I think it is mostly psychology via ratios. For example a number of institutional investors go by EPS. If shares in this industry are trading at a 20 x multiple and your companies shares are trading at a 10x multiple, you can try to buy back shares to get your multiple higher. Again, just one example but I'm sure the boards of directors, who are elected mainly by the institutional investors determine what will multiples and ratios they need to hit to be in the magic zone for algorithms and also investor psychology.
Buybacks get you a higher EPS number, I don’t see why would you expect the multiple to increase. But it’s true that there are many effects in play: signaling, offer/demand of shares, apparent improvement in ratios vs peers...
