The Spangleshard - A Statistical Analysis of Worth (2005)
by taladryel

At first glance, the Spangleshard seems like a veritable godsend. Amaze your friends! Dazzle your enemies! Shrug off cannon wounds as mere pinpricks! How could GW have possibly made the mistake of giving us such a supremely useful yet incredibly cheap magic item?

Which is where my jaded and cynical side decided to crunch some numbers (commentaries from certain members of the Ogre Stronghold having nothing to do with prompting said decision whatsoever…).

The Assumptions

A T5 character is hit with S3, S4, S5, S6 and S7 attacks (wounding on 6s, 5s, 4s, 3s and 2s, respectively).

The probability of rolling any one number (1-6) on a D6 while rolling to wound against said T5 character is always the same (16.7%). Similarly for Spangleshard rolls (chance of rolling any number from 1 to 6 while trying to 'negate' a successful wound roll is 16.7%).

The chances of causing a wound are:
S3 hit = 16.7% (1/6 chance of wounding)
S4 hit = 33.3% (2/6 chance of wounding)
S5 hit = 50.0% (3/6 chance of wounding)
S6 hit = 66.7% (4/6 chance of wounding)
S7+ hit = 83.3% (5/6 chance of wounding)

The Spangleshard will negate the wound roll if it is higher by 1 or more.

The Formula

Chance to Wound - (16.7% * Chance to roll 1 over + 16.7% * Chance to roll 2 over + 16.7% * Chance to roll 3 over + 16.7% * Chance to roll 4 over) = Adjusted Chance to Wound (ACTW).

In other words, there are two dice rolls made consecutively. The first determines your 'wound' score, and whether you wound successfully. The second negates the wound if you roll 1-4 'higher' than the first roll (it is impossible to roll 5 higher, since the lowest 'wounding' roll is a 2).

So in the case of a S5 hit, the calculation would be something like: Chance to Wound with S5 – Chance to Wound on a 5 and rolling 6 with the Spangleshard – Chance to Wound on a 4 and rolling a 5-6 with the Spangleshard = ACTW at S5. You can't wound on a 3, so the calculation stops there (otherwise it would continue).

The results of the calculation are:
ACTW (S3 hit) = 16.7% - 0.0% = 16.7% (obviously)
ACTW (S4 hit) = 33.3% - (16.7% * 16.7%) = 30.6%
ACTW (S5 hit) = 50.0% - (16.7% * 16.7%) – (16.7% * 33.3%) = 41.7%
ACTW (S6 hit) = 66.7% - (16.7% * 16.7%) – (16.7% * 33.3%) – (16.7% * 50.0%) = 50.0%
ACTW (S7+ hit) = 83.3% - (16.7% * 16.7%) – (16.7% * 33.3%) – (16.7% * 50.0%) – (16.7% * 66.7%) = 55.6%

Net Chance to Wound, adjusted by the Spangleshard 'roll':
S3 hit = 16.7%, shard reduction = 0.0 percentage points
S4 hit = 30.6%, shard reduction = 2.8 percentage points
S5 hit = 41.7%, shard reduction = 8.3 percentage points
S6 hit = 50.0%, shard reduction = 16.7 percentage points
S7+ hit = 55.6%, shard reduction = 27.8 percentage points

Conclusion

Even if you stand there and get pelted with cannon fire, the Spangleshard only drops your chances of avoiding a wound by max 27.8 percentage points. Moreover, most attacks you'll be facing are less than that which implies even less of a reduction.

At the same time, a 5+ Ward (Wyrdstone necklace) will always work 33.3% of the time and will categorically work against lower-strength hits. If you're not into having a wound put on your character 16.7% of your games (which, mind you, can be healed by Gut Maw), you can take the good old reliable Talisman of Protection (Common item, 6+ Ward) and get a solid 16.7% chance of avoiding a wound at all strength (so the Spangleshard will only outperform against hits with S7+).

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