Article Says Real Reason for Slow Play is Short Tee Time Intervals

[18rounds]

I would love that job! (tbh I have actually looked into it, but not sure what my prospects would be here in NL).

Interesting business idea. May need to do the first few for free or in exchange for golf to get some results and case studies. Your package for the course could include collecting data on what is slowing the course down, making recommendations for correcting the problem and training staff and marshals. You could also consult with the course to help implement new technology such as gps carts or video surveillance. Interesting concept.

[HanNL]

Interesting business idea. May need to do the first few for free or in exchange for golf to get some results and case studies.

Your package for the course could include collecting data on what is slowing the course down, making recommendations for correcting the problem and training staff and marshals.

You could also consult with the course to help implement new technology such as gps carts or video surveillance.

Interesting concept.

I actually sent a message to the owner of Pace Manager (consulting business for golf courses) to check whether they have a presence in Europe :).

[RandallT]

Tee Interval	SuperSlow			Slow			Normal			Fast			SuperFast
	Time (hrs)	# Groups per Day	Revenue ($K)	Time (hrs)	# Groups per Day	Revenue ($K)	Time (hrs)	# Groups per Day	Revenue ($K)	Time (hrs)	# Groups per Day	Revenue ($K)	Time (hrs)	# Groups per Day	Revenue ($K)
7	6.1	61	$14.6	5.3	66	$15.8	4.7	74	$17.8	4.3	83	$19.9	3.8	91	$21.8
8	6.1	61	$14.6	5.3	66	$15.8	4.7	74	$17.8	4.3	82	$19.7	3.3	83	$19.9
9	6.1	61	$14.6	5.3	66	$15.8	4.7	73	$17.5	3.8	74	$17.8	3.3	74	$17.8
10	6.1	61	$14.6	5.3	66	$15.8	4.2	67	$16.1	3.7	67	$16.1	3.2	67	$16.1
11	6.1	61	$14.6	4.7	61	$14.6	4.1	61	$14.6	3.7	61	$14.6	3.2	61	$14.6
12	5.3	56	$13.4	4.6	56	$13.4	4.1	56	$13.4	3.7	56	$13.4	3.2	56	$13.4
13	5.2	51	$12.2	4.6	51	$12.2	4.1	51	$12.2	3.7	51	$12.2	3.2	51	$12.2
14	5.1	48	$11.5	4.5	48	$11.5	4.1	48	$11.5	3.7	48	$11.5	3.2	48	$11.5
15	5.1	45	$10.8	4.5	45	$10.8	4.1	45	$10.8	3.7	45	$10.8	3.2	45	$10.8
								60

I've created a spreadsheet simulation of how the flow works throughout the day on a course, and I can adjust various parameters. Like Han above, I'll post a link to it eventually (but at the moment, it's ugly!).

Anyway, when I simulate 5 different types of players (SuperSlow 5+hrs, Slow 4.5hrs, Normal 4.1hrs, Fast 3.7hrs, SuperFast 3.2hrs), you get the results above. It assumed 10 hours of straight tee times at full capacity ($60 per person for this data). Lots of limitations and caveats, but there are some interesting things:

1. At a 10 minute tee time interval, there is VERY LITTLE incentive for the course to speed up play.  From Slow to SuperFast players, the total revenue difference is only $300 or so.  There is a $1K/day incentive to keep play from being SuperSlow (5+ hours).

2. At 11 minute intervals, there is ZERO difference in revenue, no matter how slow your players.  Too many gaps in the course, and you could cram more people on!

3. At 9 minute intervals, there is a $3K/day incentive to get people playing at a 4hr pace or better.  If you have players playing at a 5hour pace, it's costing you.

4. At a 10minute interval, a normal pace group will make it around in 4.2 hours.  If you put those same players on a 9minute interval, that adds 30 minutes to their round because of backlogs.

Anyway, I'm not sure if the thesis of slow play being caused by tee intervals is supported by this simulation data.  From what I see, theoretically, if you reduce from 11 minutes to 7 minutes, you would typically add .6hours to the round (36minutes).  But that's mainly because it's hard to cram people onto the course at faster than 9 minute intervals.  The backlog is on the first tee mainly.

