Continuing to flog the dead horse of post-scarcity fantasy, I thought I’d bring my day job to bear on the task, and test the cost-effectiveness of a cleric-based public health measure to reduce infant mortality in a developing (medieval) nation.
Introduction
Infant mortality was a significant public health problem in the medieval era, and in the absence of explicit evidence to the contrary it is reasonable to assume that it is also a significant cause of morbidity and mortality in medieval fantasy settings. Reduction of infant mortality leads to increased wealth as families devote resources to tasks other than childbirth, and also to reduced family sizes, a significant element of economic growth in most developing nations. Furthermore, control over fertility is considered a significant element of women’s emancipation, and reduced infant mortality reduces family size.
As a public health task the reduction of infant mortality is not particularly challenging, but ultimately relies on access to advanced medical care for the small minority of mothers for whom drastic complications arise. Such medical care is not available in many developing nations, but in medieval fantasy settings it is easily provided by divine spell-casters, through the wide range of magical healing technology available. Until recently, it was believed that this technology was too rare and expensive to be used for non-adventuring tasks. In this report we investigate the cost-effectiveness of devoting divine magic to averting infant mortality, under two different intervention models, and show that even under the extremely inequitable economic conditions of a classic medieval fantasy setting, this intervention is cheap, cost-effective, and likely to lead to significant economic gains at very low cost.
Methods
A simple decision model was developed for a medieval fantasy setting under the assumption that its mortality profile was approximately similar to that of Afghanistan. The model was tested for a small community of 2000, but consideration given to its extension beyond this small community. Two intervention models were tested:
- The Clerical Attendance model: in which clerics attend every birth at the point where complications ensue, and use either of the cure light wounds, cure moderate wounds, and Remove Disease spells to intervene and prevent infant mortality
- The Potion Distribution model: Because medieval fantasy settings have very poor transport networks, an alternative model based on distributing potions to skilled birth-attendants was considered
Both models were compared to a control model in which skilled birth-attendants were the only healthcare available to the population. Under the Clerical Attendance Model, it is assumed that these women can call a cleric when a woman begins to experience difficulties in labour, and relative risks of infant mortality were assumed on the basis that clerical intervention would improve childbirth outcomes but would sometimes come too late. Under the Potion Distribution Model, the skilled attendant would apply the potion when it was judged necessary, eliminating the need for a cleric to be present and significantly improving outcomes.
The population of the medieval fantasy setting was assumed to have a demographic profile approximately equivalent to modern day Afghanistan:
- High birth rate: 37.5 per 1000
- High infant mortality: 134 per 1000 live births
Population was assumed to be 30 million where overall population figures were required. For a hamlet of 2000 people, this leads to the following outcomes:
- 75 births
- 10.0275 infant deaths
Infant mortality was modeled on the assumption that women fall into 3 risk categories, with different probabilities of complications in each category. Where complications occur they were assumed to always lead to mortality under the control case (skilled birth attendant only). The ratio of risk groups was:
- Low risk: 50 births, risk of complications 1.75 %
- Medium risk: 22 births, risk of complications 30%
- High Risk: 3 births, risk of complications 85%
This produces 10.025 deaths from 75 births, so is closely similar to the expected number of deaths. The interventions were expected to experience similar rates of complications (used for calculating costs) but reduced death rates. For the Clerical Attendance model, relative risks of death were:
- Low risk: 0 risk of complications (RR=0)
- Medium risk: 0.33
- High risk: 0.25
That is, medium risk women had 1/3 the chance of dying of complications under this intervention, and high risk women 1/4 the risk.
For the Potion Distribution model, deaths in all 3 groups were assumed to be eliminated completely.
Costs for the both models were calculated on the assumption that when complications occurred the following spells were necessary:
- Low risk: Cure Light Wounds
- Medium Risk: Cure Moderate Wounds
- High Risk: Cure Light Wounds, Cure Moderate Wounds, Remove Disease
Spells were cast at a cost of 50gp per level; potions were generated at the costs given in the Dungeon Master’s Guide.
