What the Multi-Ball Allowances Mean to You

By Gordon H. Ewen

Note: This originally appeared in the January/February 1978 issue of Golf Journal. The information has been updated to reflect current USGA Handicapping procedures.

If by some chance you have been searching the world over for a subject guaranteed to (a) arouse intense emotions, and (b) elicit vehement opinions, seek no further. On a scale of 1 to 10, the USGA Handicap System registers a solid 12 in both departments.

One reason is that like the chevron on a PFC's sleeve or the star on a general's shoulder, a golfer's handicap is a kind of personal symbol of status. Very personal. I know of a least one fairly classy player whose laundry labels read something like this: "P.J. Hannigan - 4." I can recall, too, the reaction of a somewhat less skillful, but equally dedicated lady player whose handicap was increased by four strokes when the system was revised two years ago. "They're adding four strokes to my handicap?" she said in stricken tones. "I'd much rather they added four inches to my waistline!"

Another source of built-in controversy lies in the fact that a good many players, regardless of whether their handicaps are high or low, are firmly convinced that the system is somehow rigged against them. Not just against players of their particular class - against them personally.

"Never mind the arithmetic," grumbles the disillusioned weekender with the scarlet "30" emblazoned defiantly on his golf shirt. "All I know is that no matter how many strokes the system gives me, some limber-back who does nothing but play golf every day is going to beat me nine times out of ten!"

Simultaneously, of course, the limber-backed chap is reflecting on the injustice of a system specifically designed to render him easy prey for any high handicapper who has a loop in his backswing, plays only on weekends, and never practices.

Statistics tell us that both players, sooner or later, will fire off irate letters to the USGA Handicap Department. Which is why those of us, no matter what our politics may be, occasionally feel a surge of empathy with the late Mayor Richard Dales of Chicago, who once declared of the local newspapers: "They have vilified me. They have crucified me. Yes, they have even criticized me!"

Happily, however, statistics also tell us that both players are wrong, and in almost equal measure. ("Almost" because of the built-in "bonus for excellence" in the individual handicapping system. Over the long run, the weekender vs. limber-back series of matches will be resolved slightly - very slightly - in favor of the latter.)

The USGA Handicap System is the great equalizer among players of differing abilities. Indeed, it is a key element in the greatness of golf as a game. Were you or I for some reason required to play a tennis match with the likes of Jimmy Connors or Ilie Nastase, the experience might well be shattering. But in golf, thanks to the Handicap System, either of us could enjoy a satisfyingly competitive match with Jack Nicklaus or Tom Watson. 

The relative equity which the system brings to individual matches, however, quickly changes to inequity in multi-ball team events at stroke play - if full handicaps continue to be used. It is a golfing fact of life (a fact of which many players are unaware) that something less than full individual handicaps are necessary when players team up for this type of competition.

Basically, the problem is that higher handicappers produce a wider range of hole-by-hole scores than better and more consistent golfers do. That means that if full handicaps are used and a team can choose its best net score on each hole, the team getting the most strokes has a definite edge.

In an effort to lessen the disparity between singles and team play, multi-ball handicap allowances ranging from 70% to 80% were made part of the USGA Handicap System in January, 1976.

The golfing world did not welcome the 1976 allowances with open arms. One reason was that multi-ball allowances were instituted simultaneously with a major revision in the individual handicapping system, a revision which increased individual handicaps by some 13%. The USGA concentrated on explaining the reasons for the general increase in individual handicaps, but did a relatively low-key job of publicizing the multi-ball allowances.

Another reason was that a number of otherwise rational golfers were somehow stricken with a kind of intellectual myopia where the allowances were concerned. Instead of seeing them for what they really were - team adjustments designed to allow multi-ball events to be played on the same relatively equal basis as individual events - they interpreted the allowances as reductions in their individual handicaps. In short order, locker rooms echoed to cries of anguish from players like the former 26-handicapper who, having been raised to 30 under the 1976 system, was convinced he was going to win every prize in sight over the coming season - only to discover his handicap had been adjusted to 21 for the first best-ball-of four event of the year.