Big caveat: these simulations assume every player is identical for each of the 5 scenarios. In real life, all it takes is one slow group to slow the whole course down.  The simulation spreadsheet shows that, of course, so the trick is whether or not it is worth it to pay a ranger to keep people moving at a 4-4.5 hour pace.

[RandallT]

Tee Interval

SuperSlow

Slow

Normal

Fast

SuperFast

 

Time (hrs)

# Groups per Day

Revenue

($K)

Time (hrs)

# Groups per Day

Revenue

($K)

Time (hrs)

# Groups per Day

Revenue

($K)

Time (hrs)

# Groups per Day

Revenue

($K)

Time (hrs)

# Groups per Day

Revenue

($K)

7

6.1

61

$14.6

5.3

66

$15.8

4.7

74

$17.8

4.3

83

$19.9

3.8

91

$21.8

8

6.1

61

$14.6

5.3

66

$15.8

4.7

74

$17.8

4.3

82

$19.7

3.3

83

$19.9

9

6.1

61

$14.6

5.3

66

$15.8

4.7

73

$17.5

3.8

74

$17.8

3.3

74

$17.8

10

6.1

61

$14.6

5.3

66

$15.8

4.2

67

$16.1

3.7

67

$16.1

3.2

67

$16.1

11

6.1

61

$14.6

4.7

61

$14.6

4.1

61

$14.6

3.7

61

$14.6

3.2

61

$14.6

12

5.3

56

$13.4

4.6

56

$13.4

4.1

56

$13.4

3.7

56

$13.4

3.2

56

$13.4

13

5.2

51

$12.2

4.6

51

$12.2

4.1

51

$12.2

3.7

51

$12.2

3.2

51

$12.2

14

5.1

48

$11.5

4.5

48

$11.5

4.1

48

$11.5

3.7

48

$11.5

3.2

48

$11.5

15

5.1

45

$10.8

4.5

45

$10.8

4.1

45

$10.8

3.7

45

$10.8

3.2

45

$10.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60

 

 

 

 

 

 

 

 

 

I've created a spreadsheet simulation of how the flow works throughout the day on a course, and I can adjust various parameters. Like Han above, I'll post a link to it eventually (but at the moment, it's ugly!).

 

Anyway, when I simulate 5 different types of players (SuperSlow 5+hrs, Slow 4.5hrs, Normal 4.1hrs, Fast 3.7hrs, SuperFast 3.2hrs), you get the results above. It assumed 10 hours of straight tee times at full capacity ($60 per person for this data). Lots of limitations and caveats, but there are some interesting things:

 

1. At a 10 minute tee time interval, there is VERY LITTLE incentive for the course to speed up play.  From Slow to SuperFast players, the total revenue difference is only $300 or so.  There is a $1K/day incentive to keep play from being SuperSlow (5+ hours).

 

2. At 11 minute intervals, there is ZERO difference in revenue, no matter how slow your players.  Too many gaps in the course, and you could cram more people on!

 

3. At 9 minute intervals, there is a $3K/day incentive to get people playing at a 4hr pace or better.  If you have players playing at a 5hour pace, it's costing you.

 

4. At a 10minute interval, a normal pace group will make it around in 4.2 hours.  If you put those same players on a 9minute interval, that adds 30 minutes to their round because of backlogs.

 

Anyway, I'm not sure if the thesis of slow play being caused by tee intervals is supported by this simulation data.  From what I see, theoretically, if you reduce from 11 minutes to 7 minutes, you would typically add .6hours to the round (36minutes).

SuperFast
Time (hrs)	# Groups per Day	Revenue ($K)
3.8	91	$21.8
3.3	83	$19.9
3.3	74	$17.8
3.2	67	$16.1
3.2	61	$14.6
3.2	56	$13.4
3.2	51	$12.2
3.2	48	$11.5
3.2	45	$10.8

The last column was chopped off. Here's another copy/paste of the SuperFast group, if interested.