Clerical load was also calculated for the Clerical Attendance model; that is, the number of clerics per 1000 required to support this model on the assumption that a cleric works no more than 200 days a year and sees one case per day.
Quality-adjusted life years (QALYs) saved were calculated assuming life expectancy in the medieval fantasy world was equal to that of Afghanistan (44 years) and outcomes expressed as incremental cost effectiveness ratios (ICERs), that is, the additional cost per QALY. Costs were in gold pieces, on the assumption that a basic medieval fantasy job (Maid) earns 36 gps per year (see Table 4-1, DMG). The wages of the skilled birth attendant were assumed to be 100Gps per year, i.e. approximately 3 x that of a maid in the era.
Sensitivity analysis was not conducted, because this is a blog.
Result
In one year, the 2000-population hamlet could expect to experience 10.025 deaths. Under the two interventions, expected deaths are as follows:
- Clerical Attendance model: 2.8
- Potion Distribution Model: 0
That is, at least 7.5 lives were saved per 2000 population. QALYs for the base case and interventions are:
- Birth Attendant Only: 2878.4
- Clerical Attendance: 3198.5
- Potion Distribution: 3322.5
And costs were:
- Birth Attendant Only: 100 Gps
- Clerical Attendance: 1978.8 Gps
- Potion Distribution: 4828.75 Gps
Giving ICERs for the two interventions of:
- Clerical Attendance: 6.2 Gps / QALY
- Potion Distribution: 10.9 Gps/ QALY
Both ICERs are significantly less than the annual income of the person saved (36 Gps). The cost per birth was:
- Clerical Attendance: 26.4
- Potion Distribution: 64.4
Thus, childbirth could be managed with improved safety at less than the cost of a cure light wounds spell, or less than a year’s wages for a lower-class job in this world; childbirth could be rendered completely safe for less than the cost of 2 such spells. The total income for this community in one year is at least 72,000 GPs, so even the more expensive program could be paid for through a tax of no more than 10%. Under such a tax system the cleric offering the services would be expected to pay at least 400 Gps tax, and this income could be easily diverted into a partial subsidization scheme for the poorest members of the community.
Note also that under the Potion Distribution model all child deaths are averted. Given that this would probably lead to a reduction in parity of, on average, 3 children per woman, this would lead to an increase in productivity of probably 2.25 years per woman, which gives an income of slightly more than the cost of the scheme under a free market model.
Clerical Load
With approximately 10 complications per 75 births, i.e. 10 complications per 2000 population, we expect that there would be 400 complications per 80000 individuals. A single 7th level Cleric could cover these 400 complications, so we expect not to need more than 1 such cleric per 80000. Under the Potion Distribution model, we need only 2.55 complications in the high risk group per 2000, or 200 complications per 157000 individuals. So we would need a single 7th level cleric per 157000 individuals, making one Remove Disease per day. This cleric would lose 6000 xp per year, so would need to adventure for the remainder of the year; or, for a more reasonable human resources regime, we could allow 1 7th level cleric per 80000 individuals on the assumption that one was adventuring at any time. To allow for death during adventuring, we should assume one cleric per 55,000 individuals. In a population the size of Afghanistan, we would require 545 clerics of this level or higher.
Reduction in Service Load
Given that reduced infant mortality leads to reduced birth rates and lower levels of parity, we would expect a rapid reduction in the number of births per year, and a concomitant reduction in costs and clerical load. Over the long term, we should expect the total cost under both schemes to drop rapidly.
Conclusion
Both schemes proposed here are highly cost-effective, being less than the income gained from the lives saved over their entire life course. Divine intervention to reduce infant mortality is an extremely effective public health intervention that simultaneously reduces personal suffering, death rates, and poverty and has significant demographic and economic effects. It can be paid for easily through a low rate of taxation and the cost reduces over time. In every sense, it is a model public health intervention. Policy-makers, hereditary kings and infernal dictators are advised to adopt this policy as soon as practicable in order to guarantee that they are Universally Loved. Churches of healing that are not already doing this gratis should hang their heads in shame. Paladins everywhere should hang their heads in shame anyway. Fantasy authors should ask themselves if they considered this cost-effectiveness analysis before they wrote their bubblegum-world stories, or if they were just being lazy.