Yet another complication arose because individual handicaps are computed and administered by state and district golf associations, but multi-ball competitions are played chiefly at the club level. In general, the associations were quick to adopt the new USGA method of computing individual handicaps; a good many clubs, however, either through lack of familiarity with the allowances or because they opted to "keep things simple," continued to use full handicaps for multi-ball play.

The 1976 Allowances had been in effect for only a few months when it became apparent that golfers in general were accepting them reluctantly, if at all. The USGA is the governing body of golf in the United States; but it governs by consent only, and must be alert to ground swells of opinion from its constituency. Accordingly, we determined to take a second long, hard look at the allowances, through the eyes of the most expert consultants available.

One expert we retained was Dr. Francis Scheid, a member of the mathematics department at Boston University, author of numerous pioneering articles on handicapping, and former president of the Plymouth (Massachusetts) Country Club. Another was Dr. Clyne Soley, a California engineer who was a leading contributor to an earlier USGA handicap study. The research effort was joined later by the volunteer team of Trygve Bogevold, a long-time member of the USGA Handicap Procedure Committee, and Dr. Richard Stroud, an aerospace scientist with Lockheed Aircraft and former president of the Sunnyvale (California) Golf Club. All four men share not only impressive mathematical talents, but a zest for golf as well.

Their research occupied the better part of a year. Although the participants, working independently, devised three very different approaches to the multi-ball problem, their conclusions were remarkably compatible. They were in general agreement, for example, that the 1976 allowances were too severe - that they unjustly penalized high handicappers. They agreed that the use of full handicaps in multi-ball stroke play, however, penalized low handicappers. And in the case of four-ball match play they were unanimous in finding that giving the full difference between handicaps produced acceptable near-equity.



USGA Handicap Allowances For Multi-Ball Team Events

 

Style of Play Old (1976)
Allowances
New (1978)
Allowances*
Four-ball (better-ball-of-two) match play 80% 100%
(full handicap difference)
Four-ball (better-ball-of-two) stroke play 80% 90%
Best-ball-of-four stroke play 70% 80%
Two-best-balls of-four stroke play** - 90%
*Effective January 1, 1978.
**Research shows that the mathematics involved in this format (which is becoming increasingly popular in club events) is essentially the same as for four-ball (better-ball-of-two) stroke play.

 

Soley worked with 5,426 scorecards collected by the USGA from men's and women's multi-ball events at 31 clubs, coast to coast. He used a four-step system to plot team scores vs. team handicaps, with the aim of determining appropriate allowances for match play and allowances necessary to give teams an equal chance to finish in the top 30% of the field in typical four-ball (better-ball-of-two) and best-ball-of-four stroke play events.

His final recommendations were identical with those ultimately adopted by the USGA: for four-ball match play, 100% of individual handicaps (more precisely, the lowest handicapper plays at scratch and the other three players receive the full difference between their handicaps and his); for four-ball stroke play, 90%; for best-ball-of-four stroke play, 80%; and for two-best-balls-of-four stroke play, 90%.

In addition to their solid basis in theory Soley's recommended allowances were also field-tested, having been used at his home club for 14 months without showing any significant advantage to any handicap level. They were easy to apply, being round numbers, and they included a slight "bonus for excellence" in favor of better and possibly more dedicated player

While Soley was studying team pairings from actual events, Scheid was working with a computer bank of 28,000 hole-by-hole rounds of 1,400 golfers at 14 Massachusetts clubs. Grouping and regrouping individual players into teams covering the widest possible range of handicap combinations, he simulated a million-plus rounds at allowances of 70%, 80%, 85%, 90%, 95%, and 100%.