[RandallT]

This thread made me go from lurker to contributor :). I'll write something in the introduction subforum in a minute.

A while back I made an Excel sheet to be able to calculate the duration of a round and what it depends on. Based on that model I noticed that the duration of a par 3 is of the most influence on the duration of the entire round. If the tee times are spaced closer together than the duration of the longest par 3 on the course, the course will be backed up.

Of course, this is based on my model, which only (as of yet) uses three hole times: one for a par 3, one for a par 4, and one for a par 5. I did incorporate delays during a hole (e.g. looking for a ball for a certain time), which of course also influences duration of a round.

For anyone who is interested in the file: download from WeTransfer. http://we.tl/hvtsX6kiyL. Please note that everything is in Dutch at the moment. Translation on request :).

Ok, HanNL- I have the geekiest of geeky spreadsheets mostly finished. I've been chipping away at it from time to time. Tweaking it and adding. I finally said "Enough!"

Here's the link--> http://we.tl/07HorHKnPM  (it is a Mac only spreadsheet using their "numbers" application). If I get inspired, I'll try to convert to Excel someday. This is my first real experience using Numbers, and I'm loving it.

First some screenshots. Then I'll explain it all. Lots of detail, so people should skip the boring parts (which is likely most of it).

Screenshot 1- SUMMARY PAGE:

Explanation:

In the simulation, you can set player profiles for 5 categories of players: SuperSlow, Slow, Normal, Fast, SuperFast. Then you can adjust the mix of those players. In this simulation, I chose that 10% SuperSlow, 20% Slow, 40% Normal, 20% Fast, 10% SuperFast.  You can also designate what percent of the slots are empty.

Once you set that, the spreadsheet calculates every hole for that distribution. The results graphed below. Not shown are the detailed tables, of course.  Every time you recalculate, you get different scenarios based on the probabilities, but the end results are typically similar.

As you can see above, SuperSlow groups do not wait! Lol But the SuperFast groups wait quite a bit.   The faster the group, the more you wait, obviously.

In the Length of Round by Tee Time graph, you see the damage a slow group can cause and its ripple effect through the day. If a fast group follows a slow group, it can only go about 5 minutes faster than the slow group ahead for 18 holes, so it takes time to get the course going quickly again.

Here is a screenshot of the "Revenue Page":

Here you can summarize as many scenarios as you like. The top row shows the current scenario. You simply cut/paste that row below to compare with others. I ran various scenarios above from 7minute intervals to 14minute intervals. I chose two different distributions of players (10/20/40/20/10 VS 5/15/60/15/5).  In both cases, I think the 10 minute tee intervals looked the best (highlighted in the teal colors.

I allow sunrise and sunset to be parameters, so it figures out how many 18 hole rounds and 9 hole rounds can be squeezed in before sunset.  It ignores 9 hole rounds in the morning or during the day. Just the last groups trying to fit in a quick 9 before dark!  You can set prices for 18 and 9 holes on the right side.

I also calculate for the 50th tee time of the day how long they have to wait from their scheduled tee time.  The shorter the interval, the longer those late groups will be bumped.  7 minute tee times are just not viable, as you see.

The wait time column adds up how long the average group waited during their round. As you squeeze the tee interval, the longer the waits on the course, obviously.

DETAILS, DETAILS, DETAILS.

Not for the faint of heart, here are screenshots of the parameters you can set (explanations below):

In the settings above, you can specify the distribution patterns for your 5 categories of golfer: SuperSlow, Slow, Normal, Fast, and Fastest. You enter how long it takes to play a shot, to putt, to walk to the ball, to walk to the green (and play short game shots around green), to walk to the next hole, how long to clear after your shot or putt (some dawdle!!), how frequent you spend time looking for a ball or making some ruling that takes time (and how long those times take).  There's also a minimum time listed, because the distribution formulas sometimes generated 0 or negative times!

You can set the mean and the standard deviation for each, which is cool. The spreadsheet then uses those parameters to generate a random number for EVERY single scenario. The graphs above show you the results of parameters you chose, so you can validate that the formulas worked.

