Spell failure chance analysis
=============================

This should be read in conjunction with
http://www.steelypips.org/nethack/343/spl1-343.html#fail which details the
spell failure calculation. This spoiler explains some of the practical
consequence of that calculation.

Armour penalties
================
Your chance of success before armour penalties (and the BASE penalty from
your class, etc) is capped at 120%. This means that if the BASE/armour
penalty is 7 or above, you can never get a 0% spell failure chance. This
means that some classes can never get a 0% spell failure chance without
a robe (and no body armour), with a minimum failure chance of:

12%: knights, rogues (and monks, but they start robed)
21%: rangers
30%: samurai, valkyries
48%: cavepeople
66%: barbarians

Additionally, only wizards can get 0% failure chances with a robe over
body armour, although healers and priests get close with 12%.

(None of this analysis applies to your class specialist spell, for which
you often get a bonus).

Experience level and spell difficulty
=====================================
The chart below lists the "difficulty" component of the NetHack spell
failure chance calculation, based on spell level, your experience level,
and your skill in the spell school.

If "difficulty" is positive, you take a substantial penalty to
spellcasting chances, impossible to overcome with other factors - even at
a 25 in your spellcasting stat you will have at least a 17% failure
chance, and at a more plausible 18 your failure chance is above 50%.

It matters much more whether it is positive or not than how positive it
is. Even at difficulty 1, there is a hefty penalty which then rises more
slowly with increased difficulty.

Negative values give a small bonus which can be used to overcome
penalties from armour and/or counteract a low spellcasting stat, but
the bonus is smaller and cannot overcome large armour penalties
completely no matter how large the negative value is.

There are many points where gaining a spell school skill level removes
positive difficulty issues, but more interesting are the points where
gaining an XL which is a multiple of 3 will suddenly drop spell failure
chance dramatically. Because of the way the calculation works, only XLs 9,
15, 21, and 27 show this effect.

Level 1 spells never have a positive difficulty.
Level 2 spells, when unskilled, get easier at level 9.
Level 3 spells, when unskilled, get easier at level 21.
Level 4 spells, at basic skill, get easier at level 15.
Level 5 spells, at basic skill, get easier at level 27.
            and when skilled,   get easier at level 9.
Level 6 spells, when skilled,   get easier at level 21.
Level 7 spells, when expert,    get easier at level 15.

Of these, the breakpoints at 15 and 21 are the most interesting. You were
probably going to get level 9 anyway, but you might not get level 21; and
if you just hit 14 and are considering the Quest, it's worth asking if
level 15 would improve your spellcasting capabilities.

Raw data:
    Spell:   1   2   3   4   5   6   7
XL 3:UNSK:  -2   2   6  10  14  18  22
    BASIC:  -8  -4   0   4   8  12  16
  SKILLED: -14 -10  -6  -2   2   6  10
   EXPERT: -20 -16 -12  -8  -4   0   4
XL 6:UNSK:  -3   1   5   9  13  17  21
    BASIC:  -9  -5  -1   3   7  11  15
  SKILLED: -15 -11  -7  -3   1   5   9
   EXPERT: -21 -17 -13  -9  -5  -1   3
XL 9:UNSK:  -4   0   4   8  12  16  20
    BASIC: -10  -6  -2   2   6  10  14
  SKILLED: -16 -12  -8  -4   0   4   8
   EXPERT: -22 -18 -14 -10  -6  -2   2
XL12:UNSK:  -5  -1   3   7  11  15  19
    BASIC: -11  -7  -3   1   5   9  13
  SKILLED: -17 -13  -9  -5  -1   3   7
   EXPERT: -23 -19 -15 -11  -7  -3   1
XL15:UNSK:  -6  -2   2   6  10  14  18
    BASIC: -12  -8  -4   0   4   8  12
  SKILLED: -18 -14 -10  -6  -2   2   6
   EXPERT: -24 -20 -16 -12  -8  -4   0
XL18:UNSK:  -7  -3   1   5   9  13  17
    BASIC: -13  -9  -5  -1   3   7  11
  SKILLED: -19 -15 -11  -7  -3   1   5
   EXPERT: -25 -21 -17 -13  -9  -5  -1
XL21:UNSK:  -8  -4   0   4   8  12  16
    BASIC: -14 -10  -6  -2   2   6  10
  SKILLED: -20 -16 -12  -8  -4   0   4
   EXPERT: -26 -22 -18 -14 -10  -6  -2
XL24:UNSK:  -9  -5  -1   3   7  11  15
    BASIC: -15 -11  -7  -3   1   5   9
  SKILLED: -21 -17 -13  -9  -5  -1   3
   EXPERT: -27 -23 -19 -15 -11  -7  -3
XL27:UNSK: -10  -6  -2   2   6  10  14
    BASIC: -16 -12  -8  -4   0   4   8
  SKILLED: -22 -18 -14 -10  -6  -2   2
   EXPERT: -28 -24 -20 -16 -12  -8  -4
XL30:UNSK: -11  -7  -3   1   5   9  13
    BASIC: -17 -13  -9  -5  -1   3   7
  SKILLED: -23 -19 -15 -11  -7  -3   1
   EXPERT: -29 -25 -21 -17 -13  -9  -5