For four-ball match play purposes he studied average team scoring performances; for four-ball, best-ball-of-four, and two-best-balls-of-four stroke play he analyzed the best 1% and best 25% or 30% of each team's scores at each allowance. (Best 1% performance represents a team's bid for winning first place in a typical club four-ball event, while best 25% or 30% is an indication of its chances of placing well up in the field.)

Scheid also simulated several hundred stroke play tournaments, each involving 200 players.

Starting with the premise that the performance of scratch teams should set the standard, Scheid set out to determine what allowances would most nearly equalize the play of various handicap teams with that of scratch teams.

Two basic findings emerged almost immediately from his exhaustive study:

  1. No single allowance can put every team in a multi-ball stroke play event on equal footing; absolute equity is simply not attainable when there is a wide variety of handicap combinations.
  2. "Spread" - the difference between partners' handicaps - is a highly significant factor. TablesA, B, and C, which are taken from Scheid's study, illustrate these key points.

 

The Bogevold-Stroud team, working with the same 5,426 scorecards as Soley used, concentrated on examining the effects of spread. They reported that each stroke of spread carries an approximate advantage of one-tenth of a stroke in a four-ball (better-ball-of-two) match and one-twentieth of a stroke in best-ball-of-four stroke play. In a four-ball match, in other words, their finding was that a scratch player and his 10-handicap partner have a full stroke advantage over a team of two 5-handicappers.



Table A

This table from Scheid's study lists the scores (shown as number of strokes under the course rating) made or bettered 25% of the time by four-ball (better-ball-of-two) teams playing at the 90% allowance now in effect for stroke play. The scores represent better-than-average, but not peak performance. Performance of a scratch team, measured on the same basis, was -4.9

Handicaps of the two partners are shown in bold type at the top and the left.

Handicaps 5 10 15 20 
5 -4.8
 

 

 
10 -5.7 -4.8
 

 
15 -5.4 -5.0 3.6
 
20 -5.3 -5.3 -4.5 -3.1

 

The lesson is ever the same: if you desire an advantage over your opponents, choose a partner whose handicap is several strokes higher or lower than your own. Preferably lower, because the bonus for excellence is factored into the allowances and the best showings are by low handicap teams with significant spread.



Table B: The Effect of Varying Handicap Allowances in Multi-Ball Stroke Play

This sequence of tables from Scheid's study shows the number of times 800 teams, representing 10 different handicap combinations, finished in the top quarter of 80 simulated four-ball (better-ball-of-two) stroke play tournaments. To hold its own, a combination would have to finish in the top quarter 200 times. Handicaps of the two partners are shown in bold type at the top and the left.


 
80% Allowance 90% Allowance 100% Allowance
Handicap 5 10 15  20 5 10 15  20 5 10 15  20
5 246
 

 

 
185
 

 

 
99
 

 

 
10 300 234
 

 
240 183
 

 
200 170
 

 
15 250 203 100
 
245 212 143
 
235 234 169
 
20 246 197 120 104 241 232 265 154 212 273 221 187

 

The figures indicate how widely the fortunes of a given team can fluctuate under different handicap allowances. A team of two 5-handicappers playing at 80%, for example, would finish in the top quarter 246 times; at 100%, the same team would achieve a top-quarter finish only 99 times.

The fortunes of a team of two 20-handicappers would be just the reverse: 104 top-quarter finishes playing at 80%, but 187 at 100%.

In addition to demonstrating the clear advantage low handicap teams have at 80% and high handicappers have at 100%, the tables also substantiate the first of Scheid's basic findings: absolute equity (i.e., an allowance which would result in each handicap combination achieving top-quarter finishes exactly 200 times) is simply unattainable. The most nearly even distribution (as well as the smallest disparity between highest and lowest figures) occurs in the 90% table.

Scheid's second basic finding - the importance of spread - is also evident. 5/5 handicap teams, for example, have consistently fewer top-quarter finishes than 5/10 or 5/15 teams.

