The Handicaps and Handicap Scramble System

History

I've been keeping score for Ed since 2007.  Ed has always tried to adjust individual handicaps to compensate for the unique playing conditions at Plumas - it's short, but very tight; long hitters that spray the ball need a little extra help relative to their flat-land index.  If you've been here before, he also adjusts based on your past rounds, so eventually we get everyone dialed in pretty well.

At first, he handicapped the scramble too, but there really wasn't a methodology.  And it's hard to go by history, because the membership in most teams isn't identical year over year.  

I thought for sure that someone had figured out a good system and published it, so before the 2008 tourney I set out to find some published way to calculate a scramble handicap so we could be a bit more systematic about it.  I thought surely GHIN, or NCGA, or somebody would have come up with one, but to my astonishment I found that there's almost nothing out there - at least with any real data behind it.  So, I decided to see if I could invent one, and use the historical data we've accumulated to test it.

The formula I came up with works pretty well: The gross spread between the first and last place teams is usually around 12-14 strokes, but the handicaps compress the net difference down to about half that.  More importantly, as the chart below shows, it gives low and high handicap teams about the same chance to win.  (Winning teams are the green dots) Experience shows that often only a couple of strokes separate the winner from also-rans, so if all four of you miss a couple of 5 footers, you can pretty much figure it cost you some prize money.

The median winning score for four-man teams is around net 15 under. For two man scrambles we don’t have much data, but it looks like about 11 under has a good chance to win.

For those interested, below is the formula, and the line of reasoning that led to it.

Rationale

In thinking about this problem I started off with a couple of extreme examples: First, suppose you have a two handicapper teamed with three 30-handicappers -- what should the team handicap be? Well, the chances that any of the 30 handicapper's shots are going to help the 2 handicapper is very low - might show him the line on a putt now and then, but that's it. So if his handicap was two before, the team handicap should be very close to two. 
 

Now what happens if we team the good golfer with players closer to his level? Obviously they help lower the team score more. So far we have two pieces of insight: First, 

• A starting point for the team handicap should be the individual handicap of the best player on the team.

Said another way, the highest handicap a team could ever have would be equal to the best player's handicap. The second insight is that 

• The closer to the best player’s index the other players’ indexes are, the more of an impact they should have on the team’s overall handicap.

It’s no news that one of the biggest differences between low hand high handicappers is consistency. Low handicappers’ scores are lower on average of course, but they also vary less than those of us duffers from round to round. I think this is because they have fewer truly disastrous holes. A mistake costs a stroke, not three or four. The scramble format tends to cover up mistakes, and so it stands to reason that when we team two 20 handicappers together, the expected benefit to their handicap will be more than if they were a pair of two handicappers, who are pretty consistent in the first place. So this leads to another insight: 

• The higher the best player’s index is to begin with, the more strokes should be taken away when another similarly skilled player joins the team. Conversely the lower the best player’s index, the less it should move when another skilled player is added.

I came up with a formula (listed below) that combines the player’s indexes to arrive at a team handicap for a scramble that behaves according to the goals outlined above.

There are two nominally adjustable parameters, which I’ve tuned based on over 50 team/rounds of actual data.  I recommend they be left alone, but I’ll mention them for completeness:

Star Factor:  This controls how big the effect of the best golfer’s index should be vs. the next best, etc.  As an example, how close does the next best player need to be to get a five handicapper down to four as a team? In the formula this is called “SF” for “Star Factor”.  I use a value of 2.0.

Index Base:  So where does this end? Could there be a golfer so good that no matter who he plays with we shouldn't give him any fewer strokes? How good would he have to be? I think the answer is yes, but that player would need to be better than a scratch golfer. In the formula below this number is called the "Index Base". It’s the “diminishing returns” point – as the best golfer on a team gets closer to this handicap, the changes to his handicap due to his teammates get smaller and smaller. This value is set to -4 (equivalent to a plus four index).  Tiger plays to about a plus eight, so this wouldn’t work for him.  But it seems to work very well for the rest of us.

Results

After eight years & 93 total teams/rounds, player indexes from 2 to 36) we've got a system that seems to work really well.  A perfect handicap system, if everyone plays to their ability, would end with all teams tied on net score.  So I judge the formula's performance based on how much the spread of gross scores is reduced in terms of the spread of net scores.  I compute this by taking a sample standard deviation of both.

The median team had a handicap of 7, and made 5 birdies to finish net 12 under.  The winning score is usually between -14 and -18, and there’s almost no skew between low and high handicap teams in terms of which ones come out on top.  We often have multiple teams tied for first place.

While in most years the formula has performed very well, in 2009 a team composed of high handicap players won the scramble by a huge margin – they finished net 20 under.  I notice though, that they were the sort of high-handicappers who tended to score “par par triple-bogey, par par quadruple-bogey”.  When teamed in a scramble they covered each other nicely and won going away.  So, the system isn't perfect, but overall it ensures good competition – miss a couple of putts you should have made, and you go from winner to out of the money -  just as it should be.

If you have comments or want to know more, just look me up after a round, or shoot me an email!

Joel Dedrick: joel@dedricks.net