Someone needs to come up with a better unit for antenna efficiency. Which non-expert can understand how much -3.5dB and -1.25dB differ?
1. A difference of 3 in dB means times 2, a difference of 10 means times 10.
2. Because dB are in logarithmic scale adding dB multiplies the effect.
3. Negative numbers work the same but with loss instead of gain.
Thus a 3 dB gain antenna will double your signal strength while a 9 dB antenna will make it (9=3+3+3) 8 times stronger (8=2x2x2). Another example: 23 dB is a 200 times gain (23=10+10+3).
How can this be right? Aren't you kind of fudging it a little?
Here's my train of thought:
First I was thinking "What the hell is going on with your math? There's no clear factor to turn base 2 into base 10 what the hell. How can what you say be true? How does this work?"
My next thought (based on your incorrect statement) was, oh, they didn't choose base 2: they chose every 3 to be another factor of 2 - so let's see why that works, why +10 is the same as * 10 if every +3 is * 2. Well, you can get to 10 by going 3 + 3 + 3 + 1 and you can also get 10 by going 2 * 2 * 2 * (1.25) = 10.
Okay, so if every +3 converts to * 2 then why exactly does the last term, +1 convert to * 1.25?
I thought, and thought about it. I couldn't make it work, based on your rules. So I checked. And the answer is it doesn't: 2^(1/3) isn't 1.25 as we would expect, it's 1.2599. That might seem "close enough" but I think it's not exactly how you say and your statements are misleading.
Thus 23 dB isn't 200 times stronger as you state (23 = 10 + 10 + 3), it's only approximately 200 times stronger. 200x stronger is 23.0103 dB, and 23 dB is 199.52 times stronger. [1]
While it's useful, and the error is pretty small, it doesn't help for those of us used to thinking in terms of bitfields or something that converts quite exactly.
It's definitely a very useful mental estimation trick though!
[1] which I checked with an online calculator here - https://www.rapidtables.com/electric/decibel.html (first I entered a level of 200 and clicked the top "convert" button, then I entered a dB of 23 and clicked the second "convert" button)
In any case, I never said that you get 100% accurate results; if you want accuracy then you should use your calculator (or your logarithmic ruler); but why use a calculator when you roughly want to understand how much a 15 dB gain would be?
Finally, there's a nice way to find out how much 1 dB is with the mentioned rule: Notice that 1 = 10-3-3-3 thus it's 10/2/2/2 = 1.25 so 1 dB is approximately 1.25 gain as you said :)
10^(3/10) = 1.995262315
Try graphing that with a linear scale, there won't be a lot to see I wager. It's true that it does take a little time to familiarize oneself with non-linear units at first (especially if one wants to add or subtract them for instance) but they have their uses. For measuring a signal they're clearly appropriate.
The gain in dBi is 10 * log10(linear gain), so the linear gain is 10^((gain in dBi) / 10). So 5 dBi is a gain of 3.16, and 6 dBi is 3.98. Log rules mean you can just subtract, so the difference is 1 dBi, meaning a 6 dBi antenna is 1.25 times more powerful than 5 dBi.
I'm not sure what alternative units you could use, because log units are more natural. Joe consumer can understand "6 dBi is 1dBi better than 5 dBi," he doesn't need to know the details any more than he needs to know exactly how much faster his car will go with 10 extra horsepower. It's the relative comparison that matters (more horsepower == more speed) and using dBi makes those relative comparisons simpler.
The downside to using dBi is that being a number related to a theoretical antenna it is higher and welcomed by advertisers: if you take out your router external antenna having a gain of say 2dBi to swap with a higher one that gains 9dBi, you don't get a gain of 9dB, but vendors still can write 9dBi on its box.
For home devices, usually smaller dipoles or longer collinears are used because they are the best choice in a scenario where the user needs to cover his/her house and not the neighbors (just keep the antennas pointed up or down, not sideways). There are many other kinds such as slotted, grid, helical, sector, patch, Yagi, etc. each one with its best use case. Building them is also fun and cheap.
Even if you don't understand log scales and you're trying to decide what to buy it's literally just bigger numbers = better.
Understanding log scales is easy. Understanding how a decibel rating on an antenna relates to your network-connected lawn ornament's expected range in meters is a whole different kettle of worms, and bigger numbers are better when they're range but not when they're cost.
-4 is not so good. -1 is very good.