My internet connection is still fraught. It will sometimes work for hours, and then not be available for days. Which makes this article fraught with potential problems. I’ll do my best – but it’s worth noting that less than an hour after last week’s post, the internet crashed and stayed down for about seven hours. If that had started just an hour earlier, the post could not have been published at all.

At something close to the last possible moment, I’ve decided to split this article into two, because if I didn’t, the second half would completely overshadow the first half.

“Uncoupling the Heisenberg Compensators” is some of my favorite technobabble from Star Trek: The Next Generation because both the character using it and the audience know that’s it’s technobabble created specifically to deceive the villain of the episode. Hence, it’s perfectly fine for it to mean absolutely nothing, in fact it doesn’t ever pretend to have any meaning whatsoever aside from that deception.

And yet, like all good technobabble, it readily hints at an implied significance while never stating anything provable outright. It sounds a little more scientific and technical and technological than “crossing the streams”, for example.

“Heisenberg”, of course, implies some relationship between the fictitious technology and the Heisenberg Uncertainty Principle, which places limits on how much we can know through direct observation. Since the technobabble supposedly relates to the teleportation technology of the show, and one of the Heisenberg limitations refers to the position of subatomic particles, this all seems to hold together.

In exactly the same way, linking the combat “plus” of a weapon to it’s magical bonus seems to make perfect sense, at least on its surface. But interesting consequences can result if you uncouple these two concepts, replacing the one-to-one identity relationship between them with a far looser, indirect, relationship.

The formal existing relationship

To the best of my knowledge, neither D&D nor Pathfinder ever state outright the equality; they simple assume it to be the case, and use the terms interchangeably if they even distinguish between them at all.

Once you become aware that the two things don’t have to possess such an equality, once you uncouple the two concepts, the game systems stop being hostages to this most fundamental of game mechanical assumptions.

What do I mean? Each magical +1 to arms or armor represents a step up an escalating power scale – either a geometric one or an exponential one, depending on who you ask. This numeric quantity is used to index the power level of the magical device, as well as being a direct input into the relevant game mechanics – armor class in the case of armor, attack bonus in the case of a weapon.

So ubiquitous is this approach that the same indexing is often used (unofficially) to describe relative magical power in entirely unrelated pieces of arcane hardware.

The assumed equality immediately saddles the game mechanics with three problems:
 

  1. The increase from +4 to +5 is the same as the increase from +1 to +2 – or from ‘plus-nothing’ to +1, for that matter. The more things you have to cram into that space, the smaller grows the capacity for nuance, for making this +4 item different to that one.
     
  2. The increase has to be reflected in a very steep progression in price and rarity, Quite often, this then has to be reflected in the capabilities of the object needed to justify that price- once again, restricting the capacity for differentiation from one object to the next.
     
  3. Consistency across several objects becomes a problem that is most easily solved with a cookie-cutter approach, again squeezing life and flavor out of the magical items emplaced. This makes the game mechanics simpler to learn and use, but further squeezes the life and individuality out of the objects.

 
None of this is good news. It certainly adds impetus to the concept of separating the concepts from each other.

This is more easily said than done; but after quite a long time with the question at the back of my mind, I think I’ve cracked the problem. That solution is the subject of today’s article.

Section 1: A sliding scale of magic

Look, if this discussion is going to make sense, I need to lay out some ground rules for nomenclature before I do anything else. So, for the rest of this article:

  • “+n” in italics will refer to the combat value of the magic item, the traditional interpretation.
  • “+n”, not in italics, will refer to the “magical plus” of the weapon, which in turn is used to determine value, construction cost and difficulty, relative power level, etc.

Okay, so the basic concept is that each +x provides and requires +x to the magic scale. Sounds simple enough, doesn’t it? But it’s a fundamental conceptual shift:

  • +0 = + base
  • +1 = + (+1) × x + base
  • +2 = + (+2 +1) × x + base = + (3 × x) + base
  • +3 = + (+3 +2 +1) × x + base = + (6 × x) + base
  • +4 = + (+4 +3 +2 +1) × x + base = + (10 × x) + base
  • +5 = + (+5 +4 +3 +2 +1) × x + base = + (15 × x) + base
  • +6 = + (+6 +5 +4 +3 +2 +1) × x + base = + (21 × x) + base
  • +7 = + (+7 +6 +5 +4 +3 +2 +1) × x + base = + (28 × x) + base
  • +8 = + (+8 +7 +6 +5 +4 +3 +2 +1) × x + base = + (36 × x) + base
  • +9 = + (+9 +8 +7 +6 +5 +4 +3 +2 +1) × x + base = + (45 × x) + base
  • +10 = + (+10 +9 +8 +7 +6 +5 +4 +3 +2 +1) × x + base = + (55 × x) + base

You’ll see why this is a useful reconstruction a little later on. Most people would also assume that “X” = 1 and “base” = 0, but it ain’t necessarily so. In fact, I recommend x=2 and base=3 for reasons that will become clear a little later.

Variation #1

Instead of +n contributing +n×x to the magic item, it contributes +(n+1)×x. Sounds like a small change, doesn’t it? But it accumulates to an amount of some significance.

