2011 Players Championship Qualification

**MEfree** · May 1, 2011

Does anyone know what the qualification criteria are for the 2011 Players Championship? Does it use the top ___ of the mathematically flawed Official World Golf Rankings as one of the categories? I have seen conflicting info as to whether the top 50 or top 100 get automatic invites.

What other events besides those below use the OWGR? Looks like the European Tour PGA Championship http://news.bbc.co.uk/sport2/hi/golf/9367827.stm

http://en.wikipedia.org/wiki/Official_World_Golf_Ranking

Tournament	Automatic entries
The Masters	Top 50
U.S. Open	Top 50 through 2011 Top 60 from 2012 ^{[ 8 ]}
The Open Championship	Top 50
PGA Championship	(Top 100) ^{see note}
WGC-Accenture Match Play Championship	Top 64 (sole criterion)
WGC-CA Championship	Top 50
WGC-Bridgestone Invitational	Top 50
WGC-HSBC Champions	Top 25
Tournament of Hope (from 2012)	Top 70 ^{[ 7 ]}

Note: The PGA Championship does not have an official automatic entry based on the Official World Golf Ranking but has invited those in the top 100 for the last several years. It makes note of its strong field by referencing the number of top 100 ranked golfers entered in its press releases. [1] [2]

**deasy55** · May 1, 2011

In what way are the World Rankings 'Mathematically Flawed'? The Maths behind them is very accurate IMO and gives a good indication of who has been the best over the last 2 years with emphasis on recent performances

**Shindig** · May 1, 2011

MEfree said:
Originally Posted by MEfree

Does anyone know what the qualification criteria are for the 2011 Players Championship? Does it use the top ___ of the mathematically flawed Official World Golf Rankings as one of the categories? I have seen conflicting info as to whether the top 50 or top 100 get automatic invites.

No, but some number of the top in the OWGR do get invites. I think the top 125 from the previous year's PGA Tour OOM get an invite, as does the #1 from the previous year's NWT OOM.

**Acropo** · May 2, 2011

Agree with Chilli. The focus is on the PGA Tour, with some additional invites. This is, after all, a PGA Tour event, not a Major or WGC, so a US-focus is quite reasonable and to be expected. Likewise, the BMW PGA championship - formerly the British PGA Championship - is a European Tour event (its biggest outside the Majors/WGCs) and its focus, also, is on European Tour-qualified entrants.

**Kazuhiro** · May 2, 2011

It's the Top 50. :)

http://nbcsports.msnbc.com/id/33407691/ns/sports-player_news/

**MEfree** · May 2, 2011

deasy55 said:
Originally Posted by deasy55

In what way are the World Rankings 'Mathematically Flawed'? The Maths behind them is very accurate IMO and gives a good indication of who has been the best over the last 2 years with emphasis on recent performances

Here is an example of their math using scoring instead of rank points, but the same principle applies with a downward bias towards players who have more older results even if they outperformed across the board:

Period	weight	Player 1 scores	Player 2 scores
most recent	1	70	68, 68
2	0.75	70, 70, 72	68, 68, 66
3	0.5	70, 70	68, 68
oldest	0.25	70, 70	68

OWGR "average"		41.75	46.56
Correct weighted average		70.32	67.73
Unweighted Average		70.25	67.75

The OWGR algorithm shows player 2 with a higher "average" than player 1 even though player 2 scored lower in every time period- the only difference is that player 1 had 1 more older result with player 2 having one more recent result.

Kazuhiro said:
Originally Posted by Kazuhiro

It's the Top 50. :)

http://nbcsports.msnbc.com/id/33407691/ns/sports-player_news/

Yes, talked to someone today at PGA Tour HQ who confirmed this is one of multiple criteria.