Some of the academic papers said that some events were "Normal" distributions, and some events were "LogNormal", so that's why I used those. It wasn't my idea.

I also added occasions for when you lose a ball or get an unplayable, and that takes time. That's in the last chart.

Also, the spreadsheet does not allow you hit a shot until the group in front has cleared, which is also configurable by type of player. The slowest groups can take longer to clear, obviously, so I wanted to account for that.

Lastly, you can set the overall conditions: tee interval in minutes, sunrise/sunset, % empty, the distribution of types of players- (how many are SuperSlow, Slow, Normal, Fast, or SuperFast). It's fun running scenarios with only SuperFast players.

I added a correction factor for par 3's that is configurable, to generate the known slow-down on those holes. It seems that  maybe those greens are tougher or tougher bunkers surround par 3's to make them play longer. Without this factor, I didn't see the groups stack up as much on Par 3's. It's artificial, but configurable to however you want. A 1.2 factor made the backups on Par 3's seem realistic to me.

The FW shot factor basically lets you configure how "simultaneous" people play. If you think each person does part of their pre-shot routine while others are playing, then you can tweak that down to like 0.5.  If you think it's strictly one guy at a time with no extra efficiencies, then leave it at 1.0.

Lastly, you can tweak this all for your course. You can pick each hole to set as a par 3, 4, or 5 to match your scenario.  If there is a hole that just plays slower, you can tweak that by changing the factor to more than 1.0.  Or less if it is a fast hole.  You can also enter if a hole has a very long walk to the next hole.  By default, they're all the same.

Anyway, that's a lot of detail. Send me questions if you like. I think that link works for only 7 days.  Send me a PM if you ever want a  copy to play with. Like I said, it's totally geeky. I haven't even shown you the detailed worksheets where you can see where each group is at any minute of the day.  Tons more data that you're not seeing.  I hope I got the calculations right in every cell. It was a bit painstaking.  Send me if I got anything wrong or bogus, or course.  I freely admit there are lots of assumptions, but I tried to make it somewhat detailed where I could.

[HanNL]

Ok, HanNL- I have the geekiest of geeky spreadsheets mostly finished. I've been chipping away at it from time to time. Tweaking it and adding. I finally said "Enough!"

Here's the link--> http://we.tl/07HorHKnPM  (it is a Mac only spreadsheet using their "numbers" application). If I get inspired, I'll try to convert to Excel someday. This is my first real experience using Numbers, and I'm loving it.

+ amazing amount of details

Wow, Randal. I'm definitely going to work through this. Thanks for this.

[RandallT]

Quote:

Originally Posted by HanNL

Quote:

Originally Posted by RandallT

Ok, HanNL- I have the geekiest of geeky spreadsheets mostly finished. I've been chipping away at it from time to time. Tweaking it and adding. I finally said "Enough!"

Here's the link--> http://we.tl/07HorHKnPM  (it is a Mac only spreadsheet using their "numbers" application). If I get inspired, I'll try to convert to Excel someday. This is my first real experience using Numbers, and I'm loving it.

+ amazing amount of details

Wow, Randal. I'm definitely going to work through this. Thanks for this.

Thanks, please do. Before I draw any conclusions from it, I want to make sure the model is somewhat ok. Garbage in and garbage out, and all that.  Anyone is free to join in and tell me what's bogus about it. Give some ideas on improving.  Just shoot me a PM, or jump in here.

I know you have enough detail to chew on, but I thought I'd walk you through the "Singles" pages and the "Group" pages.

SINGLES

Most of the random generation occurs on the "Singles" pages (front nine and back nine). On the far left each player is generated a number between 1-100. From that, that player's row is assigned a speed (Slowest, Slow, Normal, Fast, Fastest). That assignment depends on the parameters you set through a lookup.

Once the speed of the player is assigned, that row will then retrieve all the parameters it needs for that speed profile from your parameters. It looks up the appropriate mean/standard deviation for all of the events in the round (playing shots, putting, travelling speeds).

Then the round starts at Hole #1.

