Great tool! I couldn't figure how to go back when I mis-clicked an answer, and ended up losing my progress.

I'll rewrite completely because I didn't explain myself very clearly

• 10,000 participants is possible since they are using Whatsapp, in a large country, and recruiting users does not seem to be a bottleneck
• 10,000 participants is relevant as it represents the scale they might hope to expand to at the next stage
• Presumably they used the number 10,000 to estimate the cost-per-treatment by finding the marginal cost per treatment and adding 1/10,000th of their expected fixed costs.
  • So if they were to expand to 100,000 or 1,000,000 participants, the cost-per-treatment would be even lower.

My guess is that a WhatsApp-based MH intervention would be almost arbitrarily scalable. 10 000 participants ($300,000) may reflect the scale of the grants they are looking for.

I would like to push back slightly on your second point: Secondly, isn't it a massive problem that you only look at the 27% that completed the program when presenting results?

By restricting to the people who completed the program, we get to understand the effect that the program itself has. This is important for understanding its therapeutic value.

Retention is also important - it is usually the biggest challenge for online or self-help mental health interventions, and it is practically a given that many people will not complete the course of treatment. 27% tells us a lot about how "sticky" the program was. It lies between the typical retention rates of pure self-help interventions and face-to-face therapy, as we would expect for an in-between intervention like this.

More important than effect size and retention - I would argue - is the topline cost-effectiveness in depression averted per $1,000 or something like that. This we can easily estimate from retention rate, effect size and cost-per-treatment.

Zakat is paid on wealth, not income, so GDP is not a great proxy. Globally there appears to be $450tr in wealth and $100tr in GDP, so perhaps multiplying GDP by 4.5 gives a decent estimate for wealth.

Also global GDP increased 43% between 2010 and 2022.

Thanks for sharing your calculations!

I'd recommend against thinking along the lines of what Muslim wealth would have to be to make the 1tr figure plausible, given that the figure seems to be made up. But I definitely agree with the idea of forming multiple estimates using different approaches.

Some ideas for getting a good figure:

• The combined GDP of Organisation of Islamic Cooperation countries is 10tr, about 10% of global GDP. This does not include most muslims in countries where they are a minority (importantly, India, Europe and North America) but it does include non-muslims in OIC countries
  • Straight off the bat we can see that $1tr is implausible. 
  • If we assume that OIC countries have 10% of global wealth, this would be $40-70Trn according to your estimate. This implies $1-1.75bn of wealth eligible for Zakat.
  • Where is all that wealth? Given that, as you say, a big chunk of wealth is help by the top 1%, I would guess that most of the wealth is in shares of companies, plus property and other physical assets. The value of such assets can easily be hidden or obfuscated by those who do not wish to pay Zakat on it.
• It seems like Zakat is enforced by law in Saudi, and collected & used by the state(!) [source 1, 2]. So the $18bn figure is probably quite reliable. 
  • Saudi GDP is about 1% of global GDP. Assuming Saudi therefore has 1% of global wealth (probably an underestimate because oil), and that 20% is a hard limit on the share of global wealth owned by muslims, I would guess 20*$18bn = $360bn is a very hard upper limit on global Zakat
  • More realistically I would assume that 10% of global wealth is owned by Muslims eligible for Zakat and that payment rates outside of Saudi are much lower - I'll say 75% lower^[1]. Then global Zakat would be $18bn*(1+9*0.25) = $85.5bn
  • Importantly, it seems like Zakat paid in Saudi is not influencable as it is kept by the state. Therefore my best estimate of the amount of influencable Zakat is $67.5bn worldwide.
• As a sense-check: where are the Gaza billions? The war in Gaza was a huge huge issue in the Muslim world this past Ramadan, and presumably a lot of Zakat donations went to helping Gazans. If it was ins the tens or hundreds of billions (ie at least 10% of $200+bn), that would be $10,000s for each person in Gaza, which should be easy to spot. But it is not coming up in some brief googling.

1. ^{^}

   I imagine the main factors are (1) simply underpaying or not paying because it must hurt to give away 2.5% of one's wealth each year and (2) fudging by underrating one's wealth (not counting or being naive about the value of one's house, livestock, car etc.)

Great summary!

There is also a mental health benefit to averting unwanted pregnancy. A meta-analysis by Wang et al. (2021) found that women with an unplanned pregnancy were 62% more likely (28% vs. 17%) to suffer postpartum depression compared to women with a planned pregnancy. We don't have good data on depression prevalence among women whose unplanned pregnancy was averted, but it seems probable that an unplanned pregnancy increases the risk of mental illness, even if only by adding another life stressor. It is very hard to measure, but I suspect that the wellbeing benefits of not having one's education cut short / career & income disrupted / living with stigma of being a single mother or with a partner you didn't choose to have a child with / etc. are high.

For us, high-impact clients include adolescents (under the age of 20), individuals living in multi-dimensional poverty, those who aren’t using or have never used contraception, and those who have no other options for the services we provide. Collectively, we aim for over 80% of our clients to be from one or more of these high-impact groups. 

I think this is a good way of trying to secure strong counterfactual impact. I notice that your cost-effectiveness estimates imply that you prevent 200 maternal deaths per 100,000 averted pregnancies. How do you arrive at this figure, given the lack of maternal mortality data for your specific demographic (unwanted pregnancy, rural, underserved, low-income country)? Nigeria has the 2nd-worst maternal mortality rate in the world, at 112 per 100,000 - but your Nigeria numbers suggest something like 500 per 100,000.

Another interesting thing is that you avert a maternal death for $3,353 - which means maybe $70-100 per extra year of life that these women get - and you avert a DALY for $4.77. This implies that averted maternal deaths only account for ~5% of the health benefits you are measuring. Where are the other 95% coming from? Importantly, are any coming from the infant or from non-health benefits converted into DALYs - because counting these would be moral assumptions worth flagging.

This looks like a particularly strong crop of new orgs. I'm excited to see NOVAH and AMI get started, which (as far as I know) are pioneering totally new interventions. Good luck.

I have a post that takes readers through a basic example of how to calculate Shapley values.

Thanks for the detailed response, Vasco! Apologies in advance that this reply is slightly rushed and scattershot.

I agree that you are right with the maths - it is 251x, not 63,000x.

• I am not comparing the cost-effectiveness of preventing events of different magnitudes.
• Instead, I am comparing the cost-effectiveness of saving lives in periods of different population losses.

OK, I did not really get this!

In your example on wars you say

• As a consequence, if the goal is minimising war deaths^[2], spending to save lives in wars 1 k times as deadly should be 0.00158 % (= (10^3)^(-1.6)) as large.

Can you give an example of what might count as "spending to save lives in wars 1k times as deadly" in this context? 

I am guessing it is spending money now on things that would save lives in very deadly wars. Something like building a nuclear bunker vs making a bullet proof vest? Thinking about the amounts we might be willing to spend on interventions that save lives in 100-death wars vs 100k-death wars, it intuitively feels like 251x is a way better multiplier than 63,000. So where am I going wrong?

When you are thinking about the PDF of $\frac{P_i}{P_f}$, are you forgetting that ∇$\frac{P_i}{P_f}$ is not proportional to ∇$P_f$? 

To give a toy example: suppose $P_i=100$. 

Then if $90<p_f<100$ we have  $1<\frac{P_i}{P_f}<1.11$

If $10<p_f<20$ we have  $5<\frac{P_i}{P_f}<10$

The "height of the PDF graph" will not capture these differences in width. This won't matter much for questions of 100 vs 100k deaths, but it might be relevant for near-existential mortality levels.