What flaws do you think there are in the handicap system?

[No Mulligans]

23 minutes ago, DaveP043 said:

I agree!  In researching stuff for this website, I've read through a bit of the CONGU Handicap Manual, and it makes the USGA manual seem crystal-clear by comparison.  But some of the things that are done under CONGU, like counting only competition scores (with very limited exceptions) and taking day-to-day difficulty into account do make sense to me.

Counting only competition scores would result in many (most?) players no longer keeping a handicap.  I've had a handicap for a couple of years and haven't played any official competitions.  So out of self interest, I hope the USGA doesn't make that change.  I've always got a GameGolf handicap though.

[Hardspoon]

16 minutes ago, No Mulligans said:

Counting only competition scores would result in many (most?) players no longer keeping a handicap.  I've had a handicap for a couple of years and haven't played any official competitions.  So out of self interest, I hope the USGA doesn't make that change.  I've always got a GameGolf handicap though.

I have a feeling that the system might move in this direction over the next 5 years...official handicaps will be for those who compete regularly, and "data-tracking" like Game Golf and apps like The Grint will be used for progress tracking by casual players.

[iacas]

5 hours ago, SG11118 said:

The handicap system has a massive database of continually posted scores from golfers with known handicaps.  Why couldn't this database of scores be utilized with statistics to more accurately and cost effectively rate golf courses?

Is it simply that the golf industry doesn't want to put a bunch of course raters out of work? 

Course raters are almost all volunteers.

Like me.

5 hours ago, Groucho Valentine said:

In would like to see the handicap system take into account course conditions that can make a course play more difficult or easy on a particular day. But i cant see how you could include it into the system. It seems like it would be too complicated. 

 

[Groucho Valentine]

4 hours ago, DaveP043 said:

I agree!  In researching stuff for this website, I've read through a bit of the CONGU Handicap Manual, and it makes the USGA manual seem crystal-clear by comparison.  But some of the things that are done under CONGU, like counting only competition scores (with very limited exceptions) and taking day-to-day difficulty into account do make sense to me.

It certainly does. It would be especially relevant for players who have 50% or more of their rounds posted through competition. As i do.  But also feel like we'd be getting into some weird bifurcation with that though. Competition vs casual. But If were going to have one system at one point, and we have compu-bots figuring out all the math, then id like to see it. 

One of the best rounds I've ever played was a 77 i shot at Galloway National. 77 doesn't sound all that great but the wind was blowing like 20 that day and gusting up to 40. Anyone who has played at Gallaway knows how much of a bitch that place is when the wind blows. I was always somewhat annoyed that the handicap system didn't reflect how well i played that day. 

[SG11118]

19 minutes ago, iacas said:

Course raters are almost all volunteers.

Like me.

 

I thought my course has to pay every couple of years to have the course re-rated.  I could be wrong.  I figured course raters got paid.  I appreciate volunteerism.  No offense meant.

I read through the 2018 Worldwide Golf Handicap System thread.  If they are talking about using statistics to adjust scores on a daily basis, it seems totally within the realm of possibility that they can also use statistics and computers to adjust the NORMAL / TYPICAL course rating and slope (or alternative system).  Glad to hear something like this is happening.  In terms of fairness, I like the idea of using statistics to compute a more exact course rating based on quantitative scores.

[Braivo]

1 minute ago, SG11118 said:

I thought my course has to pay every couple of years to have the course re-rated.  I could be wrong.  I figured course raters got paid.  I appreciate volunteerism.  No offense meant.

I read through the 2018 Worldwide Golf Handicap System thread.  If they are talking about using statistics to adjust scores on a daily basis, it seems totally within the realm of possibility that they can also use statistics and computers to adjust the NORMAL / TYPICAL course rating and slope (or alternative system).  Glad to hear something like this is happening.  In terms of fairness, I like the idea of using statistics to compute a more exact course rating based on quantitative scores.

I agree. With a large enough sample size it should be easy to figure out a rating based on posted scores from that course. Seems far more efficient and scientific than the current method. 

[iacas]

On July 11, 2016 at 3:00 PM, SG11118 said:

I read through the 2018 Worldwide Golf Handicap System thread.  If they are talking about using statistics to adjust scores on a daily basis, it seems totally within the realm of possibility that they can also use statistics and computers to adjust the NORMAL / TYPICAL course rating and slope (or alternative system).  Glad to hear something like this is happening.  In terms of fairness, I like the idea of using statistics to compute a more exact course rating based on quantitative scores.

