# You can just multiply point estimates (if you only care about EV)

Many people think you need probability distributions; they think using point estimates will mess up your EV calculations. That's false; you'll get the same result whether you multiply distributions or multiply their EVs. You can ask a chatbot: "Briefly explain linearity of expectation and independence (E\[XY\] = E\[X\]E\[Y\])." To multiply EV point estimates, you just need to make sure the point estimates are EV rather than median, the distributions are independent (or at least uncorrelated), and you're not doing anything fancier than adding and multiplying.[^hqgisfa0fll] (However, you need distributions if you want median, credible intervals, etc.)

I generally use point estimates in my EV calculations. In some contexts the natural way to estimate EV is to first estimate a distribution, but in my work it usually makes sense to estimate EV directly. And using point estimates makes it easier to understand models, compare parameters from different people/models, notice inconsistencies, etc.

Using distributions is dangerous; if you get the tails wrong it can wreck you.[^a5ezg2z0skg] And again, distributions are harder to understand, and making your models less scrutable—to yourself and others—is a massive cost. Using distributions might help you notice which parameters are unstable, but you can also just do that without distributions.

I occasionally use distributions for EV estimates because (1) sometimes it's necessary[^3bo9yh2looq] or (2) sometimes the best way to estimate EV (or explain your estimate to others) is to estimate the distribution and then take the mean. Sometimes these "distributions" are crude, with just a few discrete buckets, because that's easier to think about.

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On the other hand (thanks to Eli Lifland for suggestions):

*   In some contexts (e.g. *forecasting AI progress*rather than *estimating EV for prioritization/grantmaking*), the output you want is (downstream of) a distribution. In those cases you absolutely should use distributions.
*   The distribution contains more information than the EV. To find the median or mode or credible intervals, you need the distribution.
*   Distributions *increase* scrutability for high-effort readers: they're harder to engage with but contain more information. In some contexts, if you want to understand or argue about EV, you have to understand or argue about distribution. (But in my work, it's often more like: you should directly estimate the expectation of a parameter, and the best way to come up with a distribution is downstream of that.)
*   Maybe Claude (or Guesstimate or Squiggle?) can make it easy to make a decent model with distributions. I'm skeptical but haven't really tried.

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*This post is part of *[*my sequence inspired by my prioritization research and donation advising work*](/s/kvBmY5GaB3qdCRQ29)*.*

[^hqgisfa0fll]: You also have to make sure you're using the expectation of the right parameter. In particular, 1/E[X] is different from E[1/X]. 

[^a5ezg2z0skg]: Minor: also arguably distributions for value of the world after this intervention minus value of the world before this intervention are fake/meaningless, since all interventions have massive random effects. This doesn't bother EVchads because the random effects have EV zero. When we talk about the distribution of effects, we have to talk about something more like direct/foreseeable effects. This doesn't really matter but it may suggest that distribution of value diff is a weird/unnatural concept. 

[^3bo9yh2looq]: E.g. what's the value of spending $1 in 2028, given uncertainty about how much others will spend? I use a distribution on "how much others will spend effectively in this area in 2028" and a function from "how much others will spend" to "EV of marginal $1."