When the results of all three studies were available, and the voluminous mathematics of multi-ball play was laid on the table, the USGA was faced with two difficult judgments.

First was the matter of coping with spread, the effects of which had been documented dramatically and conclusively. What, if anything, could be done to temper that effect? The Bogevold-Stroud team recommended placing a five-stroke limit on spread and playing all multi-ball competitions at 100% of handicap.

The USGA concluded that while writing such a limit into a Handicap System might be good mathematics, it would be bad sociology. For one thing, to limit spread would be to deny old friends with widely disparate handicaps the pleasure of teaming up in a club match or a member-guest. For another (considering that the average man'' handicap is a dozen or more strokes lower than the average women''), such a limit would be impractical for mixed multi-ball events.

Should a club decide to restrict spread in one of its own events, of course, the USGA has no objection: a club has every right to set the terms of its own competition. (One very workable solution to the spread problem, as a matter of fact, would be for the Committee to divide the field into flights based on spread.) The USGA simply declines to incorporate such limits into the official Handicap System.

Similarly, we have no objection to the common practice of limiting participation in pro-amateur competitions to players with handicaps of 18 or below. We do take a strong position, however, that the pro-am best-ball-of-four should be played at the 80% allowance.



Table C: The Effect of Different Handicap Combinations in Best-Ball-of-Four Stroke Play

Scheid also investigated the patterns of success or failure produced by different types of teams playing with varying allowances in best-ball-of-four stroke play competition. He simulated 200 tournaments, each involving 50 teams. Teams ranged from four low handicappers (LLLL) to four high handicappers (HHHH). For the study, handicaps under 10 were considered low; near 15, middle; and over 20, high.

The table shows the number of top-15 (i.e., in the top 30% of the field) finishes by each type of team under the handicap allowances indicated. To hold its own, a team would need 429 top-15 finishes.

Note that the 80% allowance provides the most nearly equitable distribution, as well as the smallest disparity between high and low figures.

Handicap
Combination
Combination
70%
Allowance
80%
Allowance
90%
LLLL 548 428 249
MMMM 305 336 356
HHHH 218 366 415
LLMM  621 495 436
MMHH 352 469 577
LMMH 442 451 476
LLHH 514 455 491

 

The second, and considerably more difficult judgment to be made involved the ever-elusive concept of equity. The question, "What is equity?" brings to mind the old chestnut about the man who was asked, "How's your wife?" He thought the question over for a few moments and then replied, "Compared to what?"

Equity compared to what? At first glance, the premise that equity in a multi-ball event lies in giving each team a relatively equal chance to win first place in a field of 200 golfers seems eminently reasonable - until one discovers that the allowances necessary to approach this goal can be so severe as to relegate a disproportionately large percentage of high handicappers to the bottom half of the field. Again, sound mathematics can be poor sociology.

In May 1977, at an all-day meeting in Chicago, the USGA Handicap Procedure Committee grappled with this problem and scored a reasonably clear-cut victory. The Committee opted for near-equity - allowances that will give every team reasonably equal odds of finishing in the upper 30% of the field. It was a conscious, reasoned decision to eliminate a preponderance of any type of handicappers from either the top or the bottom of the heap.

The Committee's recommendations were subsequently approved by the USGA Executive Committee and are now in effect.

In light of the careful research from which the allowances were developed, however, a club choosing to deviate from the specified percentages must realize that doing so can play havoc with the results of its competitions. For an example, albeit an extreme one, Scheid's studies indicate that if a best-ball-of-four stroke play event is played at full handicap instead of at the stipulated 80% allowance, a team of two 15-handicappers and two over-20 players has six times better odds of winning than a team whose members all have handicaps under 10! What television suggests can happen when you fool with Mother Nature can also happen when you fool with the mathematics of multi-ball allowances.

All things considered, the current allowances make sense and should be used. They are based on solid research; they are the fairest and most practical that could be devised; and they will add to your enjoyment of golf.