Keep in mind that as you change the course ratings, the handicaps of the people will change, too. The two are, by definition, linked. So really, this type of thing might only work when a course makes changes: you could track how the same players are affected by the different course.

And ultimately, I doubt much would change. Suppose you used nine courses in the area as the basis for rating the tenth: you'd have enough golfers with established handicaps that you could probably reasonably do something like that. But then… what? Do you take those golfers and use courses 2-10 and re-rate course #1 based on their scores and the other nine? Or do you do five at a time, and kind of rotate them throughout?

And how does that get affected by the daily scores… what if one course sets up easily for a month because the wind stays down for an extended stretch, or the courses are firm and afford extra roll and shorter approaches?

It's a more complex problem than just "use the golfers' scores to generate the course rating." Because the course rating defines what you can say about the golfers' scores!

[SG11118]

14 hours ago, iacas said:

Keep in mind that as you change the course ratings, the handicaps of the people will change, too. The two are, by definition, linked. So really, this type of thing might only work when a course makes changes: you could track how the same players are affected by the different course.

And ultimately, I doubt much would change. Suppose you used nine courses in the area as the basis for rating the tenth: you'd have enough golfers with established handicaps that you could probably reasonably do something like that. But then… what? Do you take those golfers and use courses 2-10 and re-rate course #1 based on their scores and the other nine? Or do you do five at a time, and kind of rotate them throughout?

And how does that get affected by the daily scores… what if one course sets up easily for a month because the wind stays down for an extended stretch, or the courses are firm and afford extra roll and shorter approaches?

It's a more complex problem than just "use the golfers' scores to generate the course rating." Because the course rating defines what you can say about the golfers' scores!

I agree with most of your post - I'll try to elaborate on what I'm thinking.

If the same player plays two courses and posts scores, we have a dataset telling us how difficult the two courses are relative to each other for a player with a given handicap.  This dataset doesn't mean a whole lot on its own, but I think if you analyzed the scores of every player who played multiple courses during the year, you probably have many millions of datasets telling us the relative difficulty of courses to other courses for golfers of a given handicap.  

I'm envisioning adjusting TYPICAL course ratings over a year time period.  Minor blips where the golf course plays easier or harder will be normalized over a year long period.  I'm also not talking about sending a team of golfers of varying handicaps out to a course to play it and use their scores to rate the course.  Not exactly sure how I envision using the daily adjustments.  I'm talking about using the aggregate of all posted scores from all players over the year and comparing the differentials to the differentials those same players scored on other courses.  Using this information, using statistics, and using every golfer who is posting scores to develop a complex computer program which will tell us how difficult every set of tees is relative to each other for a variety of handicap players, and adjusting course ratings and slopes based on this intricate network of information.

When golfers play their "home" course where a majority of their rounds are played, there really will be no value to what I'm taking about.  Player handicaps and course handicaps are definitely linked, so if a player continually posts scores from the same set of tees, there will be no information available as to how difficult the set of tees really is and whether the current ratings for the course are appropriate.  The true value is when "guests" post scores on a course.  They provide a relative comparison of how difficult a course is to other courses they have played.

 

[natureboy]

On 7/11/2016 at 3:00 PM, SG11118 said:

If they are talking about using statistics to adjust scores on a daily basis, it seems totally within the realm of possibility that they can also use statistics and computers to adjust the NORMAL / TYPICAL course rating and slope (or alternative system).  Glad to hear something like this is happening.  In terms of fairness, I like the idea of using statistics to compute a more exact course rating based on quantitative scores.

To a large extent (though IMO not perfectly) the refinement of the Course Rating system when slope was added did this. They compared their rating system to tons of actual scores by different HCPs to verify its validity.

Even if the course and slope system is not 'perfect' it' still very statistically valid. It's better on multi-round averages than single rounds, but implementing the 'daily average' will add an extra tick of accuracy. I think it would be feasible to use an algorithm to identify a population of scratch golfers who play multiple courses and use that to 'back in' to a course rating.

