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Old 03-16-2015, 07:27 PM   #1
country flag Geolith
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Default Average Points at Grand Slams (Open Era)

With courtesy of Litotes numbers and tables on total accumulated GS points i've made a few tables to show how far players have progressed in the respective GS tournaments on average.
What i've done is dividing their total points by the number of appearances to determine the stage they've reached on average.

Please take into account that the points grow exponentially and the arithmetic mean doesn't represent the true average, but will always appear to be higher.

Notes:
** -Player competed in GS before OpenEra already and his average points might be biased because of low number of appearances in his peak years.
* -Player didn't compete often enough to reflect a lifetime performance.
Pts -Average Points
Stage -Average Stage
App -Appearances
Rank - Total Points Ranking
Active Players in bold

I only included results until the first "4th round average".

As of 16th March 2015:

Australian Open
Code:
Pts	Stage		Name		Tot Pts	App	Rank
1202	F	Guillermo Vilas *	6010	5	11
1129	SF	Andre Agassi		10160	9	3
1070	SF	Arthur Ashe **		4280	4	18
879	SF	Roger Federer		14060	16	1
844	SF	Novak Djokovic		9280	11	5
835	SF	Mats Wilander		8345	10	6
827	SF	Stefan Edberg		10750	13	2
781	SF	Ken Rosewall **		6250	8	10
778	SF	Ivan Lendl		9335	12	4
758	SF	John Newcombe **	6820	9	8
695	QF	Pete Sampras		7640	11	7
687	QF	Johan Kriek		5495	8	13
647	QF	Rafael Nadal		6470	10	9
595	QF	Jim Courier		5945	10	12
552	QF	Yevgeny Kafelnikov	4415	8	17
506	QF	Andy Murray		5060	10	15
500	QF	Marat Safin		4995	10	16
477	QF	Boris Becker		5245	11	14
388	QF	Jo-Wilfried Tsonga	3100	8	27
376	QF	Andy Roddick		4140	11	19
331	4R	Pat Cash		3645	11	21
Wimbledon
Code:
Pts	Stage		Name		Tot Pts	App	Rank
1334	F	Björn Borg		12010	9	5
1098	SF	Pete Sampras		15370	14	2
1097	SF	Roger Federer		17555	16	1
917	SF	Rod Laver		4585	5	4
891	SF	Boris Becker		13365	15	6
859	SF	John Newcombe **	6010	7	16
810	SF	John McEnroe		11345	14	8
804	SF	Novak Djokovic		8035	10	9
797	SF	Rafael Nadal		7970	10	13
706	QF	Andy Murray		6350	9	7
685	QF	Stefan Edberg		8215	12	3
666	QF	Jimmy Connors		13995	21	10
595	QF	Ken Rosewall **		3570	6	27
528	QF	Goran Ivanisevic	7915	15	11
511	QF	Andre Agassi		6640	13	12
472	QF	Ivan Lendl		6605	14	15
446	QF	Andy Roddick		5355	12	14
423	QF	Pat Rafter		3805	9	24
368	QF	Roscoe Tanner		4045	11	20
360	4R	Pat Cash		3955	11	22
US Open
Code:
Pts	Stage		Name		Tot Pts	App	Rank
1088	SF	Pete Sampras		15230	14	2
969	SF	Roger Federer		14530	15	3
914	SF	Novak Djokovic		9140	10	7
880	SF	Ivan Lendl		14080	16	4
851	SF	Jimmy Connors		18720	22	1
778	SF	John McEnroe		12450	16	6
736	SF	Rafael Nadal		7360	10	8
734	SF	Ken Rosewall **		5135	7	17
700	QF	Andre Agassi		13295	19	5
698	QF	Björn Borg		6285	9	11
660	QF	John Newcombe **	4620	7	19
553	QF	Stefan Edberg		6630	12	9
523	QF	Andy Murray		5225	10	15
484	QF	Pat Rafter		4355	9	22
471	QF	Lleyton Hewitt		6595	14	10
457	QF	Boris Becker		5025	11	18
438	QF	Andy Roddick		5695	13	13
433	QF	Mats Wilander		5200	12	16
357	4R	Guillermo Vilas		5350	15	14
French Open
Code:
Pts	Stage		Name		Tot Pts	App	Rank
1818	F	Rafael Nadal		18180	10	1
1568	F	Björn Borg		12540	8	2
810	SF	Mats Wilander		9715	12	5
655	QF	Ivan Lendl		9825	15	3
650	QF	Gustavo Kuerten		7155	11	8
629	QF	Jim Courier		6920	11	9
614	QF	Novak Djokovic		6135	10	11
613	QF	Roger Federer		9800	16	4
526	QF	Sergi Bruguera		6310	12	10
474	QF	Andre Agassi		7580	16	7
450	QF	Guillermo Vilas		8095	18	6
441	QF	Jan Kodes		5730	13	12
429	QF	Juan Carlos Ferrero	5145	12	13
374	QF	Yevgeny Kafelnikov	4115	11	20
348	4R	Jimmy Connors		4520	13	17
Overall
Code:
Pts	Stage		Name		Tot Pts	App	Rank
1145	SF	Björn Borg		30925	27	8
1009	SF	Rafael Nadal		40340	40	4
889	SF	Roger Federer		56035	63	1
844	SF	Novak Djokovic		34590	41	7
777	SF	Pete Sampras		40385	52	3
751	SF	Rod Laver **		12775	17	22
711	QF	Andre Agassi		37675	53	6
699	QF	Ivan Lendl		39845	57	5
697	QF	Jimmy Connors		40435	58	2
686	QF	John Newcombe **	17830	26	17
639	QF	John McEnroe		28760	45	9
596	QF	Andy Murray		20275	34	14
577	QF	Boris Becker		26525	46	11
569	QF	Mats Wilander		25025	44	12
528	QF	Stefan Edberg		28525	54	10
511	QF	Arthur Ashe **		15845	31	19
432	QF	Ken Rosewall **		18155	42	15
428	QF	Jim Courier		17980	42	16
419	QF	Guillermo Vilas		20540	49	13
341	4R	Andy Roddick		15690	46	20
Chances are high i forgot somebody or mistyped some numbers. Please let me know in case you acknowledge such errors, thanks.
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Old 03-17-2015, 09:53 PM   #2
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Default Re: Average Points at Grand Slams (Open Era)