  • +0 = + 1 × x + base
  • +1 = + (+1+1) × x + base = + (2 × x) + base
  • +2 = + (+2 +1 +2) × x + base = + (5 × x) + base
  • +3 = + (+3 +1 +5) × x + base = + (9 × x) + base
  • +4 = + (+4 +1 +9) × x + base = + (14 × x) + base
  • +5 = + (+5 +1 +14) × x + base = + (20 × x) + base
  • +6 = + (+6 +1 +20) × x + base = + (27 × x) + base
  • +7 = + (+7 +1 +27) × x + base = + (35 × x) + base
  • +8 = + (+8 +1 +35) × x + base = + (44 × x) + base
  • +9 = + (+9 +1 +44) × x + base = + (54 × x) + base
  • +10 = + (+10 +1 +54) × x + base = + (65 × x) + base

Once again, my recommendation is x=2 and base=3.

Variation #2

Instead of +n contributing +n×x or +(n+1)×x to the magic item, it contributes +(n+1)×x for the first two +n levels, then +(n+3)×x for the next two levels, then +(n+5)×x for the two after that, and so on.

  • +0 = + 1 × x + base
  • +1 = + (+1+1) × x + base = + (2 × x) + base
  • +2 = + (+2 +1 +2) × x + base = + (5 × x) + base
  • +3 = + (+3 +3 +5) × x + base = + (11 × x) + base
  • +4 = + (+4 +3 +11) × x + base = + (18 × x) + base
  • +5 = + (+5 +5 +18) × x + base = + (28 × x) + base
  • +6 = + (+6 +5 +28) × x + base = + (39 × x) + base
  • +7 = + (+7 +7 +39) × x + base = + (53 × x) + base
  • +8 = + (+8 +7 +53) × x + base = + (68 × x) + base
  • +9 = + (+9 +9 +68) × x + base = + (86 × x) + base
  • +10 = + (+10 +9 +86) × x + base = + (105 × x) + base

Clearly, this breaks the gap between +(#) and +(#+1) into smaller, more numerous pieces. But by varying the rate of increase, it also increases power levels within a magic item in a non-linear fashion.

My recommendations for x and base remain unchanged.

As you can see, these widen the gap – the number of magical pluses – between combat-plusses from one to many steps, with the separation from one combat plus to the next widening as the combat effectiveness, or its equivalent valuation, rises. It takes more to go from a +4 to a +5 than it does to go from +3 to +4.

The rest of this article will assume that the primary option has been chosen, with the recommended values, i. e.

  • +0 = + 3
  • +1 = + (+1) × 2 + 3 = + 5
  • +2 = + (+2 +1) × 2 + 3 = + (3 × 2) + 3 = + 9
  • +3 = + (+3 +2 +1) × 2 + 3 = + (6 × 2) + 3 = + 15
  • +4 = + (+4 +3 +2 +1) × 2 + 3 = + (10 × 2) + 3 = + 23
  • +5 = + (+5 +4 +3 +2 +1) × 2 + 3 = + (15 × 2) + 3 = + 33
  • +6 = + (+6 +5 +4 +3 +2 +1) × 2 + 3 = + (21 × 2) + 3 = + 45
  • +7 = + (+7 +6 +5 +4 +3 +2 +1) × 2 + 3 = + (28 × 2) + 3 = + 59
  • +8 = + (+8 +7 +6 +5 +4 +3 +2 +1) × 2 + 3 = + (36 × 2) + 3 = + 75
  • +9 = + (+9 +8 +7 +6 +5 +4 +3 +2 +1) × 2 + 3 = + (45 × 2) + 3 = + 93
  • +10 = + (+10 +9 +8 +7 +6 +5 +4 +3 +2 +1) × 2 + 3 = + (55 × 2) + 3 = + 113

…but I will still try to mention the consequences of choosing differently as I go along (I may stop once I think I have the point across, though)

Section 2: Fixed Price increases

If you have a wider and increasing gap between combat plusses due to an increase in the number of intervals between one and the next, and a price that increases geometrically according to the number of magical plusses and not combat plusses, you need a much smaller increase to achieve a significant but predictable growth in value / cost.

As things stand, a fairly aggressive exponential increase is needed to reflect the rarity and increasing (and compounding) value of combat plus, so all +2 weapons look and cost the same (relative to the base price of the weapon).

The value that I am recommending for each magical plus as an increase might seem like a complicated one: × cube-root 2 or × 1.259921 but it’s one that I think will generate reasonable values. But there is lots of room for variations, so you can pick one that feels right to you.

Let’s translate the results:

  • +0 = base × 1.259921^3 = × 2
  • +1 = base × 1.259921^5 = × 3.17
  • +2 = base × 1.259921^9 = × 8
  • +3 = base × 1.259921^15 = × 32
  • +4 = base × 1.259921^23 = × 203.19
  • +5 = base × 1.259921^33 = × 2048
  • +6 = base × 1.259921^45 = × 32 767.94
  • +7 = base × 1.259921^59 = × 832 253.38
  • +8 = base × 1.259921^75 = × 33 554 332.34
  • +9 = base × 1.259921^93 = × 2 147 475 739
  • +10 = base × 1.259921^113 = × 21 817 169 763 015.48

This scale of increase works for Pathfinder, where items can have up to +10 – though it does go a little off the chart at the end (but that’s because this is misstating the principle. Each level is actually defining the maximum of a range:

  • +0 = base × 1.259921^3 = × 0 – 2
  • +1 = base × 1.259921^5 = × 2 – 3.17
  • +2 = base × 1.259921^9 = × 3.17 – 8
  • +3 = base × 1.259921^15 = × 8 – 32
  • +4 = base × 1.259921^23 = × 32 – 203.19
  • +5 = base × 1.259921^33 = × 203.19 – 2048
  • +6 = base × 1.259921^45 = × 2048 – 32 767.94
  • +7 = base × 1.259921^59 = × 32 767.94 – 832 253.38
  • +8 = base × 1.259921^75 = × 832 253.39 – 33 554 332.34
  • +9 = base × 1.259921^93 = × 33 554 332.34 – 2 147 475 739
  • +10 = base × 1.259921^113 = × 2 147 475 739 – 21 817 169 763 015.48

…).