IMO, the rating system under-weights accuracy hazard factors for Bogey golfers, but it's still 'close enough' to spot on across many rounds. An advantage to having the system as it is versus an automatically computed HCP / Course Rating is that it's a bit more transparent. You can calculate an unofficial HCP on your own using the available CR information or cross-check your official HCP with your own tabulation.

Perhaps the best thing to do would be to use the 'raw data' occasionally (~ every 5 years?) as a cross-check to tweak and refine the rating system so it aligns even better with the quantitative data.

Edited July 18, 2016 by natureboy

[SG11118]

On ‎7‎/‎17‎/‎2016 at 8:26 PM, natureboy said:

To a large extent (though IMO not perfectly) the refinement of the Course Rating system when slope was added did this. They compared their rating system to tons of actual scores by different HCPs to verify its validity.

Even if the course and slope system is not 'perfect' it' still very statistically valid. It's better on multi-round averages than single rounds, but implementing the 'daily average' will add an extra tick of accuracy. I think it would be feasible to use an algorithm to identify a population of scratch golfers who play multiple courses and use that to 'back in' to a course rating.

IMO, the rating system under-weights accuracy hazard factors for Bogey golfers, but it's still 'close enough' to spot on across many rounds. An advantage to having the system as it is versus an automatically computed HCP / Course Rating is that it's a bit more transparent. You can calculate an unofficial HCP on your own using the available CR information or cross-check your official HCP with your own tabulation.

Perhaps the best thing to do would be to use the 'raw data' occasionally (~ every 5 years?) as a cross-check to tweak and refine the rating system so it aligns even better with the quantitative data.

For the most part, I think the rating system is fairly close the way it is done now.  However, when I used to live in Arizona, I found it was much easier for me to post a better differential, than when I went back up north to visit during the summer.  For the most part I attributed this to the trees up north.  I could get by with spraying my shots more in Arizona because there was almost always a clear high path to hit toward the green.  When I played up north, my approach path to the green was often blocked by trees.  I'm guessing there are maybe some regional rating differences like this that might come to light if actual scores were used as the basis. 

I don't know that I care about transparency in rating a set of tees.  I'm sure the rating factors used to rate a course and the slope are based on general statistics, but I don't know that this should be trusted more than the statistics of real posted scores.  I guess if we really wanted to be transparent, we could post the graph of scores vs. handicaps from the past year for each set of tees to show everyone a graph of the data that was used. 

In my previous post I was talking about comparing a players scores on one course vs another to get a dataset to compare the two courses.  Thinking about it some more, we probably don't even need to compare courses against each other.  This is what I would suggest: 

1.  All sets of tees are re-rated each year using the scores from January 1 through Dec 31 using posted scores from that year.  Posted scores of golfers and their associated handicap when they post the score are kept for the year for each set of tees.  (we may want to use rolling scores from last 2 or 3 years to eliminate some statistical variability that may come from only using one year?)

2. If a player posts more than one score from a given set of tees in a year, some sort of an average score and average handicap is recorded for that golfer, and the rest of the scores are thrown out.  (This will prevent too many scores from any one player from skewing the statistics - particularly until the new course rating system runs for a few years.  This will also put a higher weight on scores of golfers who travel and play multiple courses in the year)

3. If you need to manually enter a score, that score is not counted for re-rating courses - scores need to be linked to a specific set of tees in typical conditions.  If they come up with a way to daily adjust scores, that score can still be used towards re-rating the course for the year (scores are not linked to the CH and Slope, so if the CH and slope are daily adjusted, it will not affect my proposal)

4. Nine hole rounds may take some thought.  For 18 (or more) hole courses, we could possibly start requiring people post their 18 hole scores as two 9 hole scores so that each nine can be rated individually?

5. A set of tees needs to have at least 200 scores that can be used for the year.  Have a computer program plot all the useable scores for the year from a given set of tees (handicap vs score) and have the computer program determine the statistical "best fit" course rating and slope for that set of tees for the given year.  That is the typical CR and slope to be used for that set of tees the next year.  This will capture the average statistical difficulty of the set of tees.  If a set of tees doesn't have over 200 scores for the calendar year, the course isn't re-rated that year, and those scores get included with the next year's scores in hopes of having enough scores. 

6. Courses may need to be rated by hand in their first year of existence, or after they go through a significant re-model.  Minor remodels can probably be adjusted using the simple current length formulas.  It may take several years for course ratings and slopes to adjust to their proper range.  Hopefully due to item 2, more weight will be applied to scores of traveling golfers than to local golfers to flush out any regional irregularities.

