math analysis of DMG loot guidelines for starting PCs above level 1

[evilbob]

The math behind what to give out in items/treasure for starting PCs above level 1 has always seemed a bit odd to me. Specifically, it generally feels a bit low. Additionally, it's clearly broken for very low levels - you can't really use it to start someone at level 2, or they'd be much richer than they should be. Well, I finally decided to just find out exactly what the math really is.

First, I decided to establish what I considered a "baseline." This is the total amount of money given at each level including all parcels, then averaged over the total party members. While this isn't really practical in a real-world setting, since realistically you'll get several items of various levels over the course of the game and practically no DM will be a perfect arbiter of loot distribution, it does help set a sort of standard for about where everyone should be if everything was distributed perfectly.

Here is a listing for 5 party members of the total loot gained at each level along with what each party member receives on average (i.e. the total divided by 5) and the sum of all loot per party member at that level. I have ignored the starting 100 gold for all calculations.

[sblock]

level	5 PCs total	each / lvl	each total
1	3760		752		752
2	5360		1072		1824
3	7600		1520		3344
4	10480		2096		5440
5	14000		2800		8240
6	18800		3760		12000
7	26800		5360		17360
8	38000		7600		24960
9	52400		10480		35440
10	70000		14000		49440
11	94000		18800		68240
12	134000		26800		95040
13	190000		38000		133040
14	262000		52400		185440
15	350000		70000		255440
16	470000		94000		349440
17	670000		134000		483440
18	950000		190000		673440
19	1310000		262000		935440
20	1750000		350000		1285440
21	2350000		470000		1755440
22	3350000		670000		2425440
23	4750000		950000		3375440
24	6550000		1310000		4685440
25	8750000		1750000		6435440
26	11750000	2350000		8785440
27	14250000	2850000		11635440
28	16250000	3250000		14885440
29	17750000	3550000		18435440
30	21875000	4375000		22810440

[/sblock]Not too surprising, right? Well, except that yes, that is 22.8 million gold you're expected to acquire over the course of 30 levels - not too shabby. And a good chart to reference all the same. The next thing I did just for comparison was to find the same values for 6-PC parties and 4-PC parties just to double check.

[sblock]

level	6PCs total	each / lvl	each total	% diff		4PCs total	each / lvl	each total	% diff
1	4440		740		740		98.40%		3080		770		770		102.39%
2	6040		1006.67		1746.67		95.76%		4520		1130		1900		104.17%
3	8280		1380		3126.67		93.50%		6600		1650		3550		106.16%
4	11800		1966.67		5093.33		93.63%		8680		2170		5720		105.15%
5	15960		2660		7753.33		94.09%		11400		2850		8570		104.00%
6	20760		3460		11213.33	93.44%		15400		3850		12420		103.50%
7	28760		4793.33		16006.67	92.20%		22600		5650		18070		104.09%
8	39960		6660		22666.67	90.81%		33000		8250		26320		105.45%
9	57560		9593.33		32260		91.03%		43400		10850		37170		104.88%
10	78360		13060		45320		91.67%		57000		14250		51420		104.00%
11	102360		17060		62380		91.41%		77000		19250		70670		103.56%
12	142360		23726.67	86106.67	90.60%		113000		28250		98920		104.08%
13	198360		33060		119166.67	89.57%		165000		41250		140170		105.36%
14	286360		47726.67	166893.33	90.00%		217000		54250		194420		104.84%
15	390360		65060		231953.33	90.81%		285000		71250		265670		104.00%
16	510360		85060		317013.33	90.72%		385000		96250		361920		103.57%
17	710360		118393.33	435406.67	90.06%		565000		141250		503170		104.08%
18	990360		165060		600466.67	89.16%		825000		206250		709420		105.34%
19	1430360		238393.33	838860		89.68%		1085000		271250		980670		104.84%
20	1950360		325060		1163920		90.55%		1425000		356250		1336920		104.00%
21	2550360		425060		1588980		90.52%		1925000		481250		1818170		103.57%
22	3550360		591726.67	2180706.67	89.91%		2825000		706250		2524420		104.08%
23	4950360		825060		3005766.67	89.05%		4125000		1031250		3555670		105.34%
24	7150360		1191726.67	4197493.33	89.59%		5425000		1356250		4911920		104.83%
25	9750360		1625060		5822553.33	90.48%		7125000		1781250		6693170		104.00%
26	12750360	2125060		7947613.33	90.46%		9625000		2406250		9099420		103.57%
27	15250360	2541726.67	10489340	90.15%		11625000	2906250		12005670	103.18%
28	17250360	2875060		13364400	89.78%		13125000	3281250		15286920	102.70%
29	18250360	3041726.67	16406126.67	88.99%		14625000	3656250		18943170	102.75%
30	21875360	3645893.33	20052020	87.91%		18750000	4687500		23630670	103.60%

