Why do we -1 the parameters in the Beta and Gamma Distributions?

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The Beta distribution has two parameters, α and β:

P^(α-1) * (1-P)^(β-1) / B(α, β)

Looking around online, I see it has something to do with degrees of freedom. There seems to be [an accepted answer to this on Stack Exchange](https://stats.stackexchange.com/q/262956/206342) but I was not able to understand that answer.

So, ELI 5 why we subtract one from the parameters.

Thanks!

In: Mathematics
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