With the introduction of monster power in patch 1.05 and a nonlinear rate of xp/mf/gf/bonus item vs monster health/damage, what is the optimal monster power to play at?
Updated for 1.07
Looks like with the increase to MP experience, the new sweet spot for xp gain has been shifted to mp5. Of course this is assuming you can optimally handle the higher MP without deaths and still maintaining a fast kill rate.
Using the official MP chart, I plotted the ratios of the gain per level vs. increase in health and damage:
I also plotted the gain vs increase in health/damage in this spreadsheet.
Note, for the damage line, when comparing it to monster health, lower is better, but for all other cases higher is better.
While it's obvious that monster damage scales favorably the higher you go (reasons discussed in the blog post above). The optimal point in terms of mf/gf seems to be at MP3-4. While the optimal gain point for bonus items and experience is at MP5.
When looking at damage, the optimal gain point shifts towards MP7+, this is due to the fact that monster damage doesn't scale up nearly as much as health.
Overall, if you can handle MP5, that seems to be the sweet spot in terms of gain of MF/GF/XP/Bonus item vs increased monster difficulty.
None of the current answers take into account the base MF/GF/XP gain increases on a character, as soon as you even take into account the 75% of each you will get from a 5 stack of NV, it becomes apparent that the LOWER the MP level, the better the ratios are.
This only holds true for MP0 on Act 3+ because ANY MP level turns mobs in act 1 and 2 into higher level guys, so even more "bonus health"
The best monster power for farming is going to be the one where you still 'one shot' everything.
I've taken 5-10 time readings for each Monster Power from 0 to 5 on my Act 3 run. The data I compiled showed that my XP/Hour, Gold/Hour and Rares/Hour are all highest for me on MP0. MP1 doesn't make a very big dent in Gold/HR or Rares/HR (<5%) but my XP/HR drops by about 10%. Each step up in MP after that lowers all 3 stats I was computing by around 7% to 15%. The even sadder part, is that as I gain even more Paragon Levels (I'm at 72 at time of writing), this graph skews even further toward MP0 as being the best per hour, because my base MF and GF continue to go up.
If you really want to know which is best, start monitoring the time it takes YOU to complete a specific run, as well as your starting/ending xp and gold. My theory is you'll find the same thing: The lower the MP, the better the farming.
This is my table
MP 1 2 3 4 5 6 7 8 9 10 Health 150 225 326 457 639 895 1253 1755 2457 3439 Damage 109.6 120.12 131.65 144.29 158.14 173.32 189.96 208.2 228.18 250.09 XP 10 20 30 45 60 75 95 115 135 160 MF 25 50 75 100 125 150 175 200 225 250 GF 25 50 75 100 125 150 175 200 225 250 Bonus Item 1 8 17 26 36 47 59 71 85 100 Extra XP per Health -0.266666667 -0.466666667 -0.601226994 -0.682713348 -0.749608764 -0.804469274 -0.844373504 -0.877492877 -0.904354904 -0.924396627
So basically all the other answers are missing an important point. If you are constantly killing enemies, then MP will not profit you in anyway.
Think about it. Health increase by 50% and XP increases only by 10%.
Your gain comes when you "walk" a lot. So optimum MP depends a lot on the percentage of your time you spent walking instead of fighting. If you fight 100% of the time, then MP1 will reduce your XP gain by 26%. MP2 will reduce your gain by 46%, etc.
You also gain more if you're aiming for infernal machine.
Looking purely for the XP side of things, I've constructed a similar sheet for Normal/Nightmare/Hell (and pulled in @spartacus's chart)
Based on charts 1 and 3, it appears that MP2 is the "most efficient", as the XP gains seem to follow a diminishing (chart 1) and linear (chart 3) ratios thereafter.
Edit again: looks like MP1 is actually the most efficient. I just added a few rows and a chart to the spreadsheet showing the differences between MP levels, and the greatest difference is 0-MP1.
what you neglect to take into consideration here is the amount of time spent there http://i.imgur.com/rQrnP.png
acording to this one and a fair amount of testing I've done, there really is no reason to play on higher then mp0 when farming xp and anything other then mp1 when farming items
The reason people move to higher MP levels in the first place, is the low utilization of their weapon. The monsters are being killed too fast, and its such a waste of good weapon power.
Lets face the facts, there is no way one can kill monsters 100% of the time - at least 50% of the time is spent on just walking.
But indeed there must be a good balance between the XP gained relative to the amount of health. MP level 5 is said to be the optimal point for that.