ffmpeg -i input.gif -movflags faststart -pix_fmt yuv420p -vf "scale=trunc(iw/2)*2:trunc(ih/2)*2" output.mp4-codec:v libx264 -preset slow -crf 23
Increase "crf" for a smaller file, decrease it for better quality.
Crying can be therapeutic, I am told.
I put 100KB for mine.
Also, you can install the Firefox extension called Video Image Block. It's a real data saver.
Lastly, look up bandwidth hero. Can help compress images on a server before it gets to you. I'm using free heroku tier for mine.
It's not surprising someone would trade off bandwidth for this.
I also think MP4 is better, it just makes sense to me why someone would use a GIF.
I can't think of a single rational reason to use a gif rather than an mp4 for something like this. The reason it's done is because some people are old dogs who can't learn new tricks. There is a good reason sites like reddit will transcode user-uploaded gifs to either mp4s or webms (the later of which isn't supported by Safari, but mp4 has no such problem.)
If you are writing the raw video tag yourself and all the appropriate attributes, it is still not as easy as an image tag.
If instead you're screwing the users just to save the webmaster some minor hassle, you should sack the webmaster.