It’s worth considering the extent of poverty in the lower classes of these worlds. A Cure Light Wounds spell costs 50gps, but the average maid earns 36 gps. Being a maid in the medieval era is not exactly the lowest class of job one can expect; it’s not tanning, bone-picking or any of the other taboo jobs, and many women aspire to this sort of work. What Paladin isn’t shagging his maid[1]? What maid isn’t lovin’ it[2]? The WHO defines “catastrophic health expense” as any health care event that costs more than 40% of your annual household consumption. Assuming no savings, cure light wounds costs a maid 140% of her annual consumption. Compare and contrast: in modern Japan a trip to hospital for a broken arm will cost me a maximum of 210,000 Yen without insurance, and if I work full time at Lawson (a pretty low-paid job) I earn 1400000 yen a year. Lower-class people in D&D are poor. But through clerics working together in an organized system, they can eliminate one of the most tragic and significant health problems facing our “advanced” world, at less than (or at least, little more than) the cost of a year’s wages for a reasonably low-class member of society. Even when these clerics are extremely rare, they can still do it. This should serve as a strong hint at the fact that even with scarce sources of magic, medieval fantasy settings should become rich very fast.
—
fn1: What do you mean “none of them”? Are you suggesting paladins are gay? That’s … blasphemy!
fn2: I’ve read George RR Martin[3], you can’t fool me
fn3: Actually I haven’t, but I’ve watched the TV series
Compromise and Conceit 
September 2, 2011 at 9:56 am
I think you’re still underestimating the cost of the provision of this care. The costs that you’re overlooking range from the trivial to the significant. So I’ll try to list out the issues that occur to me.
Transport costs and Management Overhead
While you’ve finally made some allowance for the fact that the clerics need to get to each birth in the CA model and the fact that the attendance will miss some cases I still think you’re failing to account for the travel costs inherent in this system.
Simply put, either the clerics or potions need to reach every tiny hamlet in Afghanistan. It’s worth noting that the DMG already notes that the cost of potions and spells are significantly higher in smaller towns, if they are even available at all. My memory of the mark-up was that it was in the hundreds of percent.
And that’s based just on the normal rate of monster attack in a country such as Afghanistan. If you were to factor in the ongoing and opposing crusade and jihads there then a markup of at least 300% is reasonable.
Furthermore, that markup is when you’re facing a cottage industry. Given that no economy of scale applies on either the spell casting or the potion making, we should assume that large scale usage not only faces the manufacturing/casting costs, but also faces a management overhead comparable to the NHS. This would account for clerical hierarchies, holy days and appropriately long and ornate robes for all those involved (plus dry cleaning).
Supply and Demand
The next issue is that you’re projecting that a massive increase in demand for either casting or potion making can occur without any matching increase in supply but not impact costs at all. There is no evidence to support the proposition that potion/spells costs are inelastic. As such we should assume a further, unknown, markup will occur.
Union activity
These problems will be further heightened by the management structures this system will require – such structures will bring potion makers/casters into common contact with each other. As such we should expect that a union will form in minimal time which will setup a monopoly pricing structure.
The new union will differ from the existing temple based structure as it will encourage common goals across temples – eliminating the current competition between temples and thus allowing higher prices to become the norm.
Furthermore, we have to remember that this union will be backed by the ability to summon holy/unholy assassins from the Outer Planes and hold almost total control over the truth magics you suggest using in your justice system. As such we should expect that union thugs will never be caught. If you thought the BLF in Australia was dodgy then this will open your eyes to the horrors of union organized magical action.
Number of Clerics required
I also want to take issue with the number of clerics you project are required. If we assume a simple 33/34/33 split across good, neutral and evil clerics then we can see that the good and evil clerics require 100% of their time to offset each other’s efforts. This means that only the neutral clerics are available for your work – priests of trade and the like. And we all know that the neutral clerics don’t care if you live or die – just ask a druid.