[/sblock]So parties with 6 PCs get somewhere around 10% less total loot, and parties with 4 PCs get somewhere around 5% more. Does this make sense? Parties with more characters may be slightly stronger and those with only 4 slightly weaker against same-level encounters... Except that's supposed to be handled with monster XP budgets... Presumably more PCs end up using less consumables? Anyway, it was interesting, and probably mostly a product of coming up with a good metric and making it "as close as we can get." However, I took away from this that giving out slightly too much treasure to a 6 PC campaign is probably a good idea.


Then I went further to show what the DMG standard n+1, n, n-1, and gold = n-1 metric equated to for each level.

[sblock]

str lvl	DMG tot		%
1	100	
2	1920		255.32%
3	2560		140.35%
4	3200		95.69%
5	4480		82.35%
6	6400		77.67%
7	9600		80.00%
8	12800		73.73%
9	16000		64.10%
10	22400		63.21%
11	32000		64.72%
12	48000		70.34%
13	64000		67.34%
14	80000		60.13%
15	112000		60.40%
16	160000		62.64%
17	240000		68.68%
18	320000		66.19%
19	400000		59.40%
20	560000		59.86%
21	800000		62.24%
22	1200000		68.36%
23	1600000		65.97%
24	2000000		59.25%
25	2800000		59.76%
26	4000000		62.16%
27	6000000		68.29%
28	8000000		68.76%
29	10000000	67.18%
30	11500000	62.38%

[/sblock]Ah, now that is interesting - and it proves me right! Levels 2 and 3 start far above the norm, but starting at level 9 and above means you're in the 60-70% range, for an average of 64.15%! Again, this is quite a drop off: 35% of your total wealth gone, presumably spent on consumables or traded down items or what have you. Or maybe just to make their metric work well. Whatever. But the idea that this seems "low" got reinforced for me. And it also let me know that the best level to start a campaign loot-wise following these guidelines is 8 or earlier, and then 12, 17, 22, and 27 or 28. So if you're starting that paragon tier campaign, why not start at 12 instead of 11? (Also worth noting: there is no "n+1" value for level 30, so I used a level 30 item value instead. If you use double that item value - two level 30 items - it jumps to 79.33%.)

So, what do you do about it? Well, like any DM I immediately tried to think of how I could "fix" this by doing it differently... Perhaps another, similar metric that is just as easy to remember? I experimented with a few numbers, finding one that I liked the best that wasn't too far from the original: n+1, n, n-1, n-1, n-2, and gold = n-1. This seemed promising because it just adds an n-1 and n-2 item to the original formula.

