How do I add a simple ranking system?

I'm about to add a very simple (hopefully) ranking system and I wanted to get some ideas on how to do it. I've never added anything like this (or multiplayer related functionality at all, for that matter) so I'm not really sure how to get started.

My game is really a single player game and there will be no interaction between players. All I'm planning on adding is a ranking system that read out "#X". Also worth mentioning is that it is a game for Android.

The game uses several variables that hopefully can be used to calculate this. The point of the game is to finish it as quickly as possible with as few restarts and jumps as possible. So I'm thinking that the number Time+Restarts+Jumps=Score (lower is better) can be used to create the list.

The problem is how to implement it. Can I create this using the multiplayer functionality in Construct? Do I need to use clay or similar? I also don't want the players to have to create a user or similar if possible, maybe just assigning a unique ID at the start of the game is enough.

Sorry about the messy post, I'm just thinking out loud. Please ask if something is not clear. Any input would be appreciated.

I suspect maybe Google Play Game Services may be the best solution, but as far as I can tell this is currently not working for Crosswalk. Starting to think I have to drop this feature all together. I have to admit it's a bit disappointing that something like this should be so hard to add.

Although Google Play Services is not supported outside of a browser, you could still use the multiplayer plugin and just store the information on your own server.

Thanks, but I don't have my own server and was hoping to avoid that as I don't really have the knowledge about it.

Would it be possible to store the score for example in a public Google Drive Excel sheet document and have that updated automatically and then display the user's rank in the app picked from that document?

Agan, just thinking out loud here