Handicapping Rationale

What's the deal with handicaps, differentials, adjusted scores, etc.?? We will be discussing three related but distinct handicap systems: 1) the old pre-2020 USGA system, 2) the new (2020) world handicap system (WHS), and 3) our very own TWGL system. TWGL used to be remarkably similar to the old USGA system, and now approximates the better features of the WHS, while eschewing its huge design blunders. Let's take a stroll down handicap lane (yes, "lame" humor).

The Basics

The Prime Directive for handicapping is the USGA/WHS linear model relating:
  1. the score (SCORE)
  2. course difficulty from a given set of tees (RATING and SLOPE)
  3. the skill of the player (INDEX or DIFFERENTIAL)

We start by imagining two theoretical players: scratch and bogey. RATING is the score expected from an idealized scratch player. The SLOPE expresses how much worse an idealized bogey golfer would score: 

    RATING = scratch_golfer_score
    SLOPE  = (bogey_golfer_score - scratch_golfer_score) * 113 / 18
Therefore a "standard" course (for which the bogey golfer shoots 18 higher than the scratch golfer) has a slope of 113. For example, if the idealized bogey golfer shoots an average of 20.2 strokes more than the scratch golfer, then the slope of the course is: 20.2 * 113 / 18 = 127 (rounded). At any rate, the linear model is expressed by the equation:
SCORE = RATING + SLOPE * INDEX
As mentioned, SLOPE is scaled by a factor of 113 - e.g. a USGA slope of 120 is equivalent to a mathematical slope of 120/113 = 1.06194... Throughout this page, we will use mathematical slope, with the scaling factor being implicit. INDEX (short for handicap index) is, of course, a measure of the player's skill level.

The general equation above is applied in two specific ways: to solve for SCORE and for DIFFERENTIAL: 

     1)  EXPECTED_SCORE = RATING + SLOPE * INDEX 

     2a) ADJUSTED_SCORE = RATING + SLOPE * DIFFERENTIAL 
     2b) DIFFERENTIAL   = (ADJUSTED_SCORE - RATING) / SLOPE
INDEX and DIFFERENTIAL play the same role in the general equation of the linear model - they express "player skill". But INDEX is a before-the-fact measure of how well the player has played recently and is used going into the round for setting handicap or expected score. DIFFERENTIAL is an after-the-fact output of the round and measures how well the player actually did score.

Expected Score and Handicap

Equation 1) is used to predict how well a player should score from a given set of tees (e.g. playing from the gold vs. white tees). When all players use the same tees, the RATING is the same for all of them and therefore can be ignored - the only difference is in the (SLOPE * INDEX) part, which of course is just the old USGA formula for one's handicap for the round. The USGA system had a half-assed way of dealing with multiple tees, but the new WHS has, to its credit, adopted a formula based on expected score, which ... ahem ... TWGL has been doing all along.

So now both the TWGL and WHS formula for course handicap is: 

   COURSE_HANDICAP = EXPECTED_SCORE         - PAR
   COURSE_HANDICAP = RATING + SLOPE * INDEX - PAR

Example: assume a player with an index of 11.7 at Maryland National, where the Gold tees play 6474 yards, rating / slope = 71.8 / 135, and the White tees play 6069 yards, rating / slope = 69.6 / 132. 

Expected score:
   Gold:    71.8 + (135/113) * 11.7 = 85.7778...  rounds to 86
   White:   69.6 + (132/113) * 11.7 = 83.2672...  rounds to 83

Course handicap (with par = 71):
   Gold:    86 - 71 = 15
   White:   83 - 71 = 12
Thus, players can compete from various tees equitably. As an aside, in the somewhat unusual case where the par rating differs between tees (e.g. par 71 from the Gold, par 70 from the White), it would be unfair to subtract out different pars, since the different slope and rating already account for course difficulty. The WHS recognizes this, but makes it complicated by adding back the difference between pars to the lower handicap. TWGL keeps it simple by using only a single par across the board, i.e. each course is treated as having only one par rating (which was called, prior to 2020, the "base" rating).

For some competitions, TWGL also uses a "score-to-beat" (STB) statistic, defined simply as expected score + 5. FWIW, the average value for STB points (STB - score) is about -1, so a positive result means a pretty good round.

Let's walk through the process of playing one round and updating the player's handicap index.

Post a Score

Player swings at ball, physics ensues, and an 18-hole score is posted. The score includes penalty strokes, may reflect an agreed maximum score per hole (TWGL says par+5), and may include net pars for unplayed holes (eg can't finish because of darkness).

Adjust the Score

Adjusting scores downward for "bad" holes (so-called "equitable stroke control" under USGA) is one of the more vexed areas of handicapping. The old USGA system was easy to use but not in fact very equitable. There was a "flat" ceiling, based on handicap. E.g. if your handicap was 10-19, your maximum score per hole was 7, 20-29 it was 8, so there was a big discontinuity.

The WHS rule is that everything gets pushed down to net double bogey. This is OK conceptually, but is tricky to implement because you need to closely compare the player's handicap against the handicap rating of each hole. Nonetheless, in order to conform to WHS, TWGL uses the same rule.

Differential for the Round

No controversy here. The formula is always: 
   DIFFERENTIAL = (ADJUSTED_SCORE - RATING) * 113 / SLOPE
as discussed above.

Handicap Index

Under the old USGA system, handicap index was computed as 0.96 times the average of the best (lowest) 10 differentials of the last 20 rounds. Under the WHS, also adopted by TWGL, it is computed simply as the average of best 8 differentials of the last 20 rounds. Note that these two changes somewhat offset each other - dropping the 0.96 factor makes handicap indexes higher, while using the best 8 rather than best 10 rounds tends to lower them.

Under WHS rules, if a player has fewer than 20 recorded rounds, there is a specified number to be taken for averaging, e.g. for 10 rounds played, you average the best 3 rounds. Also, in certain cases of fewer than 7 rounds played, an extra one or two strokes is deducted from the index. Obviously, the handicap calculation gets "smoother" with more rounds used as the basis.

WHS fails

WHS has a few extra wacky provisions tacked on to the above scheme. The general intent is to make very sure that a player does not get an undeservedly high handicap (even though it's hard to see how that happens given the guardrails already adopted: adjustments and "best 8 of 20"). For the record:
Playing Conditions Calculation
If you play in the rain, your score might be artificially high, therefore subtract some number from all players' adjusted scores for that day. To add insult to injury, this magic PCC adjustment number is the result of a secret proprietary algorithm provided to participating golf clubs. So much for transparency.
Limit on Upward Movement
Your index can't increase by more than a fixed amount within a year.
Exceptional Score
If you post a score at least seven below expected, reduce the resulting handicap index by an extra amount (beyond the normal effect of a low round).
All fine ideas except for being impractical and unfair. TWGL doesn't do that.

Purpose of Handicap Index

Note that the resulting handicap index is very far from representing a player's average score. Rather, it is intended to represent a score that the player is reasonably capable of shooting. It is biased downward from the average amount by which a player exceeds the course rating in two ways:
  1. It is based on only the 8 best of the last 20 scores.
  2. Score adjustment screens out the disaster holes
Back to TWGL Home Page