## Thursday, October 23, 2014

### Can the USGA Slope Rating Decrease as Yardage Increases?

There are cases where the USGA Slope Rating decreases as the yardage increases.   It is never clear, however, whether this anomaly is due to an error by the Rating Committee or an oddity in the course design.  This post examines one such situation to determine the most likely explanation.
Our example is drawn from the files of the Oregon Golf Association (OGA) in 2006.  The yardages and Slope Ratings of the course in question are shown in Table 1 below.

Table 1
Yardages and Slope Ratings for Women

 Tee Yardage Slope Rating Green/Silver 6249 150 Green 6559 148

As Table 1 shows, the Slope Rating decreases as yardage increases.  A player with a 14.0 Index would receive 19 strokes if she played the Green/Silver tees, but only 18 Strokes if she moved back to the Green tees.   An examination of the Slope Rating formula reveals why the decrease in Slope Rating is unlikely.

Slope Rating = 4.24·((Y/120 + BOV +51.3) – ( Y/180 + SOV +40.1))
= .0118·Y + 4.24·(BOV –SOV) +47.5
Where,
Y = Effective Course Yardage
BOV = Bogey Obstacle Value
SOV = Scratch Obstacle Value

The Slope Rating is an increasing function of yardage.  For each 100 yard increase in yardage, the Slope Rating—all things being equal—will increase by approximately 1.2 rating points.  For the 310 yard increase in length in the example, the Slope Rating would increase by 3.7 rating points.  The only way for the Slope Rating to increase with distance is for the SOV to increase more than the BOV.  It is difficult to conceive of a course design where this could happen.

Where an error may have occurred can be found by examining the SOVs and BOVs implicit in the new ratings.  Table 2 shows the BOV for the Green tees is actually lower than from the Green/Silver tees. This is highly unlikely.  The bogey player should have shorter approach shots from the Green/Silver tees which should reduce the BOV.  If the shorter tees bring more hazards in to play, the bogey player can just use less club so that her landing area is the same as from the longer tees (i.e., there is no change in obstacle values).

Table 2
Obstacle Values

 Tees SOV BOV Green/Silver 0.5 7.2 Green 1.1 6.5

The case for an error in ratings is strong.  The OGA, however, did not see it that way.
Jim Gibbons, Executive Director, of the OGA wrote the following:

We have received your review of the course ratings. Nancy Holmes has
started the process to double check our ratings, but initial review shows we
are correct.  The bogey rating for women from the Green/Silver tees of 110.6
slopes to a 150 based upon the course rating of 75.3 at 6249 yards.  This
relates to a 19 handicap to shoot(sic) a net 75.3 for women.
The Green tees at 6559 have a course rating of 77.6 with a bogey rating of
112.5 (because some obstacles are located with less impact).  This provides a
handicap of 18 to shoot (sic) the net score of 77.6.
The rating process has changed since the previous ratings were done. Green
speeds and rough heights may be different. A check of the BOV between the
Green/Silver and the Green (tees) will be made and if there is a change that will
be posted.  Realize that the BOV sometimes is lower from the longer tees, but
many organizations will adjust the numbers to avoid having to explain the
reason.  We choose to do the rating correctly.

Mr. Gibbons does not really give a defense of the Slope Ratings. He is correct that the various course and bogey ratings yield the peculiar Slope Ratings. This math was never in question. The issue was whether the Obstacle Values were estimated correctly. He states this will be addressed in the future, but never did. Gibbons ends with the audacious claim that the BOV is frequently lower from the longer tees than reported because other associations fudge the numbers. I suspect he never filed a complaint to the USGA to that effect.

The course was re-rated in 2014. The new BOVs and Slope Ratings are shown in Table 3. Both the BOV and the Slope Rating increase with distance as expected. The difference in the Slope Ratings between the two sets of tees is 7 rating points (+2 to -5). Since the course was essentially unchanged between ratings, a difference of 7 rating points is too large to be attributed to random error. Given the more reasonable 2014 ratings, it is likely that the 2006 ratings were due to Committee error rather than course design.

Table 3
2014 BOVs and Slope Ratings

 Tees BOV Slope Rating Green/Silver 6.7 147 Green 7.2 153
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While the 2014 ratings are more sensible, it is difficult to prove they are more accurate than the ratings of 2006. Rating Committees take measurements, assign number to subjective judgments, and plug those results into a model that has never been empirically verified. Ratings come out of the computer and are sent to the golf course. You can’t argue with a rating, but only the logic behind the rating. Since the OGA never presents that logic, there can be no debate.