I Have an idea, don't know how to implement it.

[Kethguard]

So i was thinking of running the premade WotC adventures starting with Hoard of the Dragon Queen with my group. My plan is when we finish one adventure, we start the next one and my players would be the kids of the last campaign. I was going to allow them to pass on a few of the old characters stats (if your dad had a high Str, you have one too) but a friend of mine pointed out that this could lead to some very OP players. i'm looking for advice on how best to pull this off as i really like the idea of a generational campaign.

[Specter]

Indeed. What is easier to pass to the next generation is skills and tolls proficiencies. If both kid and dad are spellcasters, you could allow some kind of Family Magical Secret too.

[Sigreid]

Does your group roll or point buy? If they roll, you could allow 5d6B3 for their parent's best stat to give them an edge at that attribute without everything going too crazy.

[Axorfett12]

I agree. Passing skills is easier than ability scores. Consider the background of the old characters and maybe add a skill or tool from those to the new characrers.

[brainface]

Indeed. What is easier to pass to the next generation is skills and tolls proficiencies. If both kid and dad are spellcasters, you could allow some kind of Family Magical Secret too.

I think you could go crazy with this with sort of a mini-feat.

The Dailsons can cast hellish rebuke once day, because they're just that mean, and rumors of diabolists in the bloodline.
The Carlyles all know elvish and can speak with wolves.
Jim here's the son of that wizard that saved the world 30 years ago. He doesn't know a bit of magic, but that weird crow that follows him around does.

Alternatively, something like background features--if your mom was the highpriestess of Pelor, people are going to remember that. If she was the highpriestess of Lloth, well, people are going to remember that too. ^^ Favors you can call on, extra languages, minor ribbon features--all the standard backgroundy stuff?

[Kethguard]

I gotta say, i love these ideas. The extra d6 to a stat roll gives a bonus while still being unique to that character, and the background ideas bring in lots a story ideas I can use as DM.