For D&D, where items very rarely go above +5, you might want to use a larger value. Or a choice with more steps – one of the alternatives offered in section 1. The trick is always balancing the size of increases at the lower end of the scale with those at the higher end.

Variation #1: × 4th root of 10

The square root of 10 is 3.1622777, and the square root of that is 1.778279.

  • +0 = base × 1.778279^3 = × 5.62
  • +1 = base × 1.778279^5 = × 17.78
  • +2 = base × 1.778279^9 = × 177.83
  • +3 = base × 1.778279^15 = × 5623.39
  • +4 = base × 1.778279^23 = × 562 338.34
  • +5 = base × 1.778279^33 = × 177 826 588
  • +6 = base × 1.778279^45 = × 1.7783 × 10^11
  • +7 = base × 1.778279^59 = × 5.623 × 10^14
  • +8 = base × 1.778279^75 = × 5.623 × 10^18
  • +9 = base × 1.778279^93 = × 1.778 × 10^23
  • +10 = base × 1.778279^113 = × 1.778 × 10^28

The utter ridiculousness of the results at +6 and above make this more suited to D&D.

Variation #2: × root 5

A simple alternative is to use the square root of 5, or 2.236068. Note that this will produce an even steeper growth curve.

  • +0 = base × 2.236068^3 = × 11.18
  • +1 = base × 2.236068^5 = × 55.9
  • +2 = base × 2.236068^9 = × 1397.54
  • +3 = base × 2.236068^15 = × 174 692.84
  • +4 = base × 2.236068^23 = × 109 183 032
  • +5 = base × 2.236068^33 = × 3.412 & times; 10^11
  • +6 = base × 2.236068^45 = × 5.33 × 10^15
  • +7 = base × 2.236068^59 = × 4.17 × 10^20
  • +8 = base × 2.236068^75 = × 1.63 × 10^26
  • +9 = base × 2.236068^93 = × 3.18 × 10^32
  • +10 = base × 2.236068^113 = × 3.10 × 10^39
Variation #3: × ½ of root 10

This variation has a steeper curve still, but ameliorates that with lower values at lower levels thanks to the “½ of”. Root 10 = 3.1622777, and half of that is 1.58113885. The result is something that is somewhere in between the base version and the first variation.

  • +0 = base × 1.58113885^3 = × 3.95
  • +1 = base × 1.58113885^5 = × 9.88
  • +2 = base × 1.58113885^9 = × 61.76
  • +3 = base × 1.58113885^15 = × 965.05
  • +4 = base × 1.58113885^23 = × 37 697.3
  • +5 = base × 1.58113885^33 = × 3.681 & times; 10^7
  • +6 = base × 1.58113885^45 = × 8.989 × 10^8
  • +7 = base × 1.58113885^59 = × 5.4857 × 10^11
  • +8 = base × 1.58113885^75 = × 8.3705 × 10^14
  • +9 = base × 1.58113885^93 = × 3.19 × 10^18
  • +10 = base × 1.58113885^113 = × 3.05 × 10^22

This would probably be my preferred choice for D&D, with some slight tweaking / rounding:

  • +0 = base × 4
  • +1 = base × 10
  • +2 = base × 60
  • +3 = base × 1000
  • +4 = base × 40 000
  • +5 = base × 4 & times; 10^7
Variation #4: × 1.25, 1.5, or 2

Some GMs and players might prefer a simpler solution – none of this “square root” malarkey wanted!

At 1.25:

  • +0 = base × 1.25^3 = × 1.95
  • +1 = base × 1.25^5 = × 3.05
  • +2 = base × 1.25^9 = × 7.45
  • +3 = base × 1.25^15 = × 28.42
  • +4 = base × 1.25^23 = × 169.41
  • +5 = base × 1.25^33 = × 1577.72
  • +6 = base × 1.25^45 = × 22 958.87
  • +7 = base × 1.25^59 = × 5.22 × 10^5
  • +8 = base × 1.25^75 = × 1.85 × 10^7
  • +9 = base × 1.25^93 = × 1.03 × 10^9
  • +10 = base × 1.25^113 = × 8.93 × 10^10

At 1.5:

  • +0 = base × 1.5^3 = × 3.38
  • +1 = base × 1.5^5 = × 7.59
  • +2 = base × 1.5^9 = × 38.44
  • +3 = base × 1.5^15 = × 437.89
  • +4 = base × 1.5^23 = × 11 222.74
  • +5 = base × 1.5^33 = × 647 159.82
  • +6 = base × 1.5^45 = × 8.4 × 10^7
  • +7 = base × 1.5^59 = × 2.45 × 10^10
  • +8 = base × 1.5^75 = × 1.61 × 10^13
  • +9 = base × 1.5^93 = × 2.38 × 10^16
  • +10 = base × 1.5^113 = × 7.91 × 10^19

(Once again, this gives reasonable numbers for +0 to +5, not so much for what happens after that).

