So, reading this, I see the following specs:
I want to track popularity of blogs. This is accomplished by comparing their aggregate "likes" or whatever (retweets, etc) over a 48 hour period to their "normal" level.
I want to update my current count of likes, retweets, on a configurable periodic interval.
I need to be able to compute the effect of likes, retweets, etc independent of each other.
Seems the simplest way would be to use your third schema. It still allows you to collect all stats simultaneously or independently. The only effect would be if independent, there will always be some window of time where your current rankings doesn't reflect the true ranking while if simultaneous, your rankings just lag the "truth" by at most the update rate.
Anyway, then, you can periodically run a query for each post_id, compute the fb likes metric over the previous 48 hours + tweets metric over the previous 48 hours, etc, and use that to update your ranking.
Ultimately, it comes down to use and architecture.
Architecture
Does the system handle "any sport"? Is the idea that you put on your architecture astronaut hat, and build a generic system that can handle any future type of sport that may not even exist today?
If so, obviously having dynamically-named tables is a huge pain, so it would make sense to have a schema that supports n sports, if required.
That said, I have a very strong bias against this approach: this is almost always more work and leads to poorer results. Making a separate UI, schema, etc, for each sport will ultimately lead to better user experience and easier to maintain code, even if it does mean some superficial amount of duplication (how to avoid/minimize this is a separate question).
How do you handle players that play multiple sports? Do they get two entries (eg, you treat as different people) or are you trying to do something specific with them?
Use
So let's assume you don't do sports dynamically (eg, if someone wants to add a new sport, it requires development effort to add it).
Is there ever a time where you're displaying players (or any other object you mentioned) from more than one sport at a time?
I could see this for a search function, where you could search by player or team name (regardless of sport), but beyond that I can't imagine many use cases.
If you never need to do this, then your approach is perfectly fine. You can stop reading here.
Alternative Schemas
Views
I'm a fan of KISS. In 15+ years of software development, I continue to fall back to the philosophy "build the simplest thing that works".
So my initial reaction, assuming a cross-sport search function is really the only use case, is to create views:
SELECT PlayerName, 'NFL' as [Sport], TeamName FROM NFL_Players JOIN NFL_Teams ...
UNION
SELECT PlayerName, 'NHL' as [Sport], TeamName FROM NHL_Players JOIN NHL_Teams ...
UNION ....
Of course, if you add a new sport, you have to add to the view. It may also be useful to include other common information but really that's dependent on what needs to get shown.
I'd try to keep all the sport-specific stuff in the View definition, so the search code doesn't need to have much or any specific code (besides maybe knowing how to link to /nhl/players/player-name vs /nfl/... or however your app does that).
Table Inheritence
Table inheritance can work, but is pretty complex. I don't have a ton of experience with it, and in fact, I think every time I've been involved in evaluating it we ended up doing something simpler (like I'm suggesting here).
So personally, I have yet to find why this would be useful, but maybe there is a convincing use case (that I don't know of) that justifies the complexity (eg, Table inheritance solves the use case better than any other solution).
Separate tables for sport-specific attributes
You could do a single players table which has attributes common to all players of all sports, and then another set of tables like nhl_players_details that contains a playerId and columns with additional info on the player. If there are a ton of common attributes, or you have many uses of "all players from all sports" then this may make sense.
Key value pairs for sport-specific attributes
Completely alternative approach: have a players table (again, with common attributes like name) and then a player_data table that has PlayerId, Sport, Attribute, Value. The attribute names entered would be sport-specific. This allows you to essentially add new attributes without modifying the schema (your code would still have to know to load/display them of course). The drawback is you lose some integrity: value would typically be a string field, so your app code would have to be resilient and handle potential failures converting the string value to a specific data type (like integer).
This concept can of course apply to Teams, Games, etc.
Best Answer
Any thing ("Entity") that can exist on its own, independently of anything else, should have its own table.
User: id, name, hashed_password, join_date, birth_date
Group: id, name
Relationships between things require generally require "linking" tables.
Post: id, user_id, group_id, post_date, post_title, post_content
The key to success is proper indexing of any field where you join between tables or on which you filter results.
Also, consider using a dummy (non-NULL) Group value for posts to a user's own "wall" - NULLs are often not included in indexes, which will make your queries for these posts run [far] slower.