Is the World Catching Up to the PGA Tour? Or Just the Math?

The minimum divisor is great. A part time player should have their score punished. Part of the JOB is to handled the travel, the food, the time away from home and family.

IMO, OWGR’s flaw is not the minimum play requirement. It is the way it “averages.”

As Ryan demonstrated in one table, OWGR uses a time factor to “devalue” entries as they get older. He used a 70 point event, but for simplicity I’ll use a 100 point win in a major championship. For the first 13 weeks, the win is worth the entire 100 points. After that, it begins to lose a little less than 1 point per week until in week 104 it is worth just over 1 point. However, for the ENTIRE 104 WEEKS, that entry adds ONE START to the divisor. So, when a player initially wins the major, it boosts his “Adjusted Points” – the numerator of the ranking equation – by 100 points and helps his ranking tremendously. But, by week 104, there is only a 1 point boost to the numerator and that aging major win – the best result possible in professional golf – actually drags his ranking downward.

The World Ranking formula is WRONG. What they should do is reduce the IMPORTANCE of old play relative to newer starts. But, the formula actually DEVALUES old starts and essentially makes a 104 week old major win exactly the same as a week 1 result of earning a single point.

Raw Ranking Points (like test scores in college) are the proper measure of player performance. 100 is the best. 0 is the worst. If you do a simple average of Woods 22 starts, he averages 47.45 points per entry. McIlroy averages 4.76 in his 44 starts. So, Woods average performance in his 22 starts (with 11 wins) is roughly 10 times what Rory has done.

If OWGR did a proper average using the time weights – a weighted average – the proper divisor would not be total starts, it would be the sum of the weights. Going back to the major win – during the first 13 weeks (with a time weight of 1.000) that win would add 100 points to the numerator and 1.000 to the divisor. But, at the end of the ranking window, it will add .0109*100=1.09 to the numerator and – rather than adding 1 (entry) to the divisor – it will add only .0109 to the divisor. In this way the old major win becomes very unimportant – only 1% as important as it was in the first 13 weeks – but it remains a 100 point event (the best result in golf).

Because OWGR devalues old starts instead of simply reducing their importance, it introduces time bias into the formulation. A new player like McIlroy who has very few old starts from week 78 to 104 gets a big boost relative to other players who have been playing consistently over the 104 week period. And, he gets a gigantic boost relative to a returning injured player like Woods who has exactly the opposite playing pattern. Nearly all of Woods 22 entries are now heavily devalued (not deemphasised) by OWGR.

Let me use a very simple college class example of how OWGR distorts reality.

Suppose a college class is going to base its final grade on midterm and a final and the midterm supposed to be half as important as the final. Suppose also, that the midterm is optional and if you don’t take it, 100% of your grade will be determined by the final.

Student A takes both tests and scores 100 on each. A proper weighted average would compute his score as (1*100+.5*100)/(1+.5)=150/1.5=100 Obviously, no matter what relative weights are assigned to the two tests, it he got 100 on both, he gets a 100 average.

But, if OWGR was scoring the student, it would look like this: (1*100+.5*100)/2 tests = 150/2 = 75. Rather than reducing the importance of the midterm, OWGR would devalue the 100 result to only 50 and then average the two tests.

So, if there was a student B who just took the final and scored 80, it would rank that student above student A who had scored 100 on both tests but somehow ended up with an average of 75.

That is the flaw in how OWGR computes its so-called average. Players who have greater proportions of recent play are heavily over ranked vs players who have the opposite playing patterns.

This math error causes relative rankings of players with different “off seasons” to swing about wildly. PGATour players get heavily overranked relative to others around the Tour Championship, and then fall tremendously relative to other players around New Years before they start to play again. Japan takes a long break from early Dec until April causing their players to be highly ranked in Dec and poorly ranked in April, etc.

If OWGR simply changed its divisor from total starts to “sum of the weights” and computed a proper weighted average, all of this seasonal bias would be removed. And, injured players would not get huge ranking penalties just before they returned to play – followed by huge ranking boosts when their injury gap moved toward the end of the 104 week ranking window and gave them a McIlroy-like playing pattern that is all front-loaded.