At 2:

  • +0 = base × 2^3 = × 8
  • +1 = base × 2^5 = × 32
  • +2 = base × 2^9 = × 512
  • +3 = base × 2^15 = × 32 768
  • +4 = base × 2^23 = × 8.39 × 10^6
  • +5 = base × 2^33 = × 8.59 & times; 10^9
  • +6 = base × 2^45 = × 3.52 × 10^13
  • +7 = base × 2^59 = × 5.76 × 10^17
  • +8 = base × 2^75 = × 3.78 × 10^22
  • +9 = base × 2^93 = × 9.9 × 10^27
  • +10 = base × 2^113 = × 1.04 × 10^34

This looks reasonable up to +3 but then gets a bit extreme for my tastes.

Variation #5: A progressive sliding scale

Under this proposal, the exponential increase in value is partially compensated for by reducing the increase that applies as magical plus increases. 2.26, 2.06, 1.86, 1.66, 1.46, 1.26, 1.06, 1.04, 1.02, 1.018, 1.016, 1.014, 1.012… I trust you can see the pattern. But this is intended to be a progressive scale – the new multiplier only applies to exponential increases not already factored in at the previous plus.

  • +0 = base × 2.26^3 = × 11.54
  • +1 = base × 11.54 × 2.06^(5-2) = 11.54 × 2.06^3 = 11.54 × 4.24 = 48.98
  • +2 = base × 48.98 × 1.86^(9-5) = 48.98 × 1.86^4 = 48.98 × 11.97 = × 586.29
  • +3 = base × 586.29 × 1.66^(15-9) = 586.29 × 1.66^6 = 586.29 × 20.92 = & times; 12 265.2
  • +4 = base × 12 265.2 × 1.46^(23-15) = 12 265.2 × 1.46^6 = 12 265.2 × 20.65 = × 253 276
  • +5 = base × 253 276 × 1.26^(33-23) = 253 276 × 1.26^8 = 253 276 × 10.09 = × 2 560 000
  • +6 = base × 2.56 × 10^6 × 1.06^(45-33) = 2.56 × 10^6 × 1.06^10 = 2.56 × 10^6 × 2.01 = × 5.14 × 10^6
  • +7 = base × 5.14 × 10^6 × 1.04^(59-45) = 5.14 × 10^6 × 1.04^14 = 5.14 × 10^6 × 1.73 = × 8.9 & times 10^6
  • +8 = base × 8.9 × 10^6 × 1.02^(75-59) = 8.9 × 10^6 × 1.02^16 = 8.9 × 10^6 × 1.38 = × 1.23 × 10^7
  • +9 = base × 1.23 × 10^7 × 1.018^(93-75) = 1.23 × 10^7 × 1.018^18 = 1.23 × 10^7 × 1.38 = 1.7 × 10^7
  • +10 = base × 1.7 × 10^7 × 1.1.016^(113-93) = 1.7 × 10^7 × 1.1016^20 = 1.7 × 10^7 × 1.37 = 2.33 × 10^7

The above uses a fairly even drop in the multiplier until a change of order of magnitude and a similar pattern throughout. Starting at the +6 level, though, the increase from one plus to the next starts to get a little small, so perhaps a different pattern should then take hold. Remember, consistency of maths might be nice, but we want results that feel pretty right. This is intended to be proof of concept and demonstration / explanation of technique, not definitive decision.

Perhaps, then, the pattern should be 2.26, 2.06, 1.86, 1.66, 1.46, 1.26, 1.16, 1.11, 1.085, 1.075, 1.065, 1.055, 1.045…

At first, this won’t differ from what we’ve already got, but at higher plus values, it should make a profound difference.

  • +0 = base × 2.26^3 = × 11.54
  • +1 = base × 11.54 × 2.06^(5-2) = 11.54 × 2.06^3 = 11.54 × 4.24 = 48.98
  • +2 = base × 48.98 × 1.86^(9-5) = 48.98 × 1.86^4 = 48.98 × 11.97 = × 586.29
  • +3 = base × 586.29 × 1.66^(15-9) = 586.29 × 1.66^6 = 586.29 × 20.92 = & times; 12 265.2
  • +4 = base × 12 265.2 × 1.46^(23-15) = 12 265.2 × 1.46^6 = 12 265.2 × 20.65 = × 253 276
  • +5 = base × 253 276 × 1.26^(33-23) = 253 276 × 1.26^8 = 253 276 × 10.09 = × 2 560 000
  • +6 = base × 2.56 × 10^6 × 1.16^(45-33) = 2.56 × 10^6 × 1.16^10 = 2.56 × 10^6 × 5.94 = × 1.52 × 10^7
  • +7 = base × 1.52 × 10^7 × 1.11^(59-45) = 1.52 × 10^7 × 1.11^14 = 1.52 × 10^7 × 4.31 = × 6.55 &times 10^7
  • +8 = base × 6.55 × 10^7 × 1.085^(75-59) = 6.55 × 10^7 × 1.085^16 = 6.55 × 10^7 × 3.69 = × 2.42 × 10^8
  • +9 = base × 2.42 × 10^8 × 1.075^(93-75) = 2.42 × 10^8 × 1.075^18 = 2.42 × 10^8 × 3.68 = 8.9 × 10^8
  • +10 = base × 8.9 × 10^8 × 1.1.065^(113-93) = 8.9 × 10^8 × 1.1065^20 = 8.9 × 10^8 × 3.52 = 3.13 × 10^9

Another alternative would be to specify a “floor value” below which the base of the exponent cannot drop, i.e. a minimum result on the series. Below, I demonstrate the effect that it has if the +6 value is the minimum result:

  • +0 = base × 2.26^3 = × 11.54
  • +1 = base × 11.54 × 2.06^(5-2) = 11.54 × 2.06^3 = 11.54 × 4.24 = 48.98
  • +2 = base × 48.98 × 1.86^(9-5) = 48.98 × 1.86^4 = 48.98 × 11.97 = × 586.29
  • +3 = base × 586.29 × 1.66^(15-9) = 586.29 × 1.66^6 = 586.29 × 20.92 = & times; 12 265.2
  • +4 = base × 12 265.2 × 1.46^(23-15) = 12 265.2 × 1.46^6 = 12 265.2 × 20.65 = × 253 276
  • +5 = base × 253 276 × 1.26^(33-23) = 253 276 × 1.26^8 = 253 276 × 10.09 = × 2 560 000
  • +6 = base × 2.56 × 10^6 × 1.16^(45-33) = 2.56 × 10^6 × 1.16^10 = 2.56 × 10^6 × 5.94 = × 1.52 × 10^7
  • +7 = base × 1.52 × 10^7 × 1.16^(59-45) = 1.52 × 10^7 × 1.16^14 = 1.52 × 10^7 × 7.99 = × 1.215 &times 10^8
  • +8 = base × 1.215 × 10^8 × 1.16^(75-59) = 1.215 × 10^8 × 1.16^16 = 1.215 × 10^8 × 10.75 = × 1.3 × 10^9
  • +9 = base × 1.3 × 10^9 × 1.16^(93-75) = 1.3 × 10^9 × 1.16^18 = 1.3 × 10^9 × 14.46 = 1.88 × 10^10
  • +10 = base × 1.88 × 10^10 × 1.16^(113-93) = 1.88 × 10^10 × 1.16^20 = 1.88 × 10^10 × 19.46 = 3.66 × 10^11

As you can see, once the threshold is increased, the multiplier for each plus starts to increase again, but because the base of the exponent is very close to 1, this happens relatively slowly.

There are innumerable other patterns. Rather than the fixed minimum, you might decide that slowly increasing the multiplier was appropriate for values of +7 or more. I’ll forego offering yet another example as I have to move on.

Ultimately, what all of these variations are doing is altering the interpreted significance of each of the increases in magical plus. That’s an important concept (hence my taking so much time and trouble to demonstrate it) – because, if you can control the number of steps in the interval (Section 1) AND the significance of each step, however symbolically (Section 2) then you have almost total control over what a given plus actually means.

A radical but simple example combining everything discussed so far

Each plus up to +6 adds 5 to the plus of the item except the first two, which add 6; above +6, each adds 4. A +0 magical object has a base value of 8 (again, you will understand why in a little while). Magical pluses increase in value progressively using the following series: 1.24, 1.8, 1.65, 1.5, 1.4, 1.55, 1.7, 1.95, 2, 2.1, 2.2, 2.3, 2.4…

Number of steps per plus:
  • +0 = + 8
  • +1 = + 6 + 8 = + 14
  • +2 = + 6 + 14 = + 20
  • +3 = + 5 + 20 = + 25
  • +4 = + 5 + 25 = + 30
  • +5 = + 5 + 30 = + 35
  • +6 = + 5 + 35 = + 40
  • +7 = + 4 + 40 = + 44
  • +8 = + 4 + 44 = + 48
  • +9 = + 4 + 48 = + 52
  • +10 = + 4 + 52 = +56

This simulates a situation in which it grows progressively harder to increase the plus of an object or weapon. If the sequence were permitted to continue, it would probably be +3, +3, +3, +3, +2, +2, +2, +2, +1, +1, +1, +1 for an absolute maximum of +22 – but I very deliberately not going there.

Valuation per plus:
  • +0 = base × 1.24^8 = × 5.59
  • +1 = base × 5.59 × 1.8^(14-8) = 5.59 × 1.8^6 = 5.59 × 34.01 = 190.11
  • +2 = base × 190.11 × 1.65^(20-14) = 190.11 × 1.65^6 = 190.11 × 20.18 = × 3836.3
  • +3 = base × 3836.3 × 1.5^(25-20) = 3836.3 × 1.5^5 = 3836.3 × 7.59 = & times; 29 131.88
  • +4 = base × 29 131.88 × 1.4^(30-25) = 29 131.88 × 1.4^5 = 29 131.88 × 5.38 = × 156 678
  • +5 = base × 156 678 × 1.55^(35-30) = 156 678 × 1.55^5 = 156 678 × 8.95 = × 1.402 × 10^6
  • +6 = base × 1.402 × 10^6 × 1.7^(40-35) = 1.402 × 10^6 × 1.7^5 = 1.402 × 10^6 × 14.2 = × 1.99 × 10^7
  • +7 = base × 1.99 × 10^7 × 10^7 × 1.95^(44-40) = 1.99 × 10^7 × 1.95^4 = 1.99 × 10^7 × 14.46 = × 2.88 &times 10^8
  • +8 = base × 2.88 &times 10^8 × 2^(48-44) = 2.88 &times 10^8 × 2^4 = 2.88 &times 10^8 × 16 = × 4.6 × 10^9
  • +9 = base × 4.6 × 10^9 × 2.1^(52-48) = 4.6 × 10^9 × 2.1^4 = 4.6 × 10^9 × 19.45 = 8.95 × 10^10
  • +10 = base × 8.95 × 10^10 × 2.2^(56-52) = 8.95 × 10^10 × 2.2^4 = 8.95 × 10^10 × 23.43 = 2.1 × 10^12

Section 3: Effect Rating

So, if the plus of an enchanted object is no longer connected directly to the plus of that object, what is it connected to? What justifies a value multiplier of (taking the base example from section 2) × 2048 for a +5 item?