[natureboy]

On 7/19/2016 at 1:56 PM, SG11118 said:

For the most part, I think the rating system is fairly close the way it is done now.  However, when I used to live in Arizona, I found it was much easier for me to post a better differential, than when I went back up north to visit during the summer.  For the most part I attributed this to the trees up north.  I could get by with spraying my shots more in Arizona because there was almost always a clear high path to hit toward the green.  When I played up north, my approach path to the green was often blocked by trees.  I'm guessing there are maybe some regional rating differences like this that might come to light if actual scores were used as the basis. 

I don't know that I care about transparency in rating a set of tees.  I'm sure the rating factors used to rate a course and the slope are based on general statistics, but I don't know that this should be trusted more than the statistics of real posted scores.  I guess if we really wanted to be transparent, we could post the graph of scores vs. handicaps from the past year for each set of tees to show everyone a graph of the data that was used. 

In my previous post I was talking about comparing a players scores on one course vs another to get a dataset to compare the two courses.  Thinking about it some more, we probably don't even need to compare courses against each other.  This is what I would suggest: 

Not sure I understand your first sentence.

I do think trees may have a larger impact on scoring than the current course rating system takes into account, but more so for higher handicap players, or at your HCP level long but wilder drivers. The course rating accuracy standard is pretty good for scratch players IMO, but less realistic for higher HCPs. Maybe you have scratch to plus distance with less accuracy than typical for your HCP?

I haven't played a desert course, but judging from TV I would imagine that besides a higher percent of clear shots to get at least close to the green, the odds of being able to take a useful unplayable lie are greater than from the woods. But a line of trees between fairways is very different from a thick stand of trees.

As far as your suggestions, the idea of entering 9-hole scores makes sense, because a lot of courses have variable 9-hole routings.

With the rest of it, I'm not sure you'd be accomplishing much beyond identifying the average score for a bunch of players on a particular course and their relative differentials. I think you need an overall reference standard. As I said before, you could probably establish this from raw data by identifying scratch players as those who generally play to par on multiple courses (within a certain range of lengths). With a scratch population identified you could establish the course rating and the bogey differential (based on an average score). Then you could back into the slope rating by tracking the performance of these bogey golfers relative to their expected differential to the scratch rating on different courses.

But the population of travelling golfers may be relatively small for some courses so an approach like this may still be statistically thin in terms of 'N'.

Edited July 22, 2016 by natureboy

[iacas]

1 hour ago, natureboy said:

I do think trees may have a larger impact on scoring than the current course rating system takes into account, but more so for higher handicap players, or at your HCP level long but wilder drivers.

Do you still think that trees 40+ yards away from the center of the fairway are not considered? Because they are. And have been. The corridor is currently, IIRC, 100 yards wide. Used to be 120.

And bogey golfer ratings consider the trees along the entire route, not just near landing areas.

[dave s]

Nothing scientific here, but my issue with hdcp system is simple: I DO NOT believe length of course is taken into consideration enough to make a match fair between a long and short hitter.

Let's say I'm a 16 and my opponent, (a long hitter) is an 8.  He's going to kill me on a 6800+ yard course.  OTOH, I can hang with anybody on a course playing 5800-6200 yards.

I don't know for sure that hdcp system takes into account course length, but I don't believe it does.  What leads me to say this is that across the scorecard, the par three that plays 211 from the back tees, 178 from blue tees and 155 from the white tees has the same hdcp number regardless of length of the hole.  The long hitter is playing an iron into the green, I'm hitting my longest club in the bag.  I'm also not getting a stroke on a hole where my opponent has a clear advantage.

Level playing field?  Not without adjusting for course DISTANCE.

dave

[SG11118]

9 hours ago, natureboy said:

With the rest of it, I'm not sure you'd be accomplishing much beyond identifying the average score for a bunch of players on a particular course and their relative differentials. I think you need an overall reference standard. As I said before, you could probably establish this from raw data by identifying scratch players as those who generally play to par on multiple courses (within a certain range of lengths). With a scratch population identified you could establish the course rating and the bogey differential (based on an average score). Then you could back into the slope rating by tracking the performance of these bogey golfers relative to their expected differential to the scratch rating on different courses.

