An interesting (and more accurate) version would involve the correlation between margin of victory and difference in rating points. Saying Team A is Number 100 and Team B is number 200 doesn't tell you anything about the difference in skill (and therefore, margin of expected victory) between these 2 teams.
And as it turns out the difference in FIFA points is also not that strong of a predictor of margin of victory (in all matches, including draws, there was a correlation of 0.256
, compared with Elo's 0.481
for my system). A team ranked at #100 will tend to beat both a team ranked at #150 and one ranked at #200, but there will not be a large difference between those two results.
This point is perhaps better illustrated by plotting the relationship between points- and goal-difference across ranking systems. I grouped matches together depending on the teams' points difference (rounding to the nearest 50 points, so one group includes all matches where teams were separated by less than 25 points; the next group includes matches where teams were separated by 25-75 points, and so on...) and evaluated the actual results in each group.
In the charts below, the solid black line represents the average goal difference within a group. For example, in the FIFA chart, in matches where both teams were very close (separated by less than 25 points, follow the vertical line from the 0 in the x-axis), the favourites scored on average 0.09 more goals than the underdogs. In matches between teams separated by around 200 points (175-225) the average goal difference increased to 0.88, and so on. We can notice that on FIFA's chart this line becomes quite flat, which means that a wider points difference will not necessarily return a wider goal (skill) difference. In the other models the trend is clearer.
As a dispersion analysis (to measure how much amplitude there is within each group of matches), the solid black line is surrounded by dashed lines. These are approximations to quartiles.* Let's say that, on the FIFA rankings, there were 600 matches where teams were separated by less than 25 points. I take the 300 "worst" results (from the favourite's perspective), average those goal differences and plot that average on the yellow line. I repeat the process for the 300 "best" results, average those goal differences and plot that average on the blue line.
The red/green dots come from a similar approach (averaging the goal difference in the best/worst 10% of matches).
Ideally you would want the distance (height) between dots on the same column to be as small as possible. This would mean that the points difference between teams is an accurate reflection of their skill difference (i.e. you wouldn't see many large wins in matches between teams ranked closed together, or close results in teams ranked far apart).
A final word on scales. The x-axis ends on different values for different rankings because each one operates on a different scale (e.g. Germany and San Marino are separated by ~1700 points on FIFA's ranking, ~1300 on Elo's and ~900 on Cubic). Effectively the x-axis stops at the point where fewer than 10 matches have been played within a group (e.g. on FIFA's case, 16 matches have been played between teams with a points difference around 1200 (between 1175 and 1225), but only 6 matches have been played between teams with a points difference around 1250 (between 1225 and 1275), so the chart will stop at 1200).
*The mathematically-minded will recognize that as goals are a discrete variable with a small amplitude, using the strict definition of quartiles would be of limited use when comparing groups.