Step 1
win% = W / (W + L)
1/win% = (W + L) / W
1/win% = (1 + L/W)
win% = 1 / (1 + L/W)

Step 2
Home Site Advantage is 54%, or 54/46 W/L or 46/54 L/W

And so:
since win% = 1 / (1 + L/W)
home_win% = 1 / (1 + L/W * 46/54)

So, if you are a .600 team at a neutral site (and .400 losing percentage), then:
home_win% = 1 / (1 + .4/.6 * 46/54) = 1 / (1 + .568) = .638 

That's a gain of +.038, very close to simply adding +.040

And if you are an .800 team?
home_win% = 1 / (1 + .2/.8 * 46/54) = 1 / (1 + .213) = .824

In this case, a gain of only +.024