Increasing sensitivity for voltage measurement
As you have discovered, the resistance of a 20 mm sphere of metal is very low. This combined with contact resistance will make it impossible to use a resistance measurement technique to differentiate between steel and brass. A much more reliable approach would be to detect ferrous balls and switch the diverter when these are detected. Let everything else go undiverted.

Rockwell Automation's Principles of Operation for Inductive Proximity Sensors gives a good explanation of practical use and operation of these devices.



Figure 1. A basic inductive proximity switch setup.



Figure 2. Response as a function of target distance.



Figure 3. Correction factors for steel and brass.

Figure 3 is the interesting one. It shows that the sensor can discriminate between steel and brass simply by increasing the distance. In your case you would:


Mount the sensor over the track looking down at the balls passing below.
Move the sensor in until it detected steel balls reliably.
Confirm that it doesn't react to brass balls.








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 4. Full circuit.

Figure 4 shows the addition of a timer with an (adjustable) off delay to hold the solenoid on for long enough that the ball has been diverted before switching back to default position.


Sensors are available to operate from 10 to 24 V DC. 
PNP types switch a load that is connected to ground and are sometimes referred to as "sourcing" type since the current comes from the switch.
NPN types switch a load that is connected to V+ and are sometimes referred to as "sinking" type since the current comes from somewhere else but is "sunk" to common through the switch.
Pick PNP or NPN to suit your timer.