The tee shot formula is: =MAX($G3,NORMINV(RAND(),$H3,$I3))×(Round Settings::$B$12). That generates a random number based on the mean and standard deviation for that speed player.

If it's a par 5 (as you set in your parameters), there is the time to travel down the fairway (randomly generated like above for the tee shot), find the ball/get a ruling, play the next shot to the green (randomly generated), clear the area (this is not additive, actually- but it prevents the next group from playing until you are clear).

If it's a par 4 or a par 5, there is the time to travel down the fairway, find the ball/get a ruling, play the next shot to the green (randomly generated), clear the area (this is not additive, actually- but it prevents the next group from playing until you are clear).

If it's a par 3, 4, or 5 (by the parameters you set), it then calculates the time to travel to the green (again a random distribution), find the ball and recover/get a ruling, putt the ball (again a random distribution), clear the green, and travel to the next hole.

Each of those elements gets calculated based on the parameters you set. I see that I had wanted to use a "LogNormal" distribution for the travel times, but I couldn't get that right in Mac Numbers. I found a formula in Excel for that, but it wasn't working right, so I tabled that until later. Oops, I never fixed that. For now, all calculations are based on a normal distribution.

GROUPS

The "groups" pages do a couple things differently than the singles pages. Since the random calculations are done, the group pages assigns each block of 4 players to a group.  It then uses an OFFSET function to group them together in 4's. For playing shots, those things are sequential and added (if each guy takes 30 seconds, that's 2 mins total). For any travelling activity, those things are simultaneous and uses a MAX function (if one guy takes 1 min, and the others take 30 seconds, the group gets 1 minute for that). The group can only go as fast as the slowest guy.

The other big difference is that for the Groups page is that it is cumulative in time, and adds in the waiting aspect. For each group, you can see what time they hit every "gate." They cannot play a shot until the group in front has moved beyond that gate by finishing the "Clear".  That allows the calculation of wait times from the fairway or the tee throughout the round.

MISCELLANEOUS

FYI- Error #1 was just found. I calculated the revenue wrong. When I went to multiply the number of 9-hole rounds by the cost of the 9-hole round, I ADDED them instead of multiplied. Duh. I wondered why the revenue was not rounded to $10, when the prices were all increments of $10.

The other aspect I want to make sure of is whether or not the overall model fits what we see on the course. Do we really spend half the time taking shots and 1/3 of the time travelling. It doesn't seem like I'm giving enough time to finding balls/making rulings/etc.  In this graph below, I have the Slowest groups only spending 17minutes looking for balls and taking drops. Seems low, and I need to tweak the parameters.

[natureboy]

GROUPS

The "groups" pages do a couple things differently than the singles pages. Since the random calculations are done, the group pages assigns each block of 4 players to a group.  It then uses an OFFSET function to group them together in 4's. For playing shots, those things are sequential and added (if each guy takes 30 seconds, that's 2 mins total). For any travelling activity, those things are simultaneous and uses a MAX function (if one guy takes 1 min, and the others take 30 seconds, the group gets 1 minute for that). The group can only go as fast as the slowest guy.

The other big difference is that for the Groups page is that it is cumulative in time, and adds in the waiting aspect. For each group, you can see what time they hit every "gate." They cannot play a shot until the group in front has moved beyond that gate by finishing the "Clear".  That allows the calculation of wait times from the fairway or the tee throughout the round.

MISCELLANEOUS

FYI- Error #1 was just found. I calculated the revenue wrong. When I went to multiply the number of 9-hole rounds by the cost of the 9-hole round, I ADDED them instead of multiplied. Duh. I wondered why the revenue was not rounded to $10, when the prices were all increments of $10.

The other aspect I want to make sure of is whether or not the overall model fits what we see on the course. Do we really spend half the time taking shots and 1/3 of the time travelling. It doesn't seem like I'm giving enough time to finding balls/making rulings/etc.  In this graph below, I have the Slowest groups only spending 17minutes looking for balls and taking drops. Seems low, and I need to tweak the parameters.

