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Subject: The value of a fourth golfer
Posted by: Guru
- [330592710] Thu, Jul 01, 2004, 12:35
While looking at some of the extra trade decisions made for this week's tournament, I got to thinking about the marginal scoring benefit of having a 4th active golfer. I can recall a number of instances when I've had a 4th golfer who didn't contribute much to the scorecard at all. But, on average, how many strokes would you expect a 4th active golfer to save?
To begin, I looked at the results of last week's tournament, the Booz Allen Classic. It seemed like a relatively normal tournament (from a scoring standpoint). Roughly half of the field made the cut, and the average score for a team which started with 4 active golfers was -38 (actually, -38.4). It was a little abnormal in the scarcity of expensive (i.e., highly ranked) golfers, however.
I did my analysis on the 184 teams that started with 4 active golfers. For each team, I calculated the actual team score, and then compared it to what the score would have been if each of the four golfers was replaced by an inactive golfer. Thus, for each foursome, there are four possible 3-golfer combinations to compare against.
As mentioned above, the average actual score for the 184 foursomes was -38.4. Comparatively, the average score of the 736 hypothetical threesomes was -30.7, for a difference of almost 8 strokes. Thus, one Q&D comparison is that the 4th active golfer improved a team's score by an average of almost 8 strokes (7.7).
There are some extremes in this sample. One team would actually have been 7 strokes better with a threesome instead of a foursome! That team had only one golfer (Daly) make the cut, who shot 11 over par on the weekend. By eliminating that specific golfer, zeroing out the weekend rounds would have been enough to offset the marginal benefit of the extra golfer in the first two rounds.
At the other extreme, one team benefited by 33 strokes. This was a team that had only two survivors for the weekend. One was Adam Scott, and the other was Daly. By eliminating Scott from that opening foursome, the team score would have been 33 strokes worse.
The distribution of these score differences is interesting. Here are some percentile breakpoints:
95%-ile: -18
90%-ile: -15
70%-ile: -10
50%-ile: -7
30%-ile: -3
23%-ile: -2
11%-ile: -1
2%-ile: 0
So, there was about a 30% chance that the team score was improved by 3 strokes or less, and an 11% chance that the improvement would have been 1 stroke or less. On the other hand, there was also a 30% chance that the 4th golfer improved the team score by 10 strokes or more.
There are some obvious caveats. This analysis makes no attempt to handicap the likehood of each threesome. All other things being equal, a manager who opts to go with only 3 active golfers would certainly try to exclude the weakest link. That's not always easy to discern, but it does seem that manager selection should add some value. So perhaps a more realistic comparison would show a reduced impact. I am going to try to see whether the price of the omitted golfer is correlated with the score improvement. Stay tuned.
And, there may have been some scoring and roster idiosyncrasies for this tournament that make it atypical. I'm sure that would have been the case had I used the U.S. Open as my test case. I'll try to do a similar analysis for the next few weeks, just to see how stable the results are.
It would also be interesing to measure the marginal scoring contribution of the 3rd active golfer. Maybe I'll extend the analysis to that as well. |
| 1 | Guru
ID: 330592710
Thu, Jul 01, 2004, 12:49
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It turns out that there is a 5.7% positive correlation between the marginal scoring benefit of a golfer and his price, but it is very slight. And, because Adam Scott was both the best golfer of the week and the most expensive one, you would certainly expect a positive correlation. However, if I exclude all of the Adam Scott results, the correlation is still 5.7%.
If golfer price is a reasonable proxy for golfer quality, then this result doesn't suggest that getting to choose which golfer to exclude has a tremendous influence on the marginal scoring difference. Then again, this tournament was missing all of the high priced golfers, so the qualitative differences in the actual field might have been slighter than normal - and not accurately reflected in the relative prices.
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| 2 | FRICK
ID: 441551913
Thu, Jul 01, 2004, 12:57
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Guru, do you have to have 4 golfers on your team to be active? I.E. Would Tiger and VJ be an active team if the other two slots were left open.
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| 3 | Guru
ID: 330592710
Thu, Jul 01, 2004, 13:02
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Nope. You must have 4 golfers on your team. Doesn't matter if they are playing that week, but if you have a vacant slot, your score for the week is zero.
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| 4 | Guru
ID: 330592710
Thu, Jul 01, 2004, 14:15
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I also looked at the scoring advantage for the 1st two rounds vs. the last two rounds.
There wasn't much difference in the averages. During the 1st two rounds, the fourth golfer improved the team score by an average of 3.4 strokes. The improvement for the final two rounds was therefore 4.3 strokes. Although the difference is only about 1 stroke, I guess you could also say it's about 25% more.
Naturally, there is more volatility in the results for the last two rounds. If the 4th golfer misses the cut, he is no help at all. But if he makes the cut, the advantage is much more significant.
For this tournament, about 70% of the roster golfers made the cut. So, 30% of the time, the 4th golfer added no benefit in the final two rounds. The other 70% of the time, that surviving golfer improved the team score by an average of roughly 6 strokes.
Consequently, you might look at value this way: If your 4th golfer misses the cut, he'll only benefit your team score by an average of about 3-4 strokes for the tournament. But if he makes the cut, the average benefit is more like 9-10 strokes.
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| 5 | Guru
ID: 330592710
Mon, Jul 05, 2004, 14:12
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First a correction, then an update.
I screwed up the price correlation in post 1. The value of the 4th golfer was actually much more correlated with price. The correlation coefficient was about 40%. The scoring benefit of a cheap golfer priced between $500-750 was only 5.5 strokes, vs. the overall average of 7.7.
Now, the update. I applied the same analysis to the Cialis Western Open scores. The results look very similar. The overall average scoring improvement of the 4th golfer was 7.0 strokes. Golfers who ended up making the cut improved the team score by 8.6 strokes, while those who missed the cut improved a team score by only 3.2 strokes.
Once again, the improvements were correlated with golfer price - this time with a correlation coefficient of 55%. Fourth golfers priced from $500-750 improved a team score by about 4.8 strokes. The improvement for those priced from $750-$1000 was 5.3 strokes, and those priced above $1000 improved the team score by 9.3 strokes.
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| 6 | StLCards
Leader
ID: 31010716
Wed, Jul 07, 2004, 13:46
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Very interesting Guru. Thanks for sharing. From this analysis is seems that (if you are out of trades) spending the money for the extra golfer would be better than going with only 3 golfers for a tournament. You could gain 5-8 strokes while losing about a half stroke due to a reduced bankroll.
I've always been curious to the value of the # of players that make the cut (as opposed to starting with only 3) as post 4 gets at a bit. I think it would be interesting to look at scores for all teams that had 4 golfers vs teams that had 3 golfers, when all started with 4. This would be better in my mind than trying to randomly select a golfer to "drop" for analysis. It seems that most players that miss the cut are playing poorly to begin with and would not be equally weighted with those that made the cut. I guess you could also compare day 1/2 scores with day 3/4 scores to see the effect as well. For the team I had with only 3 golfers last week my net difference was 3 strokes over 2 days. Interestingly enough, that player (Zack Johnson) helped my team (unique birdies) by 3 strokes over the first 2 days.
I was surprised at first when you said there was little correlation between a 4th golfer helping a team and price, so I felt much better with your correction :) Otherwise it would seem to say a lower priced player will score equally as a higher priced one, which would make price pretty unimportant from a long term perspective.
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