But the population of travelling golfers may be relatively small for some courses so an approach like this may still be statistically thin in terms of 'N'.

I'd argue that a plot of scores vs handicap on a set of tees from a wide variety of unique golfers will tell us exactly what we are looking for already.  A score of each of the 0.0 golfers who golf the course will be on this plot just the same as a score for every other handicap of golfer.  Statistically you should be able to fit a line on this plotting of scores.  Where the line is when it crosses the 0.0 handicap line will be the new Course Rating for that set of tees.  If the slope of this line is different than 1 stroke per 1 handicap unit, that difference in slope will determine the new course slope (I don't know if I advocate continuing to drop the 10 worst of the golfers 20 latest scores, but if we do, the line may need to be statistically adjusted slightly to account for this). 

I guess you could argue that when we are switching from one course rating system to another, the respective handicaps of the golfers that we'd be plotting against their scores is still based on the old system, so would be slightly in question for the first couple of years.  However, by limiting the posted scores to one per golfer per year, I've tried to over-weigh the impact of guest play and traveling golfers on the system to try and bring about uniformity from region to region as much as possible.

I've acknowledged, there may be some statistical problems with some sets of tees not getting enough unique golfers over a one year period.  If another set of tees on the same course does get enough play, we could possibly utilize the CR and slope for this set of tees along with the statistically lacking set of results from the tee in question to fit in a new CR and slope for it.  If a course can't get enough unique play over a one year period, it is acceptable to stretch the time frame of the plot to multiple years.

34 minutes ago, dave s said:

I don't know for sure that hdcp system takes into account course length, but I don't believe it does.  What leads me to say this is that across the scorecard, the par three that plays 211 from the back tees, 178 from blue tees and 155 from the white tees has the same hdcp number regardless of length of the hole.  The long hitter is playing an iron into the green, I'm hitting my longest club in the bag.  I'm also not getting a stroke on a hole where my opponent has a clear advantage.

If anything, the current system of rating courses takes length into account too much in setting course handicaps and slopes.

You need to keep in mind, the individual course currently sets the hole handicap numbers, not the rating agency.  It sounds like your beef is more with the course setting its hole ratings than with the overall course rating and slope?  It isn't exactly a perfect system.  In a perfect system, a higher handicap golfer would gain a fraction of a stroke on every hole based on the disadvantage on that hole.  Due to golf not being scored with fractions, there are going to be certain holes on the course where you will be at a slight disadvantage vs longer hitters with better handicaps, and other holes where you will be at an advantage vs longer hitters with better handicaps.  

[Yukari]

I haven't read the entire post, but one problem I see is someone who has a wide range of scores versus someone with a narrower range of scores.  Even within high handicappers, some have a relatively very range of scores, meaning they are more consistent compared to someone whose score ranges all over the place.

[newtogolf]

2 hours ago, dave s said:

Nothing scientific here, but my issue with hdcp system is simple: I DO NOT believe length of course is taken into consideration enough to make a match fair between a long and short hitter.

Let's say I'm a 16 and my opponent, (a long hitter) is an 8.  He's going to kill me on a 6800+ yard course.  OTOH, I can hang with anybody on a course playing 5800-6200 yards.

I don't know for sure that hdcp system takes into account course length, but I don't believe it does.  What leads me to say this is that across the scorecard, the par three that plays 211 from the back tees, 178 from blue tees and 155 from the white tees has the same hdcp number regardless of length of the hole.  The long hitter is playing an iron into the green, I'm hitting my longest club in the bag.  I'm also not getting a stroke on a hole where my opponent has a clear advantage.

Level playing field?  Not without adjusting for course DISTANCE.

dave

Your handicap index is based on your scores and the course ratings / slope from the set of tees you play from.  If you play from shorter courses regularly your index will be higher than someone who shoots the same scores from longer tees.  Someone who plays from longer tees and scores the same as you is considered a better golfer and the handicap system will provide you with additional strokes to compensate for the difference.  

Your example is flawed because you're comparing yourself to an 8 index.  If you're a 16 index regularly playing from a given set of tees and you play a 16 handicap who regularly plays from a longer set of tees do you feel you don't get enough strokes to compensate for the difference in course length?   