**deasy55** · May 3, 2011

MEfree said:
Originally Posted by MEfree

Here is an example of their math using scoring instead of rank points, but the same principle applies with a downward bias towards players who have more older results even if they outperformed across the board:

Period

weight

Player 1 scores

Player 2 scores

most recent

1

70

68, 68

2

0.75

70, 70, 72

68, 68, 66

3

0.5

70, 70

68, 68

oldest

0.25

70, 70

68

OWGR "average"

41.75

46.56

Correct weighted average

70.32

67.73

Unweighted Average

70.25

67.75

The OWGR algorithm shows player 2 with a higher "average" than player 1 even though player 2 scored lower in every time period- the only difference is that player 1 had 1 more older result with player 2 having one more recent result.

You can't work it that way. I can't even get around to exlaining how ridiculous that example was.

**MEfree** · May 3, 2011

deasy55 said:
Originally Posted by deasy55

You can't work it that way. I can't even get around to exlaining how ridiculous that example was.

What part was ridiculous? The way the OWGR computes "average" or the way I computed weighted and unweighted average? Would you prefer the following OWGR "average" calculations for two hypothetical players, 1 who earns 10 rank points per event and 1 who earns 9 rank points per event...OWGR would have 2 ranked ahead of 1.

Under the current OWGR formula, Player 2 ends up with a higher "average" points despite the
fact that Player 1 beat him in all 41 events they played in together and Player 1 performed
at the same level for the 11 events that he played that Player 2 did not compete. This makes no sense!
A true weighted average would have player 1 at 10 and player 2 at 9


Week (ago)	Weight	P-1 Rank Pts	P-1 Adj Pts	P-2 Rank Pts	P-2 Adj Pts
1	1.00	10	10.00	9	9.00
2	1.00
3	1.00	10	10.00	9	9.00
4	1.00
5	1.00	10	10.00	9	9.00
6	1.00
7	1.00	10	10.00	9	9.00
8	1.00
9	1.00	10	10.00	9	9.00
10	1.00
11	1.00	10	10.00	9	9.00
12	1.00
13	1.00	10	10.00	9	9.00
14	0.9891
15	0.9783	10	9.78	9	8.80
16	0.9674
17	0.9565	10	9.57	9	8.61
18	0.9457
19	0.9348	10	9.35	9	8.41
20	0.9239
21	0.9130	10	9.13	9	8.22
22	0.9022
23	0.8913	10	8.91	9	8.02
24	0.8804
25	0.8696	10	8.70	9	7.83
26	0.8587
27	0.8478	10	8.48	9	7.63
28	0.8370
29	0.8261	10	8.26	9	7.43
30	0.8152
31	0.8043	10	8.04	9	7.24
32	0.7935
33	0.7826	10	7.83	9	7.04
34	0.7717
35	0.7609	10	7.61	9	6.85
36	0.7500
37	0.7391	10	7.39	9	6.65
38	0.7283
39	0.7174	10	7.17	9	6.46
40	0.7065
41	0.6957	10	6.96	9	6.26
42	0.6848
43	0.6739	10	6.74	9	6.07
44	0.6630
45	0.6522	10	6.52	9	5.87
46	0.6413
47	0.6304	10	6.30	9	5.67
48	0.6196
49	0.6087	10	6.09	9	5.48
50	0.5978
51	0.5870	10	5.87	9	5.28
52	0.5761
53	0.5652	10	5.65	9	5.09
54	0.5543
55	0.5435	10	5.43	9	4.89
56	0.5326
57	0.5217	10	5.22	9	4.70
58	0.5109
59	0.5000	10	5.00	9	4.50
60	0.4891
61	0.4783	10	4.78	9	4.30
62	0.4674
63	0.4565	10	4.57	9	4.11
64	0.4457
65	0.4348	10	4.35	9	3.91
66	0.4239
67	0.4130	10	4.13	9	3.72
68	0.4022
69	0.3913	10	3.91	9	3.52
70	0.3804
71	0.3696	10	3.70	9	3.33
72	0.3587
73	0.3478	10	3.48	9	3.13
74	0.3370
75	0.3261	10	3.26	9	2.93
76	0.3152
77	0.3043	10	3.04	9	2.74
78	0.2935
79	0.2826	10	2.83	9	2.54
80	0.2717
81	0.2609	10	2.61	9	2.35
82	0.2500
83	0.2391	10	2.39
84	0.2283
85	0.2174	10	2.17
86	0.2065
87	0.1957	10	1.96
88	0.1848
89	0.1739	10	1.74
90	0.1630
91	0.1522	10	1.52
92	0.1413
93	0.1304	10	1.30
94	0.1196
95	0.1087	10	1.09
96	0.0978
97	0.0870	10	0.87
98	0.0761
99	0.0652	10	0.65
100	0.0543
101	0.0435	10	0.43
102	0.0326
103	0.0217	10	0.22
104	0.0109
		520	295	369	252.59
		Events	52	Events	41
		"Average Pts"	5.67	"Average Pts"	6.16

**Shindig** · May 3, 2011

MEfree said:
Originally Posted by MEfree

What part was ridiculous? The way the OWGR computes "average" or the way I computed weighted and unweighted average? Would you prefer the following OWGR "average" calculations for two hypothetical players, 1 who earns 10 rank points per event and 1 who earns 9 rank points per event...OWGR would have 2 ranked ahead of 1.

Well, your first example (earlier in the thread) was trying to apply an OWGR-type formula to something it isn't meant to compute.

Your second example is a deliberately adversarial example; any mathematical ranking system has problems like this. Maybe you'd be better off telling us what general problems you find with the OWGR.

If your calculations are correct (I haven't checked, but I haven't any reason to believe there's anything wrong in them), all you've really shown is actually something the governing bodies are working to address; the first stage, as they've been implementing, is lowering the maximum divisor level.

**MEfree** · May 4, 2011

Shindig said:
Originally Posted by Shindig

Well, your first example (earlier in the thread) was trying to apply an OWGR-type formula to something it isn't meant to compute.

Your second example is a deliberately adversarial example; any mathematical ranking system has problems like this. Maybe you'd be better off telling us what general problems you find with the OWGR.

If your calculations are correct (I haven't checked, but I haven't any reason to believe there's anything wrong in them), all you've really shown is actually something the governing bodies are working to address; the first stage, as they've been implementing, is lowering the maximum divisor level.

The beauty about math is that the same method that correctly computes an average for one thing can be used to compute an average for anything whether it is average sales per month, visitors per day, page views per month, shots per round or ranking points per event. While rankings will almost always have subjective criteria that can be debated until the end of time (i.e. which is a stronger finish- 5th at the Masters or winning a Japanese Tour event?), there is no reason for their averaging method to be mathematically deficient.

You are correct that my second example was designed to highlight the current flaw in the system- namely that players get artificially penalized for having played a heavy schedule towards the older part of the 2 year ranking period regardless of how well they played...If their averaging algorithm was mathematically sound, I would have no issue and not be able to come up with any deliberately adversarial examples. Which would you rather have- a system in which it is easy to come up with objective adversarial examples or one where the only adversarial examples are of a subjective nature?

There is an easy and more accurate way to fix this than lowering the maximum divisor (which will effect some players, but not necessarily improve the rankings overall). Lowering the maximum divisor is kinda like aiming farther left to fix a slice- it might help you in some situations, but won't fix everything. Correctly applied math will have the effect of squaring up the club face and have the club move in the direction of the target- a much better way to fix a slice IMHO.

Overall, I think the OWGR has got it mostly right and, on the surface, it does seem that they want to get the system working as well as possible. Let's hope this is done sooner rather than later as I see there is at least 1 player who should be in the Top 50 that is not getting a Players Championship invite.

**Shindig** · May 4, 2011

MEfree said:
Originally Posted by MEfree

The beauty about math is that the same method that correctly computes an average for one thing can be used to compute an average for anything whether it is average sales per month, visitors per day, page views per month, shots per round or ranking points per event. While rankings will almost always have subjective criteria that can be debated until the end of time (i.e. which is a stronger finish- 5th at the Masters or winning a Japanese Tour event?), there is no reason for their averaging method to be mathematically deficient.