The answer is that the magical plus of a +5 object (defined in section 1 in the designated example as a +33 Magical effect, which consists of that designated magical plus (applied to both attack and damage values, in the case of a weapon), plus everything else that the object can do.

That is to say, Effect Rating = Power Rating + Utility + Thresholds + Activations + Links to previous effects, all in combination, for each additional power in the item.

But first, a little housekeeping:

It’s always struck me as a little odd (not to say inequitable) for an armor’s plus-rating to only affect Armor Class while a weapon’s plus-rating adds to both attack (“to-hit” if you’re old-school) AND damage. Especially since enchanted armor tends to cost a great deal more than a weapon.

There are several ways of addressing this inequality.
 

  • You could rule that an armor’s plus-rating also added to saving throws. That was one of my earliest solutions to the dilemma.
     
  • If you thought that was being a little too generous, you could restrict the benefit to one chosen and appropriate save type – Reflex Saves for armors of speed or lightness, FORT saves for armors of special resilience, and so on.
     
  • You could rule that an armor’s plus-rating also added to the wearer’s hit points.
     
  • If you thought that was a little to generous, you could restrict that benefit to those character levels at which a character gained a Feat (3.x & Pathfinder), or equivalent. Thus fighters might get the benefit every 2nd level, while Mages might get the benefit every 5th. Or anything you like in between.
     
  • Or, you could attack the inequity from the other side, by decoupling the attack bonus from the weapon damage bonus. A “+3 +1” weapon would have a total plusrating of 4, consisting of +3 to attack and +1 to damage. Of course, this means that a traditional weapon would suddenly have double the magical plus-rating that you thought it had, but that’s a small price to pay.

 
The solution that you choose to use is up to you. You can even employ multiple variations on the theme at the same time, so long as the equity balance is restored.

I would have no problem with a +7 rated suit of armor that gave +3to AC, +2 to Hit Points., and +2 to Reflex Saves – in a game where damage bonus and attack bonus were decoupled.

Okay, so where was I? Oh, yes: So for each additional ability conferred by or contained within an object, the Magical plus ‘consumed’ by that ability consists of the total of Power Rating + Utility + Thresholds + Activations + Links to previous effects.

It should now be clear why the various proposals in Section 1 offered a potential magical plus-rating for an object with a plus-rating of zero – it’s so that everyday objects without the equivalent of a plus-rating could still be enchanted to carry a permanent magical effect.

The higher the “base” rating in section 1, the stronger the magical effect that can be added to an object without incurring the equivalent of a plus-rating, and the more that an enchanted object – ANY enchanted object – is worth, as shown in Section 2.

The reason for doing all this is about to become clear, but it’s worth spelling it out explicitly: in a word, Flexibility. Not all +4 maces need to be exactly the same, and a +4 mace can be completely different to a +4 longsword. In fact, almost unlimited flexibility in design is achieved by the act of the Decoupling.

So, let’s put some meat on the bones – five types of Magical plus were listed; let’s define and discuss them.

Section 3a: Power Rating

Most power ratings are simple – it’s either spell level or spell-level equivalent, or it’s plus-rating.

There will be exceptions (there are always exceptions). But this should provide ample standards to permit the evaluation of any ability, especially if Metamagics are taken into account (speaking of which, there are some original metamagics that greatly enhance the flexibility of spells on offer in Broadening Magical Horizons: Some Feats from Fumanor and Shards Of Divinity. Using them and the standard Metamagics, you can customize any given spell to any effective Power Rating that is desirable).

The Power Rating of a plus enhancement is the value of the plus enhancement. Damage and Attack bonuses may count as separate plus values. However, such plus is considered an innate part of the item and as such is ‘always on’ for free.

If there is, nevertheless, some activation (see Section 3c below), subtract the cost of Always On (of the relevant sub-type) from the cost of that activation to get the adjustment to the resulting Effect Rating for the plus enhancement.

    For example, if the ‘always on’ type is the bog-standard version that most of us think of immediately, that is a +5 value that is ‘built in’ to a magical Plus. If there is, nevertheless, an activation of value +3 let’s say, the Power Rating of the plus WITH the activation is plus +3 -5. So a +4 item of this type would have a Power Rating of 2.

Section 3b: Utility

This encompasses two disparate factors, each of which needs to be considered separately.

Enhancement of something that a character can be expected to be capable of anyway confers a -1 modifier to Effect Rating (but Effect Ratings can never be less than 1). The alternative is to confer on a character an ability that they can not be reasonably expected to be capable of (even if some individuals can possess that capability); this increases the Effect Rating of an ability by 1.

Secondly, there is a Contextual Appraisal. In any given game world, some abilities will be more generally useful than others; those abilities should attract a +1 Effect Rating which should provide some form of enhancement benefit to the ability. Other abilities may be less generally useful than others, and come with a -1 Effect Rating. For example, in a world in which Undead are a major factor, abilities to Turn or enhance the Turning of Undead are obviously going to be more valuable. In a swamp world, or simply a swampy environment, fire magic can either be more useful or less (depending on whether or not conditions hamper the effectiveness of such magic), and so on.

