# A Simple Math Question **URL:** \ **Category:** Factual Questions\ **Created:** [December 9, 2021, 11:41pm UTC](https://boards.straightdope.com/t/a-simple-math-question/955809 "2021-12-09T23:41:40Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Paul\_was\_in\_Saudi](https://avatars.discourse-cdn.com/v4/letter/p/b77776/32.png) [@Paul\_was\_in\_Saudi](https://boards.straightdope.com/u/Paul_was_in_Saudi)\ **Post date:** [December 9, 2021, 11:41pm UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/1 "2021-12-09T23:41:40Z")
ABC News is playing in the background. They are talking about vaccines and booster shots. Without the booster (or something) **protection is 25 times less.** Not 25% less. The graphic read 25 X less. What does this mean? If protection would be (say) 100 with the booster, then what would it be without it? It seems to me they are sort of saying it backward. Perhaps they meant to talk about percentages. In any case, I am lost. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 9, 2021, 11:50pm UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/2 "2021-12-09T23:50:22Z")
I think this is the explanation: [https://abcnews.go.com/Health/wireStory/pfizer-covid-booster-offers-protection-omicron-81620705](https://abcnews.go.com/Health/wireStory/pfizer-covid-booster-offers-protection-omicron-81620705) > Pfizer and its partner BioNTech said that while two doses may not be strong enough to prevent infection, lab tests showed a booster **increased by 25-fold people’s levels of antibodies** capable of fighting off omicron. Not level of protection, antibody titer. That 25X figure sounds dramatic, but I think it’s a poor way to express how effective the booster is. A booster simulates repeat infection, so with immunological memory from the first two doses, you’d certainly expect antibody titer to jump dramatically in the short term. But that in itself doesn’t tell you much. Longer term protection would be a function of _sustained_ higher antibody titer, and affinity maturation leading to _better_ antibodies. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [December 10, 2021, 12:02am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/3 "2021-12-10T00:02:06Z")
I recall a thread about this sort of language before, and while there were some holdouts who declared it to be nonsense, I think the general agreement is that an english statement that X is Y times smaller than Z means X = Z / Y. It’s the linguistic counterpart to Z is Y times larger than X (Z = X\*Y). So, 25 times less means divide by 25. Also agreed with @Riemann that what they’re reporting is a specific lab result and doesn’t translate into anything like “you are 25 times more likely to get Omicron than Delta” or “25 times more likely to be symptomatic/very sick/any other measurable real-world health condition”. ---
**Author:** ![Paul\_was\_in\_Saudi](https://avatars.discourse-cdn.com/v4/letter/p/b77776/32.png) [@Paul\_was\_in\_Saudi](https://boards.straightdope.com/u/Paul_was_in_Saudi)\ **Post date:** [December 10, 2021, 12:31am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/4 "2021-12-10T00:31:19Z")
> [@iamthewalrus\_3](#): > > So, 25 times less means divide by 25. So if the level of protection would have been 100 with the booster, then without it the level would be 04? Still seems like a roundabout way to say it. Thank you. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [December 10, 2021, 12:35am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/5 "2021-12-10T00:35:41Z")
Yep. I think it’s one of those language constructions that seems totally natural to some people and totally nonsensical to others. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 10, 2021, 1:41am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/6 "2021-12-10T01:41:32Z")
> [@Paul\_was\_in\_Saudi](#): > > So if the level of protection would have been 100 with the booster, then without it the level would be 04? > [@iamthewalrus\_3](#): > > Yep. Except no - because the 25X is not level of protection, it’s antibody titer! The two are absolutely NOT synonymous. If the **antibody titer** is 100 with the booster, it was 4 without. The news report doesn’t tell us how much more **protection** the booster gives. I’d expect that to be something more of the order of 2X, it’s certainly not 25X. And the 25X is almost certainly transient anyway. ---
**Author:** ![Snipe70e](https://avatars.discourse-cdn.com/v4/letter/s/51bf81/32.png) [@Snipe70e](https://boards.straightdope.com/u/Snipe70e)\ **Post date:** [December 10, 2021, 1:46am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/7 "2021-12-10T01:46:49Z")
Doesn’t mean a thing. You can not have anything 25 times less, That ain’t possable. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 10, 2021, 1:48am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/8 "2021-12-10T01:48:38Z")
> [@Snipe70e](#): > > You can not have anything 25 times less, That ain’t possable. It’s only impossible under one possible interpretation. The non-impossible interpretation is the one @iamthewalrus_3 has described above, and that’s obviously what it means. Once you have eliminated the impossible, whatever remains, however implausible you may personally feel it to be, is the truth. ---
**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\ **Post date:** [December 10, 2021, 1:56am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/9 "2021-12-10T01:56:38Z")
> [@Paul\_was\_in\_Saudi](#): > > Without the booster (or something) **protection is 25 times less.** Not 25% less. The graphic read 25 X less. > > What does this mean? It doesn’t actually _ **mean** _ a goddamn thing, in the circumstances. For it to be a meaningful phrase, there would have to be a third referent (e.g. _B is half as effective as A. C is one fiftieth as effective as A. Therefore C is 25 times less effective than B._) Now, there are some smarty-pants who will insist that 25 times _less_ effective means one twenty-fifth _as_ effective, and that language doesn’t work like arithmetic. This signifies one thing: that I’m sharing the planet with people who are wrong about things. I don’t have to _like_ this fact, but I have to accept that it _is_ a fact. ---
