NPC Wizard Corruption in DCC

Well, I won't be winning any awards for regularity in posting...

It occurred to me that there is no system in place for determining corruption for NPC wizards in DCC.  Judges running a hexcrawl with wandering monster checks could roll up an NPC wizard in any of several ways (master of a random castle, member of a bandit gang or pirate crew, etc), and whether that wizard has any lingering corruption from his dealings in magic depends largely on how creative (or lazy) the Judge is on the fly.  But that's just not good enough for me...if there are numbers to crunch, I have to crunch them.

So, it seems to me that the average number of XP gained in an encounter is 2, not simply because the possible outcomes range from 0-4, but also due the dangers involved.  A character who only ever deals with 0XP encounters won't gain any levels, but those who only ever deal with 4XP encounters (generally involving fatalities) are unlikely to live long enough to gain many. 

I further estimate that a wizard will cast about one spell per encounter.  Easy encounters might not need any spellcasting, and desperately dangerous ones might require more than one, but given that, in many cases, spell effects from one casting can carry over into multiple encounters, one spell per encounter doesn't sound too far off.  Summoned creatures can hang around for quite a while, charmed characters will stay charmed for at least a day with a spell check of 14+, etc.  Also, wizards can use magic items without gaining corruption (usually).

Given these estimates, a wizard who goes from level 1 to level 2 has had on average (50-10)/2=20 encounters and cast 20 spells, each with a 1 in 20 chance of a spell fumble.  There's a good chance that he'll get away without any corruption, and a vanishingly small chance that he'll end up with 20 corruptions.  Without going into all the mathematical details, this is a pretty standard binomial distribution, and working out the percentages isn't all that difficult.  Table I shows the range of possible spell fumbles experienced by wizards of different levels, expressed in percentile terms.

 Table I

#failures	Level 2	Level 3	Level 4	Level 5	Level 6	Level 7	Level 8	Level 9	Level 10	#failures
0	01-36	01-08	01							0
1	37-74	09-28	02-06	01						1
2	75-93	29-54	07-17	02-03						2
3	94-99	55-76	18-34	04-08	01					3
4	00	77-90	35-53	09-17	02-03					4
5		91-96	54-71	18-30	04-07	01				5
6		97-99	72-84	31-45	08-13	02				6
7		00	85-92	46-60	14-22	03-04				7
8			93-97	61-73	23-33	05-08	01			8
9			98-99	74-83	34-46	09-14	02			9
10			00	84-90	47-59	15-22	03-04			10
11				91-94	60-71	23-31	05-07	01		11
12				95-97	72-81	32-42	08-11	02		12
13				98-99	82-88	43-53	12-17	03		13
14				00	89-93	54-64	18-21	04-05		14
15					94-96	65-74	22-30	06-08	01	15
16					97-98	75-82	31-40	09-12	02	16
17					99	83-88	41-50	13-17	03	17
18					00	89-93	51-60	18-23	04-05	18
19						94-96	61-69	24-30	06-07	19
20						97-98	70-77	31-38	08-10	20
						99	78-83	39-47	11-14	21
						00	84-88	48-56	15-19	22
							89-92	57-64	20-25	23
							93-95	65-72	26-32	24
							96-97	73-79	33-40	25
							98	80-85	41-48	26
							99	86-90	49-56	27
							00	91-94	57-64	28
								95-96	65-72	29
								97	73-78	30
								98	79-84	31
								99	85-87	32
								00	88-90	33
									91-92	34
									93-94	35
									95-96	36
									97	37
									98	38
									99	39
									00	40

 At this point, you need to randomly determine which spell from the caster's spell list was being cast when the failure occurred.  Roll on that spell's table for a spellcheck of 1 to figure out whether that failure ended up with corruption, patron taint, a misfire, or all three.  (Misfires are so fleeting in effect that we're not generally concerned with them here.)  Don't forget the effects of Luck, not only on the chances of a misfire instead of corruption, but also burning a point of Luck to avoid a corruption effect.  As an option, the Judge can allow the NPC wizard a few points of additional Luck only for the purposes of avoiding corruption and patron taint; this should probably not be more than about half the wizard's level, or only the highest level wizards will ever be corrupted.  At any rate, the Judge must decide for the wizard whether to burn Luck to avoid this corruption before moving on to the next corruption roll.