So this boils down to interpreting scatter charts.
Say you plot two normally-distributed numbers against one another. You get something that looks like this:
If instead you plot two d6 rolls against one another, you see this:
with sharp cutoffs because the d6 roll is bounded at 1 below and 6 above, and with a regular grid because the d6 roll is always an integer.
Various relationships between the variables can show up in the scatter chart
If Y is the sum of two d6 rolls, and X is the first roll, you see this:
You can think of this graph as being made up of various stripes:
The vertical green line is ‘every value the second die can roll, given that the first die rolled a 2’.
The diagonal orange line is ‘every value the first die can roll, given that the second die rolled a 4’.
Suppose that X = twice the first die plus the second die, and Y = twice the second die plus the first die:
Again the points form a grid, and again we can see patterns. Since the green line has 6 points on it and moves [up 2 and right 1] each step, we can see something that takes 6 discrete values and applies 2x its value to Y and 1x its value to X.
Now plot Bella’s scores against Liboulen’s:
This is a bit more complicated because there are three variables rather than two. But you can still imagine the same lines:
and you can disentangle the corresponding variables.
So this boils down to interpreting scatter charts.
Say you plot two normally-distributed numbers against one another. You get something that looks like this:
If instead you plot two d6 rolls against one another, you see this:
with sharp cutoffs because the d6 roll is bounded at 1 below and 6 above, and with a regular grid because the d6 roll is always an integer.
Various relationships between the variables can show up in the scatter chart
If Y is the sum of two d6 rolls, and X is the first roll, you see this:
You can think of this graph as being made up of various stripes:
The vertical green line is ‘every value the second die can roll, given that the first die rolled a 2’.
The diagonal orange line is ‘every value the first die can roll, given that the second die rolled a 4’.
Suppose that X = twice the first die plus the second die, and Y = twice the second die plus the first die:
Again the points form a grid, and again we can see patterns. Since the green line has 6 points on it and moves [up 2 and right 1] each step, we can see something that takes 6 discrete values and applies 2x its value to Y and 1x its value to X.
Now plot Bella’s scores against Liboulen’s:
This is a bit more complicated because there are three variables rather than two. But you can still imagine the same lines:
and you can disentangle the corresponding variables.
Thank you very much! This is very clear!