If it's at all helpful, a 35 handicapper (~ avg score of 110) will hit an average of 3.5 balls per round to either O.B., Hazard, or Lost. Since that's a multi-round average and I expect the variance is pretty high, you'd have some super-slow groups that could potentially spend in the vicinity of 25 minutes searching...though just because you are wayward doesn't necessarily mean you play slow. An 'outlier' group like that might gum up the works a bit.

Curious, if you take the super slow and slow groups off the course, how much faster is the round for the other categories?

Wow the chart graphics for Mac's 'Numbers' really blow away Excel, though I suppose there are specialty programs for the pretty charts.

[RandallT]

If it's at all helpful, a 35 handicapper (~ avg score of 110) will hit an average of 3.5 balls per round to either O.B., Hazard, or Lost. Since that's a multi-round average and I expect the variance is pretty high, you'd have some super-slow groups that could potentially spend in the vicinity of 25 minutes searching...though just because you are wayward doesn't necessarily mean you play slow. An 'outlier' group like that might gum up the works a bit.

Curious, if you take the super slow and slow groups off the course, how much faster is the round for the other categories?

Wow the chart graphics for Mac's 'Numbers' really blow away Excel, though I suppose there are specialty programs for the pretty charts.

Yah, I enjoy Mac Numbers. These are all just basic templates, and I agree it looks better. There are some things that are not quite as powerful, but overall, they are comparable for most uses of spreadsheets.  The graphing still seems tricky to set up, but that's probably just me. Anyway, thanks for the feedback.

As you requested, I ran a simulation where there were ONLY normal, fast, and super-fast players (33% each). Of course, these types of players only perform to the levels that I "programmed" them to play, and they could be tweaked to play at any speed. In general, I calibrated their parameters to result in play at: Normal- 4.1 hr rounds in groups, Fast 3.6 hr rounds, SuperFast 3.1 hr groups. It's tricky to calibrate them though, since there are so many parameters (tee time interval, plus all the individual parameters, etc). But they're close to those times- give or take.

Anyway, I set the Slow and SuperSlow groups to 0%. But then I manually inserted a group of 4 super-slow players in the middle of the day.  I've put it all in the "SPOILER" thing below, since I meant the simulation to just analyze tee times to further the discussion here about tee time analysis. Once I finalize a few things, I'll post the results of some tee time analysis with the spreadsheet to see if it conflicts with the original premise in the OP.

For now, enjoy the data!

The slow group was inserted manually at 1:40PM. The raw data chart for the tee times is at the bottom. They are the "1111" group. Others are all composed randomly assigned 3 (Normal), 4 (Fast), or 5(SuperFast). Approximately 1/3 of each type.

As you can see, each subsequent group after the slow group (which takes almost 5 hours) can only speed up by a few minutes over the slow group. It appears to take about 5 hours for the course to recover to the speed it was averaging before.

