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11.02.2013
Should they even be called leading points?


There seems to have been a lot of confusion caused by calling
these points, leading points


Leading points are supposed to be there to encourage a pilot to
lead as we saw in the last article in this series. At least that's what the GAP
authors thought. But really what are they?


Here's a picture of an idealized race, keeping all the essential facts but
ignoring those complications that may confuse us:




Case 1a.


The course is 100 km long. Both pilots fly the course and get to goal in two
hours. The second pilot starts ten minutes after the first pilot and flies at
the same speed as the first pilot getting to goal ten minutes later. The first
pilot is obviously leading. He leads the whole time. The second pilot is
following, he never leads. He never takes any chances as he has the leading
pilot out in front of him marking the thermals (so as a slower pilot he is
helped to fly as fast as the first pilot).


So, if there are leading points to be had and the first pilot did all the
leading, shouldn't he get all the leading points? After all the second pilot
just used the first pilot to help him keep up his speed?


The leading points formula used in GAP 2002 gives the first pilot one hundred
percent of the available leading points, but it also gives the second pilot
sixty two percent of the available leading points. If a hundred points are on
offer, that's a 100 to 62 split. A mere thirty eight point bonus for taking all
the risk of being out in front. I assume a ten minute start time interval in all
cases.


In our idealized case, with 112 leading points available, the first pilot gets
1000 points and the second pilot gets 904 losing 54 out of the possible 80
arrival points for arriving second with only two pilots at goal and losing 42
leading points (receiving 69 of the available 112 leading points).


Let's look at another case:




Case 2.


This time both pilots start out together, but the first pilot gets a little
ahead right away and continues to keep ahead ever widening the gap. Like in the
previous case he is leading all the way and the second pilot is behind him
flying slower but in a position to keep an eye on the first pilot and use him to
not go even slower. So if the first pilot is leading all the way shouldn't he
get all the leading points?


In this case, the second pilot gets seventy six percent of the available leading
points without ever leading while the first pilot get one hundred percent. The
first pilot, the leading pilot, gets a mere twenty four point reward for doing
all the leading on a day when there are a hundred available leading points.


In our idealized case the second pilot gets 813 points, losing 107 points on
speed, 54 points by arriving second and finally losing 26 points by getting 85
of the 112 leading points that are available.


Let's look at another idealized case:




Case 3.


In this case the two pilots start out together but the first pilot is quickly
leading out as in the previous case. But the second pilot is not able to make
goal. Leading points are available to pilots who don't make goal and the idea is
to encourage pilots to go out in front early by giving them a bonus even if they
don't make goal. But in this case there was no leading done by the pilot who
didn't make goal.


So what does the leading points formula give to this pilot? He gets fifty eight
percent of the available leading points while the first pilot gets one hundred
percent.


The second pilot gets 481 points, with 59 of them "leading" points. He gets no
speed or arrival position points, of course.


Another idealized case:




Case 4a.


In this case the first pilot takes off early, but because he is out on his own
flies relatively slowly taking two hours and ten minutes to fly the course. The
second pilot takes off ten minutes later, flies half the course following the
first pilot and then goes ahead to finish the course in an hour and fifty
minutes thereby getting the additional speed points and the additional arrival
position points. The areas under their flight curves are the same. Therefore,
both pilots got all of the leading points, but each of them lead only half the
way.


The second pilot receives 1000 points, while the first pilot receives 772,
losing 175 points in speed points, and 53 points in arrival position points, but
getting the full 112 leading points. That is while both pilots "lead" for half
the time, they each get the full leading points.


Finally, a last idealized case:




Case 5a.


The first pilot takes off early. The second pilot takes off ten minutes later
and catches the first pilot 50 km down the course line. They fly together to
goal. The pilots have the same arrival position points. The second pilot has
more speed points. Obviously, they have the same distance points. The second
pilot gets eight five percent of the leading points while the first pilot gets
100%.


The second pilot receives 983 points losing 27 leading points out of 112
available. The first pilot receives 890. He loses 110 speed points. He would
lose an additional 54 points if the second pilot nosed him out at the goal.
Perhaps we should use arrival time points instead of arrival position points,
especially as the calculation of pilot position by GPS can be off a bit. More on
this later.


Obviously it is well worth it to start ten minutes later at the next start time
clock opening losing a few leading points to gain extra speed points.


Now I've looked at only two pilots in the race, and as we've seen in the
previous articles the actual points available for leading points (and arrival
position points) are determined by what percentage of pilots make goal. More
points go to distance and less to speed, arrival, and leading if less than 100%
of the pilot make goal as was true in all but one of the cases above.


Ah, ha, wait a minute, does that mean that these two were leading? Perhaps, but
what it really means is that these two were in front of the others and whether
they were leading or not is not known from just looking at these charts. In
fact, the first pilot may not have been leading at all, but just be in front.


So what is the picture that pilots have in their minds when they think of
leading points and what is the actual situation?


Leading points are not really leading points, they are more like "being near the
front" points. That is, you can stick with the lead gaggle and not risk much by
staying with it and not leading out at all and still lose very few points if any
to someone who does go out in front. The rewards are so paltry from actually
taking the risk to go out in front on your own, that only when the risk is quite
small (say you can see a great looking cu ahead) does it make any sense to do
so.


Leading points are not for leading and they are not enough to make for a
favorable risk to reward ratio that the GAP authors apparently were striving
for. We should throw that name for these points in the dustbin. Practically we
should just fold them back into the speed points as they have not accomplished
their mission and give a false signal.



http://OzReport.com/1360598650
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