The driven element of a yagi type beam is a dipole of some sort. It may be 'folded', or loaded (traps), but it's typically a 1/2 wave length, or dipole.
As other elements are added to the driven element, director(s), and reflector(s), the input impedance of the driven element is lowered. Depending on the number of 'other' elements, the input impedance can get down to something around 20-30 ohms. Depends on the number of elements, their spacing, (and at times the color of the sky I think). That's why a gamma (or beta, or delta) match is then used, they tend to raise the input impedance back to something around 50 ohms. Feeding a multi-element beam directly can still be done but usually a balun is needed to get that 50 ohms back (but then you may not consider it directly fed anymore).
There is no 5 dB difference between matching systems, that's about the only B.S. about the whole thing (unless it's MY antenna, and MY antennas are always 5 dB stronger than anybody elses! You believe that too, right?).
Ain't this electronic @#$% fun?
- 'Doc