[phailhaus]

The broader point is that percentages can be misleading, and are often because of that. It makes things sound better. But usually, the more accurate thing to do is use odds-notation ("1 in 50" instead of 98%). Percentages have a kind of singularity at the edges, where small numerical changes have massive real effects. Going from a success rate of 98% to 99% doesn't sound like much, but that's failing 1 in 50 vs 1 in 100. You've doubled the efficacy.

[parineum]

It's contextual depending on which end of the probability is the desired outcome.

SPF is like this. SPF 30 allows 1/30th (3%) of the UV through it, blocking 29/30ths (97%). SPF 50 (2%) allows 1/50th, blocking 49/50ths (98%). Using the denominator, in this case, expressed the efficacy much more intuitively.

Comparing SPF 30 vs 50 better expresses the increase in efficacy than 97% vs 98% does.

One could also express it as the amount that passes the filter but it is Sun _Protection_ Factor not Sun _Transparency_ Factor.

[jrowen]

On the other hand, it's completely unintuitive that "Sun Protection Factor 30 = 1/30th of UV light passes through it", and I had no idea there was any correlation before this comment.

The only intuitive bit about that system is "bigger number does more." I feel like I would have more readily understood it if it just said "blocks 97% (or 98%) of UV light" instead of numbers I assumed were somewhat arbitrary.

[parineum]

The intuitive part comes when comparing two options.

If you use 20 instead of 10, you'll be exposed to half as much UV even though it's only an additional 5% of protection.

The number could just be the percentage of exposure (5 v 10) and express the same relationship but the denominator has the advantage of bigger numbers being more protective while still being more intuitively comparable.

Many people would see 90% vs 95% and not intuit that it's twice the protection.

[jrowen]

I'll grant that it's complicated, as the comments on this post have demonstrated.

But half the exposure isn't quite equivalent to twice the protection.

All my life I just thought they were somewhat arbitrary numbers, I didn't correlate them to any actual measurable quantity, and I would assume it's the same for most people. So while I would agree that that representation "gets the job done," I don't think it contributes to a deeper understanding.

I do feel like if you saw "90%, 95%, 97%, and 98%" on the shelf it would start to make some kind of sense, and then when people talk about it ("what's the difference between 97 and 98?") the underlying concept would become more apparent. Using a kind of converted magic number scale that doesn't work like other things seems unhelpful, but I'm certainly not an expert nor the intended audience.

[cubefox]

In many cases, odds are indeed better than probabilities, namely when a small difference at the probability edges indicate a large real difference.

But sometimes small differences at the edges are indeed small, particularly for expected values. Say you win 100 dollars with 98% probability vs with 99.9% probability.

The expected value (probability * dollars) of the latter is only slightly higher than the former ($99.9-$98=$1.90) even though the difference in odds is very large: (0.999/0.001)/(0.98/0.02)≈20.39. So the 99.9% probability is odds 999 to 1, 98% probability is 49 to 1, so the former has more than 20 times higher odds, but the expected amount of money you win is almost the same.

[abustamam]

Tangentially, but 5-day vs 4-day workweek is somewhat similar. You've not only reduced your working days by 20%, but you've also increased your days off by 50%.

[AnimalMuppet]

No, you've raised the efficacy from 98 to 99, which is not much of a change. What you have done is halved the inefficacy, which is a big change.

[ryan_n]

Isn't this pretty much the entire point of the article.

[phailhaus]

Look at the HN comments and you'll see many saying they don't get the point