	Total Time	Playing Time	Wait Time	First Tee Delay	Group Makeup
6:30 AM	225	135	0	0w	3443 (Fast)
6:40 AM	221	121	20	0w	4535 (Fastest)
6:50 AM	232	138	2	0w	3443 (Fast)
7:00 AM	231	130	19	0w	4354 (Fastest)
7:10 AM	227	118	29	0w	5454 (Fastest)
7:20 AM	228	134	13	0w	5344 (Fastest)
7:30 AM	225	120	25	0w	5445 (Fastest)
7:40 AM	227	137	6	0w	5333 (Fast)
7:50 AM	223	117	23	0w	5545 (Fastest)
8:00 AM	220	121	15	0w	5534 (Fastest)
8:10 AM	217	126	13	0w	4445 (Fastest)
8:20 AM	228	140	0	0w	5333 (Fast)
8:30 AM	231	139	5	0w	3344 (Fast)
8:40 AM	230	133	12	0w	3534 (Fast)
8:50 AM	227	131	13	0w	3544 (Fastest)
9:00 AM	223	125	17	0w	5355 (Fastest)
9:10 AM	225	133	4	0w	4534 (Fastest)
9:20 AM	222	132	8	0w	4345 (Fastest)
9:30 AM	219	118	20	0w	5455 (Fastest)
9:40 AM	222	138	0	0w	3344 (Fast)
9:50 AM	221	123	17	0w	3554 (Fastest)
10:00 AM	224	134	0	0w	3435 (Fast)
10:10 AM	225	138	0	0w	4433 (Fast)
10:20 AM	233	144	0	0w	4333 (Normal)
10:30 AM	235	138	10	0w	5333 (Fast)
10:40 AM	233	123	33	0w	5544 (Fastest)
10:50 AM	231	126	25	0w	3455 (Fastest)
11:00 AM	228	128	17	0w	3445 (Fastest)
11:10 AM	227	130	15	0w	5533 (Fastest)
11:20 AM	224	121	25	0w	5454 (Fastest)
11:30 AM	222	139	3	0w	4343 (Fast)
11:40 AM	222	141	1	0w	3335 (Fast)
11:50 AM	224	135	1	0w	4335 (Fast)
12:00 PM	239	142	0	0w	3433 (Normal)
12:10 PM	237	133	20	0w	5335 (Fastest)
12:20 PM	233	123	34	0w	5444 (Fastest)
12:30 PM	230	125	27	0w	5543 (Fastest)
12:40 PM	227	120	27	0w	3555 (Fastest)
12:50 PM	225	136	1	0w	3434 (Fast)
1:00 PM	221	118	30	0w	4455 (Fastest)
1:10 PM	225	140	1	0w	3443 (Fast)
1:20 PM	222	133	9	0w	5344 (Fastest)
1:30 PM	219	128	10	0w	3544 (Fastest)
1:40 PM	287	176	0	0w	1111 (Slowest)
1:50 PM	283	123	83	0w	5544 (Fastest)
2:00 PM	280	116	88	0w	4555 (Fastest)
2:10 PM	276	124	76	0w	3455 (Fastest)
2:20 PM	274	125	66	0w	5543 (Fastest)
2:30 PM	272	131	57	0w	4533 (Fast)
2:40 PM	269	131	59	0w	3553 (Fastest)
2:50 PM	266	131	56	0w	4435 (Fastest)
3:00 PM	264	121	64	0w	4455 (Fastest)
3:10 PM	260	120	61	0w	5454 (Fastest)
3:20 PM	257	138	38	0w	4343 (Fast)
3:30 PM	254	128	48	0w	5335 (Fastest)
3:40 PM	251	134	31	0w	3534 (Fast)
3:50 PM	253	148	19	0w	3433 (Normal)
4:00 PM	250	129	40	0w	3355 (Fastest)
4:10 PM	249	139	25	0w	3345 (Fast)
4:20 PM	244	122	41	0w	5355 (Fastest)
4:30 PM	244	139	21	0w	3353 (Fast)
4:40 PM	240	130	34	0w	4435 (Fastest)
4:50 PM	239	128	32	0w	3553 (Fastest)
5:00 PM	241	137	14	0w	3534 (Fast)
5:10 PM	238	114	51	0w	5554 (Fastest)
5:20 PM	236	129	22	0w	3445 (Fastest)
5:30 PM	232	131	20	0w	4453 (Fastest)
5:40 PM	231	128	25	0w	3554 (Fastest)
5:50 PM	227	118	38	0w	5554 (Fastest)
6:00 PM	223	119	27	0w	3555 (Fastest)
6:10 PM	238	140	0	0w	3433 (Normal)
6:20 PM	235	132	17	0w	4434 (Fast)
6:30 PM	232	131	19	0w	5533 (Fastest)
6:40 PM	229	131	14	0w	4345 (Fastest)
6:50 PM	229	117	39	0w	5455 (Fastest)
7:00 PM	226	137	9	0w	3543 (Fast)
7:10 PM	225	124	15	0w	5354 (Fastest)
7:20 PM	222	122	13	0w	5553 (Fastest)
7:30 PM	224	137	1	0w	3335 (Fast)
7:40 PM	220	132	4	0w	3445 (Fastest)
7:50 PM	219	129	0	0w	5353 (Fastest)
8:00 PM	217	125	10	0w	4355 (Fastest)
8:10 PM	240	149	0	0w	3333 (Normal)
8:20 PM	238	135	21	0w	4335 (Fast)
8:30 PM	237	136	9	0w	3345 (Fast)
8:40 PM	235	125	29	0w	3555 (Fastest)
8:50 PM	231	119	36	0w	5544 (Fastest)
9:00 PM	228	131	18	0w	4345 (Fastest)

[HanNL]

As you can see, each subsequent group after the slow group (which takes almost 5 hours) can only speed up by a few minutes over the slow group. It appears to take about 5 hours for the course to recover to the speed it was averaging before.

