Earlier quoted context omitted.
You might want to check your pagespeed insights to verify that. I noticed that our pagespeed score was very poor (due to google using new methods to calculate those scores). Adding webp versions of images reduced the size of those images significantly, and brought our pagespeed scores back to more reasonable values in google's eyes.
It’s unlikely that WebP was what helped there, but rather more lossy encoding (presuming it was JPEGs you were replacing). Yes, WebP is smaller for a given perception quality level, but it’s typically not that much smaller; you could have achieved results almost as good by reencoding to the same perception quality as you used on the WebPs but still as JPEGs.
So in this case webp was a third of the size of a jpg. Typically, webp will be about 30-50% smaller than an equivalent jpg, which is a pretty significant amount.