**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\ **Post date:** [December 10, 2021, 2:02am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/10 "2021-12-10T02:02:12Z")
> [@iamthewalrus\_3](#): > > It’s the linguistic counterpart to Z is Y times larger than X (Z = X\*Y). They’re also wrong about this. When Z is Y times larger than X, Z = X(Y + 1). ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 10, 2021, 2:06am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/11 "2021-12-10T02:06:36Z")
It bothers me, too, but it’s absolutely everywhere. We have to admit that this is the idiom and understand it whenever it’s used. If we don’t, we lose the intended meaning and what good does that do? ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 10, 2021, 2:07am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/12 "2021-12-10T02:07:23Z")
> [@kaylasdad99](#): > > Now, there are some smarty-pants who will insist that 25 times _less_ effective means one twenty-fifth _as_ effective, and that language doesn’t work like arithmetic. This signifies one thing: that I’m sharing the planet with people who are wrong about things. I don’t have to _like_ this fact, but I have to accept that it _is_ a fact. So to paraphrase, removing the bluster: (1) the meaning is unambiguous; (2) it’s not your preferred terminology. ---
**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\ **Post date:** [December 10, 2021, 2:22am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/13 "2021-12-10T02:22:04Z")
> [@Exapno\_Mapcase](#): > > We have to admit that this is the idiom and understand it whenever it’s used. If we don’t, we lose the intended meaning and what good does that do? Oh, I _understand_ it just fine. But I also hew firmly to my position that if they want to _intend_ something, they should learn how to _say_ it. ---
**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\ **Post date:** [December 10, 2021, 2:29am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/14 "2021-12-10T02:29:39Z")
> [@Riemann](#): > > So to paraphrase, removing the bluster: > > (1) the meaning is unambiguous; > (2) it’s not your preferred terminology. Of course it isn’t. Why in the name of heaven would I _prefer_ the terminology that’s _wrong_? ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 10, 2021, 2:32am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/15 "2021-12-10T02:32:48Z")
> [@kaylasdad99](#): > > Of course it isn’t. Why in the name of heaven would I _prefer_ the terminology that’s _wrong_ ? So to paraphrase, removing the bluster: ---
**Author:** ![DesertDog](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desertdog/32/11503_2.png) [@DesertDog](https://boards.straightdope.com/u/DesertDog)\ **Post date:** [December 10, 2021, 2:40am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/16 "2021-12-10T02:40:30Z")
> [@iamthewalrus\_3](#): > > I think it’s one of those language constructions that seems totally natural to some people and totally nonsensical to others. Put me in the nonsensical camp. _1/25th the protection_ makes much more sense to me than _25 times less protection_. 25 _times_ the protection for the other way around is okay. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [December 10, 2021, 3:00am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/17 "2021-12-10T03:00:11Z")
> [@kaylasdad99](#): > > This signifies one thing: that I’m sharing the planet with people who are wrong about things. Darn, you too eh? I thought I was the only one. Anyway. As noted. The 25 times is just plain meaningless as a metric of protection. As it is a booster shot it could simply be a measure of how good the residual vaccination protection is when challenged, and have no relation to the effect of the booster. Memory T cell capability over time is what will matter and of necessity that takes time and more effort to gauge. But journalists and media flacks love the appearance of providing quantitative information. And so they do. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 10, 2021, 3:19am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/18 "2021-12-10T03:19:56Z")
Idiom say, I couldn’t care less what you think. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 10, 2021, 4:41am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/19 "2021-12-10T04:41:42Z")
A problem with the “X times less” wording is that people who read that phrase have all different ideas of what it means, or think it is meaningless. So it fails to reliably convey useful information. But wait, it gets worse: Since that phrasing is so poorly understood, it may mean that the person who _wrote_ it that way doesn’t understand what it means (or what he’s trying to mean) to begin with. So when I see a phrase like that, I can’t be sure what the writer is trying to say. I tend to interpret a phrase like “X times less” to mean “one Xth as much”, providing that seems to make sense and seems plausible. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 10, 2021, 4:44am UTC](https://boards.straightdope.com/t/a-simple-math-question/955809/20 "2021-12-10T04:44:41Z")
> [@Riemann](#): > > Once you have eliminated the impossible, whatever remains, however implausible you may personally feel it to be, is the truth. I prefer the impossible. “The impossible often has a kind of integrity to it which the merely improbable lacks." – Douglas Adams [Next page](https://boards.straightdope.com/t/a-simple-math-question/955809.md?page=2)