[sblock]

str lvl	DMG tot		%
1	100	
2		
3	3440		188.60%
4	4400		131.58%
5	6000		110.29%
6	8240		100.00%
7	12400		103.33%
8	17200		99.08%
9	22000		88.14%
10	30000		84.65%
11	41200		83.33%
12	62000		90.86%
13	86000		90.49%
14	110000		82.68%
15	150000		80.89%
16	206000		80.65%
17	310000		88.71%
18	430000		88.95%
19	550000		81.67%
20	750000		80.18%
21	1030000		80.13%
22	1550000		88.30%
23	2150000		88.64%
24	2750000		81.47%
25	3750000		80.04%
26	5150000		80.03%
27	7750000		88.21%
28	10750000	92.39%
29	13750000	92.37%
30	16250000	88.15%

[/sblock]Well, this does change the formula so that now from level 9 and up I get closer to 80-90% of the average value, for a total average of 85.5%. Being off by about 15% seems more generous and possibly more realistic, depending on your PCs' playstyles - and in any case closer to the style that I would prefer.

I won't make a chart (edit: I made a chart; see post 11), but as you might suspect adding an n-1 item (only) to the DMG guidelines put the totals in the 70-80% range.

Another idea was adding an n+2 to the original. This actually puts the loot level right at 95% to 100% (although it drops to around 90 sometimes), and if you're looking to equal the amount distributed to players without any loss for consumables or other expenditures, it's not a bad route (past level 8). (Edit: see post 11 for more numbers regarding n+2.)


However, these formula all still give a common problem: namely, that it forms a weird inverted logarithmic scale, where early levels give too much, and then later levels settle into a weird bouncing pattern that changes every time you hit a new loot level plateau (every 5 levels). Again, this is good for a general metric, and great for shorthand - which is, I'm sure, why they did it. But what if you're looking for something a little more... accurate? A little more specific?

Well, the best I could do was come up with a chart - which means it'll never actually be used (possibly even by me), but I think it's really one of the better ways to give a consistent guideline for starting loot levels. Clearly, I favor the >80% range, so you can certainly change this chart for your own needs if you feel that's too generous.

It only requires a chart through level 9, at which point it just switches to the constant formula above: so paragon through epic, you're golden. It's really just heroic tier that this chart is meant to fix. Also, it may be easier and more practical to substitute gold for the n-1 and n-2 extra items, since it makes it simpler for the players. These charts are all based on numerical values, so sub for gold as you see fit.

[sblock]

str lvl	items			gold
1*				100
2	n-1			n-1
3	n, n-1			n-1
4*	n+1, n, n-1		n-1
5*	n+1, n, n-1		n-1
6	n+1, n, n-1, n-1	n-1
7	n+1, n, n-1, n-1	n-1
8	n+1, n, n-1, n-1	n-1
9+	n+1, n, n-1, n-1, n-2	n-1
		
*same as DMG guidelines

[/sblock]And finally, if you wish to make the starting gold values incredibly close to what the average player would have at each level (and you don't mind hitting 101% at level 12):

[sblock]

str lvl	items			gold
1*				100
2	n-1			n-1
3	n, n-1			n-1
4*	n+1, n, n-1		n-1
5	n+1, n, n-1, n-1	n-1
6	n+1, n, n-1, n-1, n-2	n-1
7	n+1, n, n-1, n-1	n-1
8	n+1, n, n-1, n-1, n-2	n-1
9+	n+2, n+1, n, n-1	n-1
		
*same as DMG guidelines

[/sblock]

What do folks think? Useful? Interesting? Neither?

 

[Mengu]

I had noticed the oddity at low levels, but this is certainly and interesting analysis.

However, I took away from this that giving out slightly too much treasure to a 6 PC campaign is probably a good idea.

This is the most useful nugget for me, since it makes me feel better about giving a little more treasure than DMG suggestion for my 6 PC party. I typically tend to convert a lot of the monetary treasure into items, ritual scrolls, alchemy items, etc. that they might need as well, because I don't really have many places where they can shop around.

 

[pokken]

What you're missing is that actually picking and choosing 70% of your wealth vs. getting random or DM assigned stuff is very, very powerful.

I've found that the characters who choose their own stuff are much more powerful.

