skyrack wrote:

Saturnhead wrote: Once GB selects a race for you to show the calculations, will that tell me when to use Direct or Converse?

Yes. I will cover what Sepharial has to say about that and what assumptions I have made on that score in my implementation.

Cool - thanks, skyrack!

Well my head hurts!!!

I was doing quite well until I got to the Direct/Converse part!

Trying to explain that in simple and clear terms is not easy.
Especially when Sepharial throws in other factors to consider in the worked examples which are not in the main text.

Anyway, a very good exercise to go though a detailed calculation and reading his words again as it has brought something to my attention that I have missed before. That is a circumstance that would only apply once in a while but good to pick up on that now.

I think I will have to put to this bed for tonight and sleep on it.
But tomorrow I will resume and hopefully have something that is understandable.

Meanwhile Gild Master may or may not win.

Well done you two with Clear Spring.

Maybe sticking to Poetry In Motion is not such a bad idea after all...

NEWMARKET 15:25

Field Game @ 7/1

It will either win or it won't.

15 MAY 2015 16:30 GMT +1:00 Newbury 51N24 1W18

Cast the chart

MC is the 10th House and all other houses have the same Cusp.
The ASC is not the cusp of the 1st House and is not required but shown here for reference.
Sepharial says to place the objects (Sun, