Level Adjustment Reduction 2: Hit Dice

In my post on LA reduction, I mentioned the possibility of doing the same thing, but taking hit dice into account.

I still want the only determining factor in when you can reduce your LA to be the experience cost, and I still want experience cost to be based only on level adjustment. So the natural option is to figure out what the average hit dice are for any given LA.

One of the very nice things about HeroForge and its ilk is that they all contain lists of the relevant information. In particular, MonsterForge contains a list of, apparently, every 3.5e creature (HeroForge contains a list of all or most of the creatures that advance solely by class level, which is much less useful).

So let's analyze the creatures. First, I eliminate every creature with an LA of 0 or --. Now, because creatures with 1 or fewer HD replace their HD with a class level, we change HD of 1 or less to instead read 0. Now it's a simple matter of taking each tier of LA and averaging together the HD of all the monsters in that tier.

The results:
LA : HD
+1 : 1.375
+2 : 3.3
+3 : 4
+4 : 7.85
+5 : 7.79
+6 : 8.2
+7 : 8.19
+8 : 11.67
+9 : 13
+18 : 7
There are only two creatures with LA+9 (the Hezrou and the Sillit), only one with LA+18 (the Aurumach Rilmani), and nothing in between or greater.

Plugging those numbers in generates a chart along these lines:
+1 : 4,375
+2 : 10,300; 12,300
+3 : 15,000; 20,000; 22,000
+4 : 22,850; 30,850; 35,850; 37,850
+5 : 26,790; 37,790; 45,790; 50,790; 52,790
+6 : 31,200; 45,200; 56,200; 64,200; 69,200; 71,200
+7 : 35,190; 52,190; 66,190; 77,190; 85,190; 90,190; 92,190
+8 : 42,670; 62,670; 79,670; 93,670; 104,670; 112,670; 117,670; 119,670
+9 : 48,000; 71,000; 91,000; 108,000; 122,000; 133,000; 141,000; 146,000; 148,000
(To reduce the Aurumach Rilmani's LA by 1 costs 78,000; the 18th step costs 520,000. I will leave it out of further calculations, because it is preposterous.)

How messy!

We can clean it up a little if we take the all-powerful rule that you Always Round Down (and take into account that HD1 = HD0 when class levels are involved):
1 : 3,000
2 : 10,000; 12,000
3 : 15,000; 20,000; 22,000
4 : 22,000; 30,000; 35,000; 37,000
5 : 26,000; 37,000; 45,000; 50,000; 52,000
6 : 31,000; 45,000; 56,000; 64,000; 69,000; 71,000
7 : 35,000; 52,000; 66,000; 77,000; 85,000; 90,000; 92,000
8 : 42,000; 62,000; 79,000; 93,000; 104,000; 112,000; 117,000; 119,000
9 : 48,000; 71,000; 91,000; 108,000; 122,000; 133,000; 141,000; 146,000; 148,000

This is still problematic in that it is inelegant. It is derived from a statistical analysis of creatures, so there's no way to recreate it without the original data set. The UA rules are nice in that they can be described as algorithms to follow.

So let's come up with an algorithm.

Let's try comparing the average difference between LA and HD. Returning to the original dataset pulled from MonsterForge, it turns out that the average creature's HD is slightly more than 2 greater than its LA.

I was all set to complain that low-LA creatures are more likely to have HD lower than their LA and high-LA creatures are more likely to have HD much higher than their LA, but a closer analysis of the data finds the greatest concentration of substantial difference is actually in LA +4 and +5.

So that works out: let's assume all creatures have 2 more HD than they have LA. The numbers are now:
1 : 6,000
2 : 11,000; 13,000
3 : 16,000; 21,000; 23,000
4 : 21,000; 29,000; 34,000; 36,000
5 : 26,000; 37,000; 45,000; 50,000; 52,000
6 : 31,000; 45,000; 56,000; 64,000; 69,000; 71,000
7 : 36,000; 53,000; 67,000; 78,000; 86,000; 91,000; 93,000
8 : 41,000; 61,000; 78,000; 92,000; 103,000; 111,000; 116,000; 118,000
9 : 46,000; 69,000; 89,000; 106,000; 120,000; 131,000; 139,000; 144,000; 146,000

Any one of these charts can work. I'm inclined to go with either this last one or the very first one, from the previous post, as they are the two which are most conceptually elegant, representable algorithmically.