Standard of/for success

Is this sentence natural? Would a native speaker phrase it this way?

His standard for/of success is much higher than mine.

Not everyone has the same standard for/of success.

Is “measure of success” or gage of success” used ever like this?
That’s not a measure of/for success/gage of/for success. Just because you have 2 cars does t mean you’ve succeeded.

Thanks

ps

Which is correct?

Would a native speaker phrase it (this way/as such)?