This means that the clerical numbers in the population need to be 3 times higher than you forecast.
As a final point on this, I think we can assume that evil clerics will gain xp faster – based on the xp efficiency gains from a position supporting total rather than selective genocide. There is every reason to believe that the good clerics are plucky underdogs opposing more powerful targets with the assistance of their party. That could result in even my 3x adjustment being an underestimate.
Agency Theory
Related to the clerical alignment issue, agency theory tells us that each employee will act in their own best interests instead of the organization. The aim should therefore be to align the employee’s interests with the companies through incentive schemes/management structures. But in your model I can’t see any allowance that would provide that.
Let me provide a microeconomic example. As an evil cleric I could subscribe to your potion making/casting program and earn a minor income with minimal xp gain (or potentially even xp loss). Or I could pretend to join your scheme then in the first small town kill everyone with an area effect spell, raise their corpses, use these undead to loot the town and then attack the next town. The income in both gold and xp will be significantly higher under my model – why should I help you?
Even for a good cleric the income from dungeon/bank [1] raiding in both gold and xp will be better. And we all know that when the good cleric saves the world the world from an attack by Cthulhu you’re not going to be claiming they should have spent time healing babies instead of leveling up.
Finally, under your model no potion maker would every level up as your plan calls for them to spend all their banked xp creating potions then getting that xp back again. Under this model there is no reason to expect any cleric to get to a higher level than required to create potions. This lack of high level clerics would only exacerbate the tarrasque problem that Afghanistan is already experiencing.
[1] In Afghanistan dungeons and banks fulfill a similar role in holding wealth locked away from the community. They are also both valid targets for good clerics.
September 7, 2011 at 7:49 pm
These are all good points, but I think a few qualifiers are in order.
Transport costs and management overhead
The distribution of potions occurs through the skilled birth attendants, and can be done through central cities – the assumptions underlying mark-up costs and other such things in the DMG assumes no involvement of the king in ensuring that potions are delivered to rural areas. Certainly monster attack and other such naughtiness would need to be included in the costs, but presumably such infrastructural effects are built into the price of a potion? This would explain why a potion of cure light wounds (1d8+1) costs more than a maid’s annual wage.
Supply and Demand
The wealth benefits for the clergy of this program would soon have them expanding their recruiting and scaling up their practice. A single cleric working 200 days a year under this cost-effectiveness model stands to make 4800 Gps per 10 births at which their potions are used, or approximately 96000 Gps a year. I think the DMG estimates the wealth of a 7th level cleric at about 100,000 Gps – that’s 7 levels of adventuring. The cleric can make a lot more money if they cast the cure light wounds potions off to a junior and focus on remove disease (that’s about 600,000 Gps a year). Clearly the clergy are going to gear up for this, and expand their clerical numbers to suit the task. This means recruiting more laity and low-level clergy, which means that they expand their base of followers and make their god more powerful – and they have every justification for being followed, as women survive pregnancy and see their children survive – what order do you think they’ll be baptizing their kids to?
So there’s no reason to think that the supply-and-demand economics would be based on a fixed productive capacity.
Number of Clerics Required
There’s no reason to think evil clerics wouldn’t join in the potion race (it’s easy money) and as I said above there’s every reason to think that the ranks of good clerics would swell, leading to a long-term imbalance in cleric numbers and the ultimate destruction of the evil forces unless they make themselves similarly useful. Also, why do you think Neutral clerics wouldn’t sell potions? And again, presumably the prices given in the DMG reflect the fact that lots of good and evil clerics are too busy killing each other to make potions.
Agency theory
I don’t think Afghanistan’s problem is Tarrasques …
September 8, 2011 at 2:12 pm
Transport costs and management overhead
The DMG is entirely agnostic on whether the King has a standing policy of supporting a Royal Mail system or if he is supporting the bandits on the road, but either way it suggests a cost increase for smaller and out of the way villages. If you’re going to quote potion prices from the DMG in your argument then you can also quote the cost mark-ups mentioned as well. Otherwise you’re just saying “If I read all the positive stuff in D&D and ignore the negative stuff it should be a utopia. In other news a carefully reading of Soviet Russia reveals that it was also a utopia!”