While a method for computing an average is the same no matter what you're averaging, it doesn't hold for a formula. The OWGR calls something an average, but it's a bit more complex of a formula, and it isn't based on the score shot (your first example). What you've done is the equivalent of substituting salt for sugar when baking a cake: sure, they're both white powdery substances, but that doesn't make them equivalent. Likewise, just because the OWGR calls something a "points average" doesn't equate to using an algebraic mean.

The end of your post tells me that your beef with the ranking is that it's letting someone into the Players' Championship, who you'd rather isn't there. Your hope seems to be that they'll change the ranking system in the next two days, so that this person (who?) will be omitted from the field before the commit date.

**sean_miller** · May 4, 2011

Shindig said:
Originally Posted by Shindig

While a method for computing an average is the same no matter what you're averaging, it doesn't hold for a formula. The OWGR calls something an average, but it's a bit more complex of a formula, and it isn't based on the score shot (your first example). What you've done is the equivalent of substituting salt for sugar when baking a cake: sure, they're both white powdery substances, but that doesn't make them equivalent. Likewise, just because the OWGR calls something a "points average" doesn't equate to using an algebraic mean.

The end of your post tells me that your beef with the ranking is that it's letting someone into the Players' Championship, who you'd rather isn't there. Your hope seems to be that they'll change the ranking system in the next two days, so that this person (who?) will be omitted from the field before the commit date.

Maybe he means someone isn't getting an automatic invitation who should be there. I see a few tournament winners from 2011 on the outside looking in. Maybe they'll get in other ways - like when some of the top guys decline.

**Shindig** · May 4, 2011

sean_miller said:
Originally Posted by sean_miller

Maybe he means someone isn't getting an automatic invitation who should be there. I see a few tournament winners from 2011 on the outside looking in. Maybe they'll get in other ways - like when some of the top guys decline.

I need to go improve my reading comprehension; I've made this mistake a few times recently.

In any case, there are always players who decline for various reasons. Hopefully we end up with a fully deserving field.

**Frank-0-Sport** · May 9, 2011

Qualification Categories - 2011 Players Championship

• Winners of PGA TOUR cosponsored or approved tournaments, whose victories are considered official, since the previous year’s PLAYERS Championship.

• The top 125 finishers on the 2010 Official PGA TOUR Money List.

• Winners of THE PLAYERS Championship (2006 to 2010); Masters Tournament (2007 to 2011, plus - for 2011 Players only - 2006 winner); U.S. Open, British Open and PGA Championship (2006 to 2010).

• Winners of THE TOUR Championship presented by Coca-Cola from 2008 to 2010.

• Winners of World Golf Championship events: Accenture Match Play Championship and CA-Doral Championship (2009 to 2011); Bridgestone Invitational (2008 to 2010).

• Any player(s), not otherwise eligible, among the top 50 leaders from the Official World Golf Ranking through the 2011 Zurich-New Orleans Open.

• Any player(s), not otherwise eligible, among the top 10 leaders from the 2011 FedExCup Points List through the 2011 Zurich-New Orleans Open.

• The winner of the 2010 Constellation Energy Senior Players Championship. Such exemption will be an addition to the nominal field of 144.

• The leading money winner from the 2010 Official Nationwide Tour Money List.

• If necessary to complete a field of 144 players, PGA TOUR members from the 2011 FedEx Cup Points List below 10th position through the 2011 Zurich-New Orleans Open, in order of their positions on such list.

The winner of the Players Championship receives -- 5 year exemptions to the PGA Tour as well as the event itself; 3 year exemptions to the Masters Tournament (2012-13-14), US Open and British Open Championship (2011-12-13); one exemption, in 2011, to the PGA Championship.

Thanx-A-Lot, Frank-0-Sport

**sean_miller** · May 9, 2011

I think the list of players not qualified is shorter.

Frank-0-Sport said:
Originally Posted by Frank-0-Sport

Qualification Categories - 2011 Players Championship

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