You acknowledge that arithmetic mean is not best suited in this case, because of the essentially exponential system of awarding ranking points, and yet you used that one?

As a consequence, some things are a bit strange about the tables. Djokovic at AO is behind Federer despite his 5 titles there, also Djokovic is better placed at USO then at Wimbledon, despite having 2 Wimbledon titles and just 1 USO. Have you played with the geometric mean also?
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Old 03-18-2015, 10:33 AM   #3
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Default Re: Average Points at Grand Slams (Open Era)

Quote:
Originally Posted by G.100sic View Post
You acknowledge that arithmetic mean is not best suited in this case, because of the essentially exponential system of awarding ranking points, and yet you used that one?
The geometric mean would in fact be the proper mean to use with exponentially growing numbers. This isn't, however, a normal geometric progression. The factor changes from 2.0x to 1.6x from the SF onwards (720*1.6 = 1200*1.6 = 2000). Because of this i was afraid that it would distort the numbers even more but maybe i'm wrong.

The main reason why i used the arithmetic mean is because i used Litotes's sums from his table in the other thread since it would have been too much work for me to calculate the geometric mean without a proper database at hand.
If you compare the tables with the winning percentage tables though you'll notice that it still more or less correlates in regard to order. The numbers themselves though are way too high and thus also the conclusions about the stage reached on average..

Quote:
Originally Posted by G.100sic View Post
As a consequence, some things are a bit strange about the tables. Djokovic at AO is behind Federer despite his 5 titles there, also Djokovic is better placed at USO then at Wimbledon, despite having 2 Wimbledon titles and just 1 USO. Have you played with the geometric mean also?
Regarding the AO i disagree. Djokovic might have one more win but he has NO SFs to his account at all and i'd still regard Federer's resumee as the better of the two (in fact the geometric mean would attribute Federer an even higher edge imo).
The 140+points difference btw USO and Wimbledon seems a bit high yes, but then again he's reached the finals 5 times there, compared to only 3 times at Wimbledon. I'll definitely run the geometric mean here to see what the outcome would be.

Tidbit: Nadal's geometric mean for the FO would be 1572 (compared to 1818) ..a considerable difference. The arithmetic mean is definitely biased towards wins and finals.
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Old 03-18-2015, 06:54 PM   #4
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Default Re: Average Points at Grand Slams (Open Era)

Quote:
Originally Posted by Geolith View Post
...The main reason why i used the arithmetic mean is because i used Litotes's sums from his table in the other thread since it would have been too much work for me to calculate the geometric mean without a proper database at hand.
If you compare the tables with the winning percentage tables though you'll notice that it still more or less correlates in regard to order. The numbers themselves though are way too high and thus also the conclusions about the stage reached on average.....
Yes, I'm aware that you would have to have all the results in order to calculate geometric mean, and that it would require significant amount of work.
Nice job, anyway!
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