One-eye, devaluing is NOT the only way to add value to more recent performances. A correct weighted average does exactly that.

If player A earns 20 points in a recent event (with a time weight of 1) and 10 points in an older tournament (with a time weight of .50). Current OWGR says he has a ranking of (20*1)+(10*.5)/ 2 events = 25/2= 12.5 (the average of 20 and 5)

If player B earns 10 in the recent event and 20 in the older event his average is 10, the average of 10 and 10.

If a correct weighted average is used (with a divisor of 1.5) the two results are 25/1.5 = 16.67 and 20/1.5=13.33 exactly the same 25% better ranking for Player A as for the incorrect weighted average BECAUSE both players happened to compete in the exact same events.

BUT, what happens if two players each have all the exact same entries and the exact same points earned (100 adjusted ranking points in 50 entries for an OWGR ranking average of 2.00) except that player 1 has a new 2 point event with a weight of 1 (adjusted value 2.00) and player 2 has a 104 week old 100 point major win with a weight of .0109 (adjusted value 1.09). OWGR for player one will be 102/51=2.00. Player 2 will be 101.09/51=1.98. Player one will get the invitation to the upcoming WGC because of a current mediocre finish while player 2 gets dinged for winning a major.

A proper weighted average very effectively adds value to recent good play vs older good play, it just doesn’t do stupid math and create absurd biases against very old starts that drag down rankings AS IF they were BAD PERFORMANCES – when they WERE NOT.

tatkin, If they “want time bias” – I think they are nuts. I think they “want” to make more recent play more important. If that is what they want to do, then I agree with what they are “trying” to do – just not the way they do it.

They transform ALL old into bad performances by devaluing them as much ass 99%. That is why new players like McIlroy and Quiros jump so high so fast. They don’t have those 20 or 20 old performances that absolutely destroy normal player averages because they were not active then.

So, what happens? They zoom right past established players who have played every bit as well (and often better) RECENTLY but still have to drag along their highly devalued old play that does not burden these new players.

A proper weighted average would make those old starts VERY INSIGNIFICANT – but they don’t become an artificial ranking burden.

oops – all old into SHOULD BE all old performances into

and – 20 to 20 SHOULD BE 20 – 30

Exactly, Ryan.

And, to maintain a penalty for insufficient play, OWGR only needs to multiply by Actual Starts / 40 after a proper weighted average is computed. That would create the exact same percentage penalty as is currently assessed by OWGR.

Woods current average of 9.16 is created by a divisor of 40 rather than his current starts of 22. So it is in effect his actual average using a divisor of 22 which is then multiplied by 22/40 to reduce it to 55% of its original value (which is a 45% penalty).

If you compute a REAL weighted average and multiply that result by 22/40 you get the exact same impact.

If we look at the current ranking indexes for Woods, Garcia and McIlroy – which are…

9.16, 7.57 and 3.98

…. and transform them to real weighted averages (and still penalizing Woods 45%) they look like this:

27.58, 13.97 and 5.87

Woods jumps from being 20% over Garcia to being nearly double his average.

Woods jumps from being a bit more than double McIlroy to more than 4 times his average.

And Gracia jumps from being about 90% above McIlroy to being 140% higher than his average.

Those changes occur because Woods average start is now devalued by 67% due to his long layoff. In contrast, Garcia’s average start is devalued by a fairly normal 46, and McIlroy only has his average start devalued by 32 since he has very few old starts.

When OWGR devalues old play – penalizing a player with a recent layoff – and then imposes a minimum play penalty (which further penalizes the player) it is essence “doubling up” on the penalties.

The three players have simple average ranking point earnings (with no time decay) of:

47.45, 12.62 and 4.76

In his 22 starts, Woods has AVERAGED almost 4 times as many ranking points as Garica and more than 10 times as many as McIlroy. OWGR makes a nearly 4 times as good margin over #2 almost disappear by:

1) using bad math to essentially halve the gap from 4 times to 2 times as good

then

2) taking almost half of Woods remaining 2-1 advantage away by penalizing him another 45% for having too few starts.

IN REALITY, no other player is remotely close to Woods output over the past 104 weeks.

Not so in OWGR-WORLD.