This is quite logical actually: each group only walks their normal speed on hole 18. The rest of the holes they are held up by the slow group.

[RandallT]

Quote:

Originally Posted by RandallT

As you can see, each subsequent group after the slow group (which takes almost 5 hours) can only speed up by a few minutes over the slow group. It appears to take about 5 hours for the course to recover to the speed it was averaging before.

This is quite logical actually: each group only walks their normal speed on hole 18. The rest of the holes they are held up by the slow group.

Exactly. Any ideas how to model (in a spreadsheet where one row is one group) how to allow a group to pass a slow group ahead? One of the bogus assumptions I make in the spreadsheet is that there is NO PASSING. The only reason is that I couldn't figure out a way to implement that concept.

As it stands now, for a group to play a shot from the tee or the fairway, the row above it (prior tee time) must have passed the appropriate gate to be "CLEAR."  In general, this is ok, because the spreadsheet calculates left to right, up to down- as I understand.  But if a fast row is allowed to pass the slow row above it (maybe a rule like 2 straight holes with over 2 minute wait?), then the slow row now depends on the fast row below it to "CLEAR" out of the way before it can play. I don't know how I'd right a nimble equation like that! (Check the row above, except if you've been passed, then check the row below... if you've been passed twice, then check two rows below.  Too hard!)

Maybe if the simulation were in a run-time environment where various state variables could be used, but in a spreadsheet, I couldn't dream up any simple model to allow for passing. Hence all of the stuck groups behind the one slow one.  In reality, the slow group might allow groups to pass, making their round even slower, but speeding up the overall play, I'd think.

For those interested, here's the calculation on Hole#2 (a par 4).  Notice that the wait cell is determined by the 4 rows highlighted. The 636.02 is set for the wait on the tee, because the group ahead isn't clear of the fairway until then. If it were a par 3 or a par 5, a different cell would be used.  The cell uses the highest value of the appropriate CLEAR cell and the time after travelling to the 2nd hole (the shaded cell on the left.

[HanNL]

The only way I can think of is making use of a (visual basic) script to simulate passing. (switching the groups in the sheet and calculate the rest of the holes from there)

[natureboy]

Exactly. Any ideas how to model (in a spreadsheet where one row is one group) how to allow a group to pass a slow group ahead? One of the bogus assumptions I make in the spreadsheet is that there is NO PASSING. The only reason is that I couldn't figure out a way to implement that concept.

As it stands now, for a group to play a shot from the tee or the fairway, the row above it (prior tee time) must have passed the appropriate gate to be "CLEAR."  In general, this is ok, because the spreadsheet calculates left to right, up to down- as I understand.  But if a fast row is allowed to pass the slow row above it (maybe a rule like 2 straight holes with over 2 minute wait?), then the slow row now depends on the fast row below it to "CLEAR" out of the way before it can play. I don't know how I'd right a nimble equation like that! (Check the row above, except if you've been passed, then check the row below... if you've been passed twice, then check two rows below.  Too hard!)

Maybe if the simulation were in a run-time environment where various state variables could be used, but in a spreadsheet, I couldn't dream up any simple model to allow for passing. Hence all of the stuck groups behind the one slow one.  In reality, the slow group might allow groups to pass, making their round even slower, but speeding up the overall play, I'd think.

Would need empirical data, but as a guess there is likely a 'friction' slowing both groups during the play-through interval. By allowing groups to play through I would expect it delays the time for the 'blockage' peak to propagate back to the 1st tee and probably lowers the magnitude of the overall delay.