[dave s]

Interesting take on course hdcp from my Thursday night league.  Our league handicaps each hole played based on actual scores.  On the back 9, hole 10 has a green that can easily be 4-putted. The hole rolls up a lot of high scores due to OB left, a bunker twice the size of a school bus (and deep!) guarding 75% of the green front and a 45 degree bank of deep rough behind the green.  It's the #1 hdcp hole in terms of stroke average on our league.  Due to its short length - par 4 at about 340 yards, it's scorecard hdcp is 12.

#11 is a 165-180 yard par 3, all carry over a ravine with large, old-growth oak trees narrowing toward the green.  It's sports the 2nd highest over par stroke average on the back 9.  The card says 14 as the hdcp because it's a par-3.

When you look at how many rounds our league has played with guys who can shoot sub-par rounds on occasion to guys who rarely break 50, what we shoot out there certainly DOES NOT match what the course indicates as proper hdcp.

We hdcp our league based on what the league shoots, not what the card says which is more fair than going by the card itself.

dave

[newtogolf]

6 minutes ago, dave s said:

Interesting take on course hdcp from my Thursday night league.  Our league handicaps each hole played based on actual scores.  On the back 9, hole 10 has a green that can easily be 4-putted. The hole rolls up a lot of high scores due to OB left, a bunker twice the size of a school bus (and deep!) guarding 75% of the green front and a 45 degree bank of deep rough behind the green.  It's the #1 hdcp hole in terms of stroke average on our league.  Due to its short length - par 4 at about 340 yards, it's scorecard hdcp is 12.

#11 is a 165-180 yard par 3, all carry over a ravine with large, old-growth oak trees narrowing toward the green.  It's sports the 2nd highest over par stroke average on the back 9.  The card says 14 as the hdcp because it's a par-3.

When you look at how many rounds our league has played with guys who can shoot sub-par rounds on occasion to guys who rarely break 50, what we shoot out there certainly DOES NOT match what the course indicates as proper hdcp.

We hdcp our league based on what the league shoots, not what the card says which is more fair than going by the card itself.

dave

 

3. How is a course rated? (The rating procedure)

All courses rated under the USGA Course Rating System are rated using the same parameters that have been established by the USGA. A male scratch player is defined by the USGA as an amateur golfer who has reached the stroke play portion of the U.S. Amateur Championship. On average, he hits his tee shot 225 yards in the air with 25 yards of roll. His second shot travels 200 yards in the air with 20 yards of roll. The male bogey golfer is defined as having a USGA handicap index of 17.5 - 22.4. By definition, he can hit his tee shot 180 yards in the air with 20 yards of roll. His second shot travels 150 yards in the air plus 20 yards of roll for a total distance of 170 yards. Therefore, the bogey golfer can reach a 370 yard hole in 2 shots and a scratch golfer can reach a 470 yard hole in 2 shots.

There are five playing-length factors that are considered for each hole: roll, elevation, wind, dogleg/forced lay-ups, and altitude. Between these five factors, or a combination of them, the overall playing length of a golf course is either lengthened or shortened from the physical yardage of a golf course.

In addition to the effective playing length of a course, there are 10 obstacles that are evaluated on each hole (nine of the obstacles are physical and one psychological). The nine obstacles are as follows: topography, fairway, green target, rough and recoverability, bunkers, out-of-bounds/extreme rough, water, trees, and green surface. If that weren’t enough, the hole is given an extra boost of difficulty under the obstacle of psychology if the rating numbers determine that the hole plays more difficult.

Each obstacle is given a numerical value ranging from zero to 10 (zero being non-existent, 10 being extreme). To avoid subjectivity, the values assigned are taken from a table in the USGA Course Rating Guide. These values are based off of the distances the obstacle is from the center of the landing zone or target.

For example: assuming there are no effective playing length corrections, the team of course raters would first evaluate the landing area for the bogey golfer 200 yards off the tee. In this area, the team would measure the width of the fairway, the distance from the center of the fairway to the nearest boundary line, trees, hazard line, and whether there are any bunkers nearby. The same procedure would be done for the scratch player’s landing area 250 yards off the tee. This evaluation process is repeated until the group reaches the green. The green width and depth are then measured as well as the amount of water and/or bunkers surrounding the green as well as how far it is to the nearest boundary line.

This process is repeated on every hole and for every tee. Through this data, a scratch and bogey rating are achieved. We are then able to use these two numbers to calculate the slope number.