Points Behind does tend to break down, however, when there's a significant disparity in points contested. For example, a 60-51 team (.541 win rate) is only 0.5 games behind a 10-0 team. You can see it in other divisions with much larger disparities- Blitz (Div B) is near the bottom by Points Behind when it's at the very top by success rate (it's just only contested about 20 points while everyone else is way ahead).
So the meaning of the comparison changes a bit. If Team A and Team B have played about the same number of games (in a league where there's a consistent set number of games at the end of the season) and neither of them is ahead or behind, that means they'll end up at the same spot if they just match each other's pace. If Team B is 5 games behind, that means- in order to catch up to Team A- it needs to not only match pace but also flip 5 losses into wins on top of that (or sweep Team A in a 5-game series; basically you need 5 "extra" wins from B and 5 "extra" wins from A).
To model this a bit further (assuming an 82 game season in loving memory of Kevin Durant's sense of pride); Needed to Catch Up assumes that Team A plays the rest of the season at a .500 win rate and reflects the record Team B needs in its remaining games to finish with the same overall record
Team A Initial Team B Initial Games Behind Needed to Catch Up
20-20 20-20 0 21-21
20-20 19-21 1 22-20
20-20 10-30 10 31-11
25-15 20-20 5 26-16
Now let's shake things up a bit and assume that Team A performs at 30/42 after these initial games
Team A Initial Team B Initial Games Behind Needed to Catch Up
20-20 20-20 0 30-12
20-20 19-21 1 31-11
20-20 10-30 10 40-2
25-15 20-20 5 35-7
So it's pretty simple here to see what Games Behind means when calculated at the stage where both teams have the same number of finished games- "In order for Team B to catch up to Team A, they need to not only match Team A's record in all following games but also flip (Games Behind) Team A losses into Team B wins"- if you're 1 Game Behind, 30-12 has to become 31-11 (12 - 1 => 30 + 1); 10 games behind it becomes 40-2 (12 - 10 => 30 + 10).
But now let's see how it works out when there's a difference in games played (going back to .500 expectation):
Team A Initial Team B Initial Games Behind Needed to Catch Up
22-20 20-18 0 22-22
22-20 20-20 1 22-20
22-20 19-21 2 23-19
22-20 10-30 11 32-10
22-20 0-30 21 42-0
30-20 20-20 5 26-16
30-20 20-10 0 26-26
41-41 10-10 0 31-31
41-41 10-0 -5 31-41
And now with .750 expectation:
Team A Initial Team B Initial Games Behind Needed to Catch Up
22-20 20-18 0 32-12
22-20 20-20 1 32-10
22-20 19-21 2 33-9
22-20 10-30 11 42-0
22-20 0-30 21 gg no re
30-20 20-20 5 34-8
30-20 20-10 0 34-18
41-41 10-10 0 31-31
41-41 10-0 -5 31-41
You'll notice that there's not a clean transition in terms of the win rate needed to catch up. Looking at just the top entries in these last two, the switch from .5 to .75 for A makes for a switch from .5 to .727 for B (which would be even less pronounced had there been a greater difference). Notice that .727 = (4 * .5 + 40 * .75) / 44. In other words, the win rate Team B (with 0 games behind) needs to maintain to compete with Team A is actually a weighted average- (# of extra games A has contested relative to B) * (.5) + (# of remaining games for A) * (A's win rate). You do all the loss-to-win flipping (which still works here, as you can see above) after that.
This is a pretty simple phenomenon- game difference doesn't compare teams based on win rate but rather based on (wins - losses); I could actually just redo this analysis as a ranking by (wins - losses) since that's essentially the same thing. This is why a 40-30 team isn't "behind" a 10-0 team or a 20-10 team; as far as the games behind stat is considered, these teams are identical. But that also means a 45-35 team is just as good as an undefeated 10-0 team by this stat, and a 2450-2430 team is superior.
I could perhaps resolve this issue by instead considering the success rate a clan would have to maintain to "catch up" to the clan that's currently contested the most points, but that would still give a 10-0 team the same rank as a 40-30 team in certain cases.
Edited 7/7/2016 10:18:56