 

[Akaiku]

I was under the impression that the gm is supposed to give you more or less what you were looking for. If you are supposed to get x % of stuff that isn't cool, what is x?

 

[Christian]

Another thing to keep in mind is that organically leveled characters will have acquired low-level permanent items, many of which they will have sold or ritually converted to residuum at 1/5 value. If you give a starting 18th-level character full treasure value of what a character would acquire from 1st to 18th level, you should make him pick up at least a half-dozen 1st to 15th-level items.

 

[Nail]

Ooooo....shiny!

Thanks, evilbob.

 

[evilbob]

Wow, a rare Nail compliment! I must have done something right...

pokken: Yeah, I agree with Akaiku: you're pretty much "supposed" to be getting stuff you chose anyway, right? I know I make my PCs make wishlists and then make them think about it because loot distribution is the new mega-timesink in 4.0 prep work.

Hand-picking items -is- more powerful, though, I agree, because you're able to prioritize exactly what you want for the level you're at. For example, Iron Armbands of Power might not be something you find until level 7, but starting at level 5 you might value those enough to make sure you start with them.

Mengu: Yeah, that's one of the more useful bits for me, too. Glad my post is not a total waste!


Part of my original post that I actually deemed too boring to keep in there detailed how part of my reservation for including n+2 or higher items is the somewhat-implied idea that you're not supposed to be "better" off with higher level characters. Sure, normally you might have an n+4 or an n+3 item by level n, but to even the playing field (as it were), part of the penalty for having such free choice is that you cannot go above n+1 for item selection.

Part of this is undone if you allow gold to replace items 1:1 or switching around items for different levels with equal total value, but on the other hand it's darn tough to actually find n+1, n, and n-1 items that you really want. It might be much easier to find n+2, n-3, and n-3, for example (I have no idea if that's equivalent, I just made it up). In any case, having a cash allotment typically isn't too overpowered simply because of how fast item prices rise; every 5 levels, there's a x5 increase in the total price difference between item levels. At level 1 it's 160, at level 5 it's 800, at 10 it's 4000, etc.

All that to say: yes, you're probably "supposed" to have a few lower-level items and junk stuff as well, but frankly any amount of gold can be used to purchase low-level items easily, since every 5 levels items are 5x as expensive. For example, if you have gold equal to a level 6 item, you can purchase five level 1 items. This works all the way up. So unless you're particularly worried, this problem effectively sorts itself out.

 

[Black Knight Irios]

Thank you for the numbers!

I always had the impression that if you started at higher levels (let's say 10+) that your equip is worse than the equip of a char you played from lvl1 to the same lvl.

I just never did research how big that difference in wealth was.

And that you get at low levels a bit to much loot was kinda obvious, too.

Thank you once more for the numbers!

 

[Evilhalfling]

well obviously the n+1/n/n-1 formula does not work for 2nd level characters -
actually thanks for doing the math on what they should have....

For High level characters I dislike your proposed fix, because I have frequently made PCs for one shots and choosing appropriate items takes long enough with the current formula. I have occasionally run into really liking an item that is n-(1-3) but that precludes the scattering of lesser items important for the character's role or personality

Your Quick fix of adding a n-1 (over level 8) seems like the easiest compromise.
especially if I chose the most appropriate item of approximately n-1.

XP coming your way...

 

[evilbob]

Thanks! Regarding speed of item selection: another whole thread could be written about this, but I will say that the thing I thought might happen is starting to happen at least for our group: the more experience we have with certain items, the faster equipping characters goes, because the list of what is best/preferred is getting shorter. Iron Armbands of Power, Boots of the Fencing Master/Eagerness, Reckless/Bloodclaw/Radiant weapons - it hasn't taken long to find items that are simply superior for just about everyone, so once you find a few of your "staples," outfitting even a high level character goes quicker every time. At this point I could give you 4-6 items for a melee character in about 10 seconds, regardless of starting level.