Does saving MP4s in a smaller output file size reduce quality?

[WTWASP]

Can anyone tell me if saving or "converting" a video to a smaller output file size than the original - but without modifying or reducing any other characteristics of the video - reduces video quality?

I tried Googling this but instead of just answering that question, the stupid search engine gives me a bazillion sites telling me HOW to reduce file size (which I already know how to do a million ways from Sunday!) - what I DON'T know is if reducing the file size will compromise the video quality? Since the conversion/saving process takes several hours on my old computer, I really cannot just do trial and error and find out that way. I simply do not have enough time left on what remains of my life to do that, lol.

I have worked out a formula for determining what a "good" file size ought to be for the aspect ration and duration of a video. I take the duration of the video and multiply it by either 12 (for 1280x720p), 15 (for 1600x660p), or 18 (for 1920x1080p). So let's say it's a 2hr movie ; if I wanted it in 1920p, I'd multiply 120 minutes x18 and get 2160 MB as the target file size. A 1280x720 aspect would be 120 mins x15 for 1800 MB, etc. Avidemux also ultimately tends to make the final product about 100-200 MB larger than the target size.

This was a great system, but now I am faced with running out of disk space and I cannot afford to buy bigger drives or get additional ones to add to the array. So I thought maybe modifying my "formulas" would help, by rolling back my "12/15/18" calculations to "9/12/15"?

My concern is if I go back and re-save my projects to the smaller file size - i.e. making that 1920x1080p 2hr movie 120mins x 15 = 1800MB - all while NOT changing any other parameters or settings (keeping aspect ratio, etc), will I lose video quality (noticeable or otherwise)?

I have noticed some videos of a 1920x1080p aspect ratio being no larger than 500 MB and yet still looking very crisp and clear - so that has me confused and uncertain.

I read somewhere "bitrate" plays a major role in determining quality versus filesize, but I am not entirely sure what that is or how it really works, nor am I looking to mess with that anyway - I just wanna keep my vids the same quality they are, but reduce the amount of "real estate" the file occupies on the HDD. 

So, can anyone give me a simple answer to the simple question of :
"Does saving MP4s in a smaller output file size reduce quality?",
since Google and other search engines cannot seem to savvy/answer the question?

Thanks.

~ W

[eumagga0x2a]

what I DON'T know is if reducing the file size will compromise the video quality?

When you use a lossy codec like MPEG-2, Xvid, H.264, HEVC, VP9 (the last three in principle allow lossless operation when quantizer is set to zero at the cost of very low compression rate and very slow operation), you lose quality each time you re-encode, i.e. even if you increase bitrate.