One year after another in the rolling rankings

[mrzz]

Ok, as I recall a lot of good posters making a bit of a confusion when discussing the rolling rankings, I opened this thread just to put a simple example which I hope will shed some light on the subject. This won't be any news to people like El Dude or GSM, but I hope it will be useful for some.

Let us simplify things to start with. Suppose we only have four tournaments (the slams) through the year. Suppose in 2015 player D have won them all, so he finished the year with 8000 points. Player M was the runner up in all four, so he finished with 4800 points. Player R had a lousy year and had zero points.

Now come 2016. Common belief is that player D will have a tougher time just because he has a lot of points to defend, but it is exactly the opposite. Suppose he, on 2016, wins the first, falls in the semis in of the second, is runner up in the third and wins the fourth tournament. In this case, his points would evolve as:

8000 after the first, 6720 after the second, 5920 after the third and 5920 after the fourth.

Yes, he has less points than 2015, as he could not defend them all, but he is not racing against his 2015 self, but rather against the others. For example, let us suppose it was player R who had his 2016 campaign instead of him, his points would evolve as:

2000 after the first, 2720 after the second, 3920 after the third and 5920 after the fourth.

Their points would coincide at the end of the year (naturally), but player D has spent the whole year (2016) with more points, thanks precisely to the 2015 points.

This finishes the argument, but just to illustrate more, let us bring player M back to the fore:

So, suppose player M has been runner up in the first tournament of 2016, runner up in the second, won the third and was again runner up in the fourth. His points would evolve as:

4800 after the first, 4800 after the second, 5600 after the third and 5600 after the fourth. This campaign would put him as #1 after the third tournament if it was player R (the guy who had nothing to defend) who had the the W SF F W campaign, but would never put him ahead of D, which, as stated above, could stay in front thanks to his 2015 points.

So, when you have a lot to defend, it is hard to keep all your points, but the more you have, the easier you stay ahead of the others.

 

[Kieran]

Good stuff, mrzz. It's one of them knotty things to explain to people, why Player A dropped in rankings after winning the event, but Player B went up. It happened at Wimbledon in 1999, Sampras beat Agassi in straights in the final, but fell to second and Dre became #1. It's the cumulative thingy, and it takes some explaining...

 

[mrzz]

Your post made me finally understand why people have this inverted intuiton about the rankings. It is because of what happens at the fall off week. As, precisely on that week, the player who has a lot to defend may lose a lot of points and thus have a sharp fall, people assume that the points to defend are a hindrance in general, and that they will keep "pushing" the player down.

As shown above, it is precisely the other way around. Another example, focusing on the fall of week:

You have two players, D and M, D has 5000 points while M has 4000 points. In this week player D has 2000 points to defend, while player M has 0. It seems that D's 2000 points are now more a hindrance than a gift, and player M has an advantage because of that. In fact, these 2000 points have helped D to stay ahead of M, and the only "problem" is that they are "older" than M's points.

D's actual problem is not those 2000 points. It is that in the whole year after the week he made those points, he only scored 3000 points (5000 - 2000), while M scored 4000 (4000-0) in this same period. So D's real problem is the fact that he was out-scored in the one year minus one week period leading to this week.

That is, if you want to keep ahead, you need to keep scoring points. Your points always help, but they don't help forever.

 

[britbox]

Nicely put mrzz... and as you have indicated regardless of "defending of points" you are still ranked exactly where you should be based on the last 12 months of results.