Paladins vs Terminators Math and Stuff

[Plasmablasts]

 

 

Why not run a simple simulation? It would be incredibly easy to program and would answer these questions much easier and with less debate.

That's just what I had been working on. Using excel, I did 5 different trial runs of 1,000 d3 dice rolls, and then looked at the outcomes.

 

For simulation #1, a 1 was rolled 332 times, a 2 was rolled 329 times, and a 3 was rolled was rolled 339 times. Thus, in this simulation, a Terminator would have been killed 668 times, while a Paladin would have been killed only 339 times. This is why Siezeman has stated that Paladins are 100% more survivable against d3 weapons, for example, as they would have been killed outright roughly half as often.

 

The other four simulations resulted in pretty much the same outcome.

 

Doing a similar simulation using a d6 for 1,000 rolls resulted in a Terminator dead from a single blow 858 times, whereas a Paladin dies 694 times.

Thanks Valerian. Unfortunately, as I think duz_ stated, your simulation only looks at shots which kill a model outright, with the other unsaved hits considered as wasted. In an actual round of shooting, those wasted unsaved hits would still have removed wounds. The simulation should account for those as well.

 

Edit: misspelling of "shots" triggered the swear filter...

Edited August 29, 2017 by Plasmablasts

[Valerian]

How do you account for damage being wasted? Because D3 is random

 

Eg Damage results / rolls : 1, 3, 2, 1, 2, 3

 

In the above case 4 terminators would die and 3 paladins would die, but you would lose 4 and 3 excess damage respectively... 

If you didn't account for that you would simply say 6 terminators died and 4 paladins.

 

duz_, are you asking about the simulations that I ran?  If so, I just did a count of all results of each possible outcome.  We know that in a real game of 40k it gets a bit more complicated than that, since a Paladin that takes a single wound (or two!) has to be allocated the next wounding hit until dead, and so on, but there is no way I'm going to try to figure out how to do that within excel.  You do bring up a fair point though, in that the way the wound allocations mechanics work, the Paladins aren't exactly twice as durable, but it's probably close enough for our purposes.

 

 

 

 

Thanks Valerian. Unfortunately, as I think duz_ stated, your simulation only looks at shots which kill a model outright, with the other :cusss consired as wasted. In an actual round of shooting, those wasted unsaved hits would still have removed wounds. The simulation should account for those as well.

 

 

Yeah, I just addressed that shortcoming above.  If I knew an easy way to account for that, I'd adjust the simulation.  We know a lot more Paladins would also die due to 1s plus 2s adding up, but then you have to account for the order of the rolls, and wasted excess damage, and that's far beyond my excel skill set.

 

V

Edited August 29, 2017 by Valerian

[Beams]

 

 

Why not run a simple simulation? It would be incredibly easy to program and would answer these questions much easier and with less debate.

That's just what I had been working on. Using excel, I did 5 different trial runs of 1,000 d3 dice rolls, and then looked at the outcomes.

 

For simulation #1, a 1 was rolled 332 times, a 2 was rolled 329 times, and a 3 was rolled was rolled 339 times. Thus, in this simulation, a Terminator would have been killed 668 times, while a Paladin would have been killed only 339 times. This is why Siezeman has stated that Paladins are 100% more survivable against d3 weapons, for example, as they would have been killed outright roughly half as often.

 

The other four simulations resulted in pretty much the same outcome.

 

Doing a similar simulation using a d6 for 1,000 rolls resulted in a Terminator dead from a single blow 858 times, whereas a Paladin dies 694 times.

You'd want to run it like this:

(Obvs. Pseudocode, using mobile)

 

KillArray[1...100]=0

While(I<1000)

{

Number of paladins=12

Current hp=3

DiceRolled=1

 

While (paladinskilled<12):

{

Dicerolled+=1

Dice=random(1-3)

Current hp+=-Dice

If hp=<0

{paladinsKilled+=1

Hp=3}

}

KillArray[Dicerolled]+=1

I++

}

Print(KillArray)

 

That way it accounts for Everytime a 1 or 2 is rolled that wouldn't kill a guy. Switch it up for Terminators by lowering the current hp constant to 2.

 

 

And then you put your findings in a nifty little chart and post it. It's easier to argue when you have a chart ;-)

Edited August 29, 2017 by Beams

[duz_]

 

duz_, are you asking about the simulations that I ran?  If so, I just did a count of all results of each possible outcome.  We know that in a real game of 40k it gets a bit more complicated than that, since a Paladin that takes a single wound (or two!) has to be allocated the next wounding hit until dead, and so on, but there is no way I'm going to try to figure out how to do that within excel.  You do bring up a fair point though, in that the way the wound allocations mechanics work, the Paladins aren't exactly twice as durable, but it's probably close enough for our purposes.

 

 

It was directed at everyone I guess I see a lot of Mathammer going around and "averages" vs simulations 

I think everyone can agree that comparing Paladins vs Terminators is a bit more complex than just using an average when it comes to D:D3 and unless someone wants to sit down and run a significant number of simulations accounting for all the possible variables then I think we could probably put this to rest?

Not to mention the whole day's posting has been completely off topic ;)

[Valerian]

Yeah, Beams, I took 'Turbopascal for Windows' in college 23 years ago.  I think I'll leave the advanced coding to someone else.

[Valerian]

 

Not to mention the whole day's posting has been completely off topic

 

 

Yeah, I've moved it all to a new thread, for any interested in furthering the discussion.  Although not necessarily relevant to the original post of the Command Point thread, it's still a worthwhile discussion, for those that enjoy the math behind it all.

 

V

[librisrouge]

I don't have anything serious to contribute other than that I am seriously digging the math going on here.

[Seizeman]

The comparison is actually very simple and does not need so much accuracy.

 

Paladins cost 15% more points than Terminators. They are at least 50% more durable against anything but flat 3 dmg weapons. That's more than enough already to justify their cost. If they would be just 50% more durable against 1 dmg weapons and 100% more against 2 dmg weapons, it would be worth anyway.

 

In melee, they do 25% more damage if armed with falchions, 50% if armed with hammers, and, if the sargeants are armed with hammers, the Paragon does 98% more damage than the justicar (and he does as much dmg vs vehicles as 3 paladins with falchions, so it is very relevant). That's also more than enought to justify them.

 

Figuring out exact math is fun and interesting, but it does not affect the conclusion at all.

 

At this point, I think it would be easier to just ask an actual mathematician XD

[Gentlemanloser]

I have a maths degree.

 

Not used it in 20 years though. So I'm more than a tad rusty. ;)

 

Ring and Group theory were fun. Stats and Mechanics, not so much!

 

We had a course in the second year where science students had to take some arts classes, but they scraped it for the arts students as they just couldn't (true story!)

 

I had childrens literature, and new media & society, which was about the emergence of this new fangled thing called the Internet, and what impact it might have on us. Lol.

[jeffersonian000]

It's just 3 pages of wasted arguing that could have been sidelined to private messaging, as the conclusion still points the original math-hammer on how much more resilient per point Paladins ate over GKT. The Geek Peening was impressive, though. Didn't even have to whip out my engineering degrees.

 

So ... Pallies over Termies this edition.

 

SJ