Section 3c: Thresholds

Requiring a minimum score in some numeric capability in order to use an ability or effect is called establishing a Threshold.
 

  • If the Threshold is easy for the likely users of a magic item to achieve, that is worth a +2 Effect Level.
     
  • If the Threshold is reasonably commonly achievable, perhaps at higher levels, that is worth a +1 Effect Level.
     
  • If the Threshold is only achievable for characters of higher levels, that is worth a +0 Effect Level.
     
  • If the Threshold is very difficult for characters to achieve, even at higher levels, that is worth a -1 Effect Level (but there is still a net minimum Effect Level of 1).
     
  • Finally, if the Threshold is likely to only be achievable through the use of additional magic, either spells, potions, or magic items, that is worth either -2, -1, or +0 Effect Level;
     

    • -2 if the magic is likely to be very hard to obtain (even if a specific character already has it, because that’s something that you can’t assume to be universally true);
       
    • -1 if the magic is going to be uncommon but not unusually rare to obtain, caveat as above;.
       
    • +0 otherwise.
Section 3d: Activations

If you have to do something to activate or trigger the magic, the difficulty / inconvenience of doing so under normal conditions also impacts on the Effect Level. This consideration excludes any Threshold requirement (you only get one bite at the cherry).
 

  • ‘Always On’ effects are a +5 Effect Value, which increases to +6 Effect Value if the character doesn’t have to be in physical possession of the object in order to gain the benefit of the effect – if it can be on a nearby shelf, for example. If the object can be even more remote from the wielder, that may be worth a +7 or even a +8 Effect Value.
     
  • If the power / effect is activated “At Will”, that is worth a +4 Effect Value, which increases to +5 if the object only needs to be in close proximity, to +6 if the object only needs to be within earshot, or to +7 if the object only needs to be visible to the wielder. Some GMs may permit the latter to be activatable through Scrying, others will not, and some will regard that as worth an extra +1 to the Effect Value.
     
  • If the power / effect is activated by a command phrase or word, that is worth a +3 Effect Value, which increases to +3 if the object doesn’t have to be within earshot (but still has to be commanded by a specific voice), and to +4 if anyone using the right word/phrase can activate the power/effect.
  • If the power / effect requires a specific Skill roll to activate, the plus to the effect value is dependent on how difficult the challenge target is to achieve:
     

    • If the target is very difficult to achieve, the Effect Value of the Activation is +1.
       
    • If the target is moderately difficult, the Effect Value of the Activation is +2.
       
    • If the target is reasonably easy, the Effect Value of the Activation is +3.
       
    • If the target is very easy to achieve, the Effect Value of the Activation is +4.
       
  • In addition, if the skill is relatively rare or unusual, the GM may add -1 to the Effect Value of a skill-based activation, whereas if it fairly ubiquitous, the GM may add +1 to the Effect Value.
     
  • Finally, if the ability is automatically triggered by some other circumstance, but the owner has to be within a reasonable range, that is worth an effective +2 Effect Level. If the owner does not need to be present, that is worth +3 Effect Level. If the owner can specify what the triggering condition is and provide some appropriate sensory capability, that is worth +4 Effect Level; if the object comes with any required sensory capability already included, that is worth +5 Effect Level.

In general, the more easily the power can be activated, the higher the Effect Level that it reflects. Note that the activation “cost” may require the creator of a magic item to restrict its Power Rating or otherwise compromise it in order to compensate for a high Activation contribution.

Another way to look at it: the more powerful a magical effect is, the more it needs to be restricted in it’s Activation in order to be accommodated in a magic item of relatively affordable magical plus or equivalent.

Section 3e: Multi-effects

If an effect is already present in an item that is of a similar nature to an ability or effect, the second ability or effect is reduced in Effect Level by 1.

Multiple such are often ‘bundled together’, in sequence from least expensive to most expensive (in terms of Effect Level, disregarding such discounting).

However, these bonuses grow progressively harder to qualify for.
 

  • One related ability is enough for a 1 discount.
     
  • Three (=1+2) are needed to qualify for a 2 discount. Note that the second and third will still qualify for a 1 discount.
     
  • Six (=1+2+3) are needed to qualify for a 3-discount on the seventh and subsequent related abilities. Some of those six will qualify for a 1 discount, some for a 2 discount.
     
  • Ten (=1+2+3+4) are needed to qualify for a discount of 4, and so on.
     

The inclusion of unrelated effects or abilities has the opposite effect.
 

  • One unrelated ability earns a +1 cost to all abilities, including this one..
     
  • Three (=1+2) unrelated abilities earn a +2 cost to all abilities.
     
  • Six (=1+2+3) increase the cost of all abilities by +3 each.
     
  • Ten (=1+2+3+4) increase the cost of each ability by +4, and so on.
     

    An example might be needed to make this clear.

    Let’s say that a magic item has 4 fire-related abilities / powers and one that is not considered by the GM to be directly fire-related.
     

    • The cheapest fire-related ability costs it’s normal Effect Level, +1 for the unrelated ability.
    • The second-cheapest fire-related ability costs it’s normal Effect Level -1 for the related ability, +1 for the unrelated ability.
    • The third-cheapest fire-related ability costs it’s normal Effect Level -1 for the first related ability, +1 for the unrelated ability.
    • The most expensive fire-related ability costs it’s normal Effect Level -2 for the three related abilities, +1 for the unrelated ability.
Section 3f: Activation / Triggers for multiple effects

If the same trigger activates more than one ability, it costs +1 for each additional ability that it activates, but needs only to be paid for once. This further encourages the consistent theming of magical devices.

If the trigger is to be separate, even if of the same kind (two different command words, for example), both have to be paid separately.

Flexibility eats into power level, consistency does not.

Section 4: Unused Capacity

There are two actions that an owner may wish to perform with a magic item that they possess, and both require at least one magical plus of unused capacity. These are “Refining an object” and “Enchanting an object”.

Magical items without any unused capacity are considered fixed (sometimes labeled ‘locked’); they cannot be Refined or further Enchanted.

Refining an object

Refining an object increases it’s unused capacity. It does so by leeching the capacity of an equal or lesser object. Like pulling on a thread, this causes the object being leeched to ‘unravel’; it becomes a worthless lump of waste material. But it’s magical plusses are added to the capacity of the object being refined (less any unused capacity it may already have).

I’ll have a lot more to say about this in part two of this article.

For now, let’s start by defining some additional nomenclature – in particular, some symbiology to describe this process:

    +a +b +(a+b)

would serve to represent it, where

    +a defines the object being leeched;
    +b defines the object being refined;
    describes the process;
    (approximately equals) connects the process to the outcome; and
    +(a+b) describes the approximate outcome of the process.

So let’s look at a couple of examples:

    +5 +5 +(10)

    +5 +10 +(15)

    +8 +12 +(20)

    +13 +19 +(32)

…and so on.

But, given the approximation, this is not very helpful. So, having established the concept, let’s refine it:

    +a+Δb +b = +(a+b)

or even,

    +a +b = +(a+b-Δb)

This is exactly the same as what we had before, except that we’ve added a new symbol, Δb, to describe the unused capacity of object b.

Δb therefore HAS to be at least one, by definition, but it could be more, because what is actually increasing by (a – Δb) is Δb.

Again, an example or two should make this clearer.

    +5 +5 [Δb=1] = +(5+5-1=9), Δb = 1+5-1 = 5.

A +5 object is leeched to enhance another +5 object which has an unused capacity of 1. The resulting object has a total capacity of 9, of which 5 are unused.

Let’s say we then use a +8 object to further refine this one:

    +8 +9 [Δb=5] = +(8+9-5=12), Δb = 5+8-5 = 8.

The +8 object is leeched to enhance the +9 object which now has an unused capacity of 5. The resulting object has a total capacity of 12, of which 8 are unused.

This is exactly what you want if you want to add another ability with a net Effect Level of 7 to the item. But let’s say for a moment that you added a 4-point ability to the +9 object before leeching the +8; this reduces the unused capacity of the +9 object back to 1, as it now contains two +4 powers. And now:

    +8 +9 [Δb=1] = +(8+9-1=16), Δb = 1+8-1 = 8.

Again, absolutely perfect, with an extra +4 ability to boot. So, why would you bother with the initial refinement?

Well, let’s say that the only reason the 7-point power is only 7 points is because it’s related to the second ability that you’re adding. That means that if you push this power into the blending of the original object and the +8 object, you will end up with no points left, and a locked item – unless, of course, the existing power is unrelated to the +7 ability, which would push the cost of it from +8 to +9, which would not actually fit in the resulting magic item.

You need the first refining process to create the conditions that make the resulting object possible. But, the first power is still unrelated to the subsequent pair of abilities, which increases the cost of the +8 ability from +7 back to +8 – so the resulting magic item is now locked, and can no longer be approved.

As you can see from this example, this can get really complicated fairly quickly. Which is why there’s a lot more to say about it in the next part, when this will be a major topic of discussion. For now, though, let’s move on to the other use, Enchanting an Object:

Enchanting an object

This is the process of ‘filling’ unused capacity with ‘content’. Unsurprisingly, then, we’ve already been discussing it, because it’s central to the question of why you would refine an object.

There are two sources of enchantment: you can migrate the magical ability currently embedded in the object that you are leeching into the refined object, a process called “Fusion” or “Fusing”

When you do so, you need to recalculate the price of the new ability being added. It may have an Activation in common with the power object B already possesses; it may be related to the power object B already possesses; or it may be unrelated.

The Skill Involved

Of course, none of this happens automatically; there is a skill roll involved, against a DC of (a+b), and a skilled artificer can modify the magic being transferred in the process, easing an existing restriction to increase the capability of the fused object (increasing the Effect Value of the second magical power) or increasing one to reduce the overall fusion without ‘locking’ the resulting object (necessary if the abilities are unrelated).

If your game system doesn’t use DCs, the “DC” becomes the target that you need to achieve or the margin of success, as appropriate.

Each such change adds 3 to the DC / target / required margin.

Direct Enchantment

The other method of Enchanting an object is to cast a spell direct into the receptive matrix, substituting the intended Activation for the process normally used to complete and activate the spell (the way you would if you were casting a spell onto the object instead of into it.

This involves a more difficult roll, against a DC (or equivalent as described above) of 2×b + a – Δb. Fail, and the spell is wasted, and the unused capacity of the target reduced by 1.

The more enchantment an object already holds, the harder it is to direct-enchant it further, and the more skill is needed to successfully do so.

And, with that preview of what is to come in Part 2 (Forging and Reforging of magic items), it’s time to end this article and prepare it for publication (while my internet connection is behaving itself!)


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