Supply and Demand
Your point about the financial benefits is a good one, based on it we can expect to see Faustusville/Afghanistan move towards a more cleric dominated environment. This would provide a production capacity increase that would offset the increased demand to some extent, but it’s probably unrealistic to believe that increasing the demand for Cure Disease potions a hundredfold will immediately lead to a hundredfold increase in level 7 Clerics. It’s more likely to increase the supply of clerics by a factor of ten, which still leaves demand outstripping supply.
The other element here is that we know that people with PC class levels are extraordinary individuals who are themselves in a limited supply. Your projected increase in clerics is coming at a cost of wizards and warriors. Though we can probably survive with the decrease in rogues thanks.
Furthermore, the people who are now becoming clerics for the income are going to be less naturally suited to the class. This is going to decrease average Wisdom bonuses through the country. Though that’s pretty much an aside as you were already not taking such bonuses into account.
“as women survive pregnancy and see their children survive – what order do you think they’ll be baptizing their kids to?”
You do realise that in your next paragraph you suggest that the Evil clerics will be doing this too right? So overall you’re actually suggesting that a recruiting boost for the evil gods is a good thing? For your next argument are you going to put forward that the London riots are good for the economy? Because riots like that are what happens when Faustusville hits a critical mass of Dark God worshippers. And paladins help us if the clerics of the Elder Gods get in on the act…
Number of Clerics required
As I already pointed out, you’re claim that Evil clerics are getting in on the act precludes the idea that the forces f Good are getting a long term boost in believers.
I concede that the DMG prices should factor in the Good and Evil clerics killing each other, but my point under this topic was around the number of clerics required to do this, not how that number related to the supply (which I had covered elsewhere).
Agency theory
Now you’re just being silly. Of course Afghanistan’s problem can be compared to a Tarrasque. An unkillable beast that strikes unreasonable fear into its opponent’s is stalking the land. No matter what action is taken it always comes back.
That narrative matches the facts on the ground regardless of which side you support.
September 8, 2011 at 6:47 pm
The point both of you keep failing to mention is: This is a world full of orcs, dragons, and giants. Even a single standard orc in AD&D is more powerful than a 0-level soldier, or even a 1st-level fighter. The cost of protecting all the healing potions as they get dispersed throughout the land would be astronomical – not to mention the opportunity cost issue that comes into play (clerics who are making healing potions all day long cannot spend their time doing what they can in the fight against evil, and clerics who spend their time fighting evil cannot make healing potions all day long).
September 9, 2011 at 8:44 am
I disagree Noisms. That is exactly the point I keep making by pointing to the price inflation effects mentioned in the DMG. Those effects show that outlying regions have to pay more for items, which is there to reflect both transport costs and (presumably) cargo protection.
As for your second point about opportunity costs, that’s accounted for in Faustus’s calculations of the number of clerics needed, where a sizeable downtime is required per year for regaining xp [1], and my point that the number of clerics must be tripled to account for good and evil clerics both having better things to do [2].
An interesting point that I think could investigate more is the importance of xp gain among the clerics doing Faustus’s work. While there is some allowance for clerics going adventuring to regain xp, what would really happen is another adventuring distortion. Because D&D awards xp for “defeating” monsters, we could expect the clerics supporters (be it the state or private enterprise) to experiment with the optimal way of clerics regaining xp they’ve used for potions. I expect that the finding would be an arena-like structure where the cleric fights a series of moderate encounters each day until the monster is unconscious. The fights wouldn’t be to the death, as that would lead to a need for additional monster capture. The fights would be managed to minimise cleric danger, such as having numerous casters all ready to Hold Person any humanoid monster the cleric fought if the fight was going badly, or equivalent intervention for non-humanoid monsters.
When you take a step back and look at this, what you see is that the clerics are required to repeatedly brutalise a captive populace in order to keep Faustus’s potion supplies running. This is similar to “The Ones Who Walk Away from Omelas” by Le Guin, though the victimised group is probably less attractive.
The other point this leads to is that having an xp gaining structure where clerics repeatedly brutalise a captive populace is probably going to lead to a long term alignment shift amongst the clerics towards evil [3]. This is another point that suggests that Faustus is working for the Dark Gods and we should ignore him.
[1] I also think that he’s underestimating the amount of time that is needed to regain xp, but that’s a more difficult point to provide evidence of.
[2] Though if Faustus is right and the good and evil clerics get in on the game too, then it doesn’t need to be tripled, but instead distorts adventuring party make-up and people’s class selection.
[3] Unless you feel that working at Abu Ghraib prison would be more likely to lead to the warden’s becoming good people…
September 9, 2011 at 6:15 pm
Noisms, I think you have a point about opportunity costs but cost-effectiveness evaluation is not designed to test these; that’s the role of cost-benefit analysis (deciding which QALYs are better to save, I think). Cost-effectiveness evaulations simply tell you whether a newer, more expensive intervention is good value for money. It’s entirely possible that it would be better to send your clerics off to fight distant wars against monsters; but I haven’t tried to address this. Of course the likelihood is that it wouldn’t be better – there are very few ways to spend money that are more worthwhile than saving children’s lives, and unless the expense is great it’s likely that it’s the best use of clerics’ time.
You could probably partially estimate this by running a new cost-effectiveness evaluation which compared two models: a control model where skilled birth attendants handle briths and clerics go to war alongside soldiers; vs. an intervention where clerics go to help skilled birth attendants and soldiers fight wars without medical aid (or just low level medical aid). In the latter intervention the clerics would be swapping healing injured and dying adults for injured and dying children.
I think you’re over-estimating the dangers of the medieval world but even so, just restricting clerics to the core of the society (major cities) would make a huge difference without incurring much risk of lost potions; the wealth gains from that could then be employed on expanding the model.
The xp issue is interesting, and definitely all the practices we’re discussing would distort the “market” for clerics – they’d rapidly gain temporal power relative to wizards due to their inherent value to dictators everywhere. It’s bread-and-circuses stuff this. Imagine for example a radical anti-royalist union that set up its own clerics and sent them into the slums to heal the poor.
I like the idea of controlled fights against monsters for xp. It kills so many birds with one stone!
September 10, 2011 at 12:16 pm
I suspect that you’re overvaluing children’s lives. So far you’ve based their value off an average wage for an average lifetime. But that fails to provide a discount factor for the fact that they don’t provide value for ages and also fails to account for costs that are avoided by their deaths.
An example of why this is important is if we expand the timeframe examined from one lifetime and keep the zero discount factor rate you’re using. Under these assumptions we can further expand each child’s value by saving they will have an average of one child who will also earn a maids wage. That breeding will continue forever. Because of the cumulative value of their descendents we can see that every child has an infinite average worth. That value remains infinite till after the person is done having kids.
While this does reflect the philosophical belief that you can’t put a dollar value on human life, it also prevents all economic decisions being made from the assumptions (other than that killing old people is cost effective).
September 10, 2011 at 12:17 pm
Ohbyeah, and the monster arena idea leads to a failure to keep hostile dungeon dwelling populations in check. You should probably factor an Orcish Horde into your cost calculations.
September 10, 2011 at 6:19 pm
I should have mentioned in the OP that I didn’t use a discount. Usually we use 3%, but I couldn’t be bothered (it involves a trivial formula!). In comparative terms it doesn’t necessarily make much difference because it allies to both sides of the comparison. But it does mean that the cost per qaly is under-estimated by a factor of one on something times the exponent of something, summed over something. Or something. Rest assured I don’t do that sort of lazy work in my day job!
September 10, 2011 at 6:21 pm
But I do like that economics allows us to have conversations where we ponder whether we have over-valued children’s lives. It’s a good look for the profession!
September 11, 2011 at 4:24 pm
I sometimes try to justify to myself that I’d spend those gold pieces helping other children in a more cost effective way. But then I remember how much that castle extension/next tier of gear I want costs and just stop lying to myself.
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