At startup, the wires to the Ducati's battery will initially draw in the neighborhood of 200 amps. That's a lot. This is for a stock engine, a higher compression engine will draw this current for a longer period of time.
If you crank it constantly for say a half a minute, and do this several times in a row without letting the motor and wiring cool down, you're going to get overheated wires, even if all of your connections are good. When the wires get hot enough the insulation will start smoking.
Thats why Owners Manuals recommend that you crank the starter motor for only five seconds at a time, with a ten second wait in between tries.
If the wire connections are loose or corroded, they are an additional source of higher resistance and heat. If a battery connection has a small resistance of say 1/2 ohm, a typical starting current of 45 amps generates over 1,000 watts of heat, more than a toaster. The initial draw of 200 amps through a 1/2 ohm resistance at a corroded or inadequate contact area connector is 20,000 watts. That's why connectors get overheated.
As the starter cables age, the tinned and crimped junction between the wires bundle and the connector itself corrodes and becomes the point of high resistance. So a replacement starter cable kit that uses a larger gauge wire is usually a good solution to starting problems. Also, look for replacement batteries having terminals that offer a large contact surface that will make a more secure connection with your cable terminal configuration.