat burglar in dark mono team is OP.
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Re: Panzers vs. Horsemen - the verdict

Postby mistervista » Sun Jul 13, 2014 9:06 am

Slikknick wrote:Let the naysayers stay ignorant and when horseman are discontinued revel in the fact that you have a 5/5 8 star horseman in your team.

Dark horseman + Cat burglar in dark mono team is OP.


1) That will never happen for most of us because we can't do the Hell stage.

2) What is OP

3) @mattyb - What is an Oath leader? I've never heard of an Oath card.
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Re: Panzers vs. Horsemen - the verdict

Postby Boop » Sun Jul 13, 2014 9:08 am

OP means over powered. And Slikk is right. I'd rather 2 5/5 Horsemen than Panzers for chapter 7+.
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Re: Panzers vs. Horsemen - the verdict

Postby popo » Sun Jul 13, 2014 9:17 am

Mattyb, if the panzer team ran double oath, it would still have higher expected damage, as panzers scale with oath. Whether oath or reaper is better holds equally for both, in terms of damage. Unless gw changes dramatically, ie much higher boss health and increasing rather than diminishing returns, there is no way that horseman is better. In other words, right now reaper x2 panzer x2 can kill boss more often than not. If someone says there's a horse deck capable of better than 10%, I would be very skeptical. A cool idea to level the playing field would be to reward overkill, so that the times when horse deck hits for 4 million would be desirable, rather than pointless.
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Re: Panzers vs. Horsemen - the verdict

Postby mattyb79 » Sun Jul 13, 2014 10:03 am

Be skeptical all you want, but I have all panzers except fire, so I ran a mono team with War for the latest guild war and killed the boss roughly 7 out of 10 times. Much higher than your 10%. I do agree with you, however, that with double reaper, panzer is a far more guaranteed option. I'm just saying as a single card comparison, panzer is not quite the almighty you claim vs horseman.
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Re: Panzers vs. Horsemen - the verdict

Postby yutyu » Sun Jul 13, 2014 11:24 am

mistervista wrote:1) That will never happen for most of us because we can't do the Hell stage.

That is wrong, none of us can do Hell stage without revives. The only exception is to be lucky enough get multiple continuous Lucky Spins during Wave 5 while fighting Apocalypse Hell.
The question is how many revives you need to complete a single stage of Hell. You need to build your sets around a balance of damage dealing, survival and healing to effectively reduce the number of revives used per stage.

mistervista wrote:3) @mattyb - What is an Oath leader? I've never heard of an Oath card.


Oath is the name for leader skill that gives 2x attack and 2x hp to a certain color in a set.
Example: Agni for Fire, Poseidon for Water and etc.

Another notable skill name is Oracle leader skill: 2.5x hp for a certain color in a set
Example: Valkyrie for Fire, Amazon for Water and etc

Also another common one, Wall leader skill: reduces damage caused by a certain color by 50%
Example: Cannoneer for Fire, Blackbeard for Water and etc
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Re: Panzers vs. Horsemen - the verdict

Postby admin » Sun Jul 13, 2014 10:18 pm

popo wrote:4) The only circumstance under which H-team has a clear edge (in expectation) is in the presence of, e.g., Lilith. Whether this is a clear advantage in reality is highly debatable, as the horseman's attack is over two turns and is quite unreliable.


There is also Pandora and Andromeda, but those cards are even harder than Lilith to obtain or find a friend that has it as leader.
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Re: Panzers vs. Horsemen - the verdict

Postby _0nyx_ » Sun Jul 13, 2014 11:55 pm

admin wrote:
popo wrote:4) The only circumstance under which H-team has a clear edge (in expectation) is in the presence of, e.g., Lilith. Whether this is a clear advantage in reality is highly debatable, as the horseman's attack is over two turns and is quite unreliable.


There is also Pandora and Andromeda, but those cards are even harder than Lilith to obtain or find a friend that has it as leader.


Wouldn't a Lilith be technically harder to obtain as it is completely random and not a static reward choice, albeit pandora and andromeda are only for the wealthy and persistent. Lilith is up for grabs at anytime, just well not very likely. You could end up never drawing a Lilith as far as I know.
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