Pressure = Force ÷ Area
In this case, since the area is circular, we can rewrite the equation as:
Pressure = Force ÷ pi*r^2
Decreasing the diameter by half is the same as decreasing the radius by half.
We can replace all constants with 1 to compare the relationship between the two scenarios.
Original scenario with original area wood:
Pressure = 1 ÷ 1^2
Pressure = 1
Scenario with 0.5 radius of original scenario:
Pressure = 1 ÷ (1/2)^2
Pressure = 1 ÷ 1/4
Pressure = 4
This confirms that your guess of 4x the pressure is correct.
So as can be seen by the relationship, pressure for circular area is inversely proportional to the radius squared.