I have owned Topaz for over 10 years and very rarely does he give passes despite daily visits. I believe he is notorious as being one of the stingiest divines! Xanthos is much more reliable so I don't think Topaz is at all similar.

wait sorry this doesn’t answer your question, but what do you mean by this? If more people in 1 day visit a specific Xanthoa, that Xanthos is less likely to give you a HOP?

Yes, there's only one player chosen per each Xanthos. At least that's what I keep reading in the Forums.

I don't think Topaz works the same way as Xanthos. because you get the Topaz passes immediately. there would be know way to base it off how many people went to that topaz in the day. you get the xanthos hop the next day

He's stingy to the point that across 3 servers in 10 years I don't think I've gotten more than 10-20 drops from him. That's perfectly normal. I had a Topaz on here and on the US server drop in the last month and it shocked me to the point that I took SC's and sent them to other ppl

Each Xanthos is essentially an individual lottery, that you enter into by stroking him, and where the prize is a HoP. At the start of each day, every Xanthos will award one HoP to one random player from among those who stroked him the previous day. The more other players who stroked him, the lower your chances of being the one selected to "win".
Your best bet to win the HoP is to find a Xanthos that's not stroked by many other players on a regular basis. Keep track of which ones give you HoPs often, and then make the five most generous Xanthí your regular ones.

Topaz is mostly good for collecting equus. I still dont think my second one has ever drop passes. I won his mom my second emerald from ascent. I think i bought first because she was cheap and pretty. Im collecting all the gemstone but if i had money to buy a pack i would get jade.

I always keep the messages from Howrse that tell you you stroked a Xanthos and won the HoP. I choose 5 of those for the next round.
Also: a lot of players have links to Xanthos (and the other community horses) on their personal page. I would not choose those from the most popular players, because chances are that many people do the same . And that, indeed, diminishes your chances.