The share price is _not_ supposed to drop after an IPO. The insiders still have a lock-up of 6 months, so a lower price would be bad for them. Moreover, the investors in the IPO also want some upside. In the end, the IPO price is a negotiated price that takes into account a lot of considerations. Once public, the price is dictated by the last trade.
And "smalltime" investors shouldn't invest in IPOs because of the so-called winner's curse.