Monte Carlo versus "The Math"

[AbdulAlhazred]

I think your results agree with the DPR analysis more than those early posts indicate. DPR should give you the MEDIAN number of rounds, which is the point when you win 50% of the fights. For example, in your first graph, the one with DPR giving 4.6 rounds and the MC giving 5.5, 57% of the fights are over by round 5.

It makes sense that the mean is skewed high. Variation from the average can only shorten the fight so much - it is going to take at least 2 rounds to kill that soldier. But on the long end, the fight can go long as 13 rounds. The 13 is going to pull things high a lot more than the 2 pulls things low. This same effect is why home prices are usually listed as median home price. One millionaire throws the mean out of whack.

Interesting project!

PS

Right and if you look at his curves they are basically pretty much T distributions. Its exactly what you would expect and you could derive the numbers analytically vs using the MC method. It might be a bit faster, but OTOH I for one am both lazy and would have to brush up on some advanced statistics...

 

[UngeheuerLich]

Thanks for soing these analyses. Using monte carlo method is a lot more interesting than comparing averages.

An interesting thing would be comparing a first level character who took expertise vs one that took weapon focus or an axe vs a great sword.
I would really like to see how important expertise is to shorten the cobat. I bet it is really low, eswpecially if you chose reaping strike as standard attack and a daily with miss half instead of reliable. (I believe, reliable only for 3dx damage isn´t worth it if you could get miss half and just a normal reaping strike with miss effect)

 

[keterys]

An interesting thing would be comparing a first level character who took expertise vs one that took weapon focus or an axe vs a great sword.

It really wouldn't be that interesting - that level of simplicity is already covered by DPR calculations and 1st level was never the interesting level for those feats and weapons really.

It will be neat if the program is fully featured enough to allow you to do things like flip a couple switches and compare to a Brash Striking and Crushing Surging Battlerager, Mordenkrads with Hammer Rhythm vs. Waraxe w/ Deadly Axe and shield, etc. But even for one character that will start to get very very complex.

The really interesting part will be what happens with a group.

 

[Blackbrrd]

It really wouldn't be that interesting - that level of simplicity is already covered by DPR calculations and 1st level was never the interesting level for those feats and weapons really.

Actually I don't agree with you here (I think it's about the first time I don't agree with you). I believe this analysis will show that there is less variation with +1 to hit than with +1 to damage, which again will show fewer deaths. Using Reaping Strike might not be the best power to showcase this since it damages on a miss.

For players it's important to have as little variation as possible and I think +1 to hit goes a long way to reduce variation.

 

[Jhaelen]

Well, I don't know. For the Monte Carlo approach to show anything interesting (to me), you'd have to be able to simulate things that aren't easily calculated.

E.g. a party fighting tactically as a team vs. a party that doesn't. Or a party expending all of their resources vs. a party not expending any resources (and everything inbetween). Or the 'ideal party' vs. parties lacking a certain role.

One on one comparison are completely uninteresting and don't show anything useful, since it's not a situation that will happen in a normal game situation.

So, to the OP: I hope you'll be able to code the basics quickly so you can start looking at relevant scenarios

 

[keterys]

Actually I don't agree with you here (I think it's about the first time I don't agree with you). I believe this analysis will show that there is less variation with +1 to hit than with +1 to damage, which again will show fewer deaths. Using Reaping Strike might not be the best power to showcase this since it damages on a miss.

For players it's important to have as little variation as possible and I think +1 to hit goes a long way to reduce variation.

I think you can make the comparison between expertise and focus interesting, but not with a dwarf fighter using reaping strike

Make it a wizard and have a successful hit with an encounter power deny the enemy an attack that round (via daze or immobilize), then sure. Or with that -2 attack at-will. I'd actually like to see the differences between that and magic missile on general principle, even outside of expertise.

I guess it'd be interesting for a barbarian with howling strike too. I'd like to see the difference between a barbarian with avalanche strike and one with vault the fallen, for that matter. And, really, those are things I can get out of DPR, but at a certain point I get lazy

 

[UngeheuerLich]

No really,

the question in other threads is: is expertise a feat tax, everyone has to get (at level 5 latest) or are there other feats (without taking bloodclaw things into considerations) which are wirth taking, even for damage output...

So why not begin with the reaping strike human? As you could see, the monte carlo method for the dwarf had nice spikes on certain hp ranges. Those are the spikes which could make 1 point of damage much more helpful than 1 point of attack bonus (at least that is what i believe)

 

[keterys]

the question in other threads is: is expertise a feat tax, everyone has to get (at level 5 latest) or are there other feats (without taking bloodclaw things into considerations) which are wirth taking, even for damage output...

I suspect you have misunderstood those other threads. A lot. But, if you'd find it interesting somehow, more power to you.

 

[UngeheuerLich]

No, i understood those threads.^^ Really.

But i really think it would be interesting to see how the effect of a +1 to hit, +2 to hit and of +3 to hit vs +1/2/3 to damage is. And how big the effect of expertise vs equal level brutes and soldiers at level 1, 10 and 20 is.
(In a world, where leaders throw no bonuses and noone ganks a single opponent etc.)

 

[Nytmare]

[LaFontaine]

In a world...

where leaders throw no bonuses...

and no one ganks a single opponent...

[/LaFontaine]