The BBB costs 12,500gp, and provides 1000 pages, weighing 1lb.
Other spellbooks cost 100gp (I think that's right) have 100 pages, weigh 3lbs, and cost 100gp per page to scribe.
So what you're comparing for cost efficiency is 1 BBB with 1000pages and 1lb versus 10 spellbooks with 1000 pages and 30lbs.
10 spellbooks cost 1000gp, so the value added by BBB is 11,500 for free scribing and 29lbs.
I would say that for a wizard a Bag of Holding is absolutely necessary once a certain level is reached, so I'll assume this wizard has one, and deduct the price of a BoH from the difference in costs. The wizard pays 9,000 up front to scribe spells for free.
I'm also going to assume that a wizard's two free spells gained at each level represent 1/4 of his total spell repitoire. This is arbitrary, but not too bad if you ask me. It means a 10th level wizard will have about 80 spells known. Seems fairly accurate to me. So a wizards scribing cost is going to be discounted by 1/4 since there is no scribing cost for either a spellbook or a BBB.
Also assumed for this is the distribution of spells. Let's say that at each new spell level, he only has two spells, and has twice the number of spells at his second lowest spell level than at his highest, and this trend continues. So A 9th level wizard would have this distribution:
1st: 32
2nd: 16
3rd: 8
4th: 4
5th: 2
That will mean that a 9th level wizard (it's easier to work out with a wiz who has just gained a new spell level) will have approxamately 114 pages of spells, not incuding cantrips.
That 114 pages will cost him 11,400gp to scribe into at least two mundane spellbooks. Except that he's getting 1/4 of that for free, so it actually only will cost him around 8,500gp.
It will "cost" him 9,000 gp to scribe those same spells into the BBB, because that's what he paid for the book. So far the BBB is the more expensive deal.
A 15th level wizard will have approxamately 1000 pages of spells. (The algorythm gets messy here because there arn't that many 1st level spells, but added weight at the low levels makes up for the relatively smaller number of higher level spells you'd expect a mean ol wizard to have.)
To scribe those 1000 pages, the wizard would incur 100,000 in costs, with a 25,000gp discount because of his free spells. So here it costs him 75,000gp to scribe those 1000 pages.
And it still "costs" him 9,000gp to scribe into a BBB. So what we have here is a tipping point between levels 9, where the costs are fairly equal, and 15 where the costs are staggeringly different, with the advantage to the BBB beginning at level 10.
For reference sake, my assumptions are:
- Every wizard will have a Type 1 Bag of Holding
- Every wizard will have a high enough STR to carry a Type 1 Bag of Holding
- Every wizard will have no preference for concentrating his spells into one book or spreading them out amongst many.
- A wizard's spells known per level will double at each level decreased, disregarding cantrips.
- 1/4 of the wizard's spells known will come from the two free spells gained at each level.
- 1/4 of the wizard's spells' pages will come from the two free spells gained at each level.
- The wizard will continue to scribe low-level spells regardless how high a level he is.
- Gold in DnD is not affected by the Time-value of money.
Holding these assumptions as true, the Boccob's Blessed Book is
never a good purchase before level 10, and a must buy after.
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But let's change some assumptions.
The first two assumptions are fairly innocuous, so I'll let those be.
The third, however, is not. There is a saying, "Put all your eggs in one basket, and GUARD THAT BASKET!" But considering that without a spellbook a wizard is only a smart guy in robes who can cast
Read Magic, I would think that a wizard would very much prefer to have his spells spread out among several books in case of destruction, caputre, or indexing purposes (All transmutation in one book, necromancy in another for instance.) So this means that it adds value to have more than one spellbook. Because of this, the Boccob's Blessed Book loses ground here, at all levels.
The retort to this is that as the wizard gets higher in levels he would be wise to invest in multiple BBB's, and while this cuts down on the advantage the BBB has at high levels, it's still more efficient than scribing everything into mundane spellbooks. Either way, however, it makes the BBB look a less attractive deal.
The fourth assumption, that spells double in number as you decrease spell levels levels, is flawed in that at the point when you stop scribing so many 1st and 2nd level spells. From that point on, you will be scribing comparatively fewer low level spells, which will decrease the total number of pages scribed. As you decrease the total number of pages scribed, the Boccob's Blessed Book becomes less attractive.
The retort to this: because you are no longer spending money on low-level spells you are spending money on higher level spells, which mean more pages per spell, which would seem to make BBB relatively more attractive. One 5th level spell has the same cost as five 1st level spells, and is arguably more useful. In the end, the costs will wash.
Now for the 1/4 assumptions... These are wholly inaccurate.
They were used for ease of calculation purposes, and they did their job. But what is the reality? For the 9th level wizard, he has 62 spells and 114 pages scribed (18 and 50 of which were free, respectively.) This means nearly 30% of his spells and almost 50% of his pages were free. This is because a higher proportion of any given wizard's high level spells will be free since you stop getting free 1st level spells at 3rd level, but you don't really stop scribing 1st level spells. This means that scribing into the mundane spellbooks is relatively cheaper at lower levels... you arn't weighed down with a host of non-free mid-level spells that drive your costs up. This changes at higher levels because of the huge number of low-level spell scribing costs you incur.
That wouldn't mean too much if you don't simultaneously relax the assumption that wizards continue scribing low level spells. Once you do that the savings for high level wizards scribing in mundane books stay at around 25%. So it's a wash, and BBBs are increasingly more cost effective at higher levels, and less so below level 12 or so.
We already delt with the next-to-last assumption, so no need to flog that horse.
The last assumption however, might mean something to higher level wizards. Another BBB is an outlay of 11,500gp, which is the equivalent of 115 pages of scribing into mundane books, which is about 5 days time of scribing. Each day that the wizard does not take full advantage of those free 115 pages he is losing money, in that he could have spent that money elsewhere and have it working for him
right now. Because of the incrimental outlay of scribing costs into mundane spellbooks, the cost of those scribed pages is always constant. Boccob's Blessed Book scribing "costs" however, increase as time goes by and the book remains unused. So, with this assumption eased, the Boccob's Blessed Book becomes more expensive than it shows.
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That little exercise was done for three reasons:
One, it was kinda fun.
Two, I have little else to do at the moment.
Three, when I began my calculations, I made the mistake of multiplying mundane spell pages by 10gp instead of 100gp per page to yield total costs. This resulted in a proof that BBBs are never a good buy, regardless of level. I was 2/3 done with this post when I realized my mistake, and went back to correct it, and went through to change some of the conclusions. After having written 2/3 of the post, I didn't want to erase it for that mistake since I had already put so much time in it, so I kept on going until I reached the present non-controvertial conclusion.
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The conclusion:
Buy one BBB at about level 11 to start saving money on scribing costs.
Buy another at around level 15 to spread your spells out among more than two books.
Gosh, that feels kinda, well, floppy and uninteresting. I want the hour and a quarter I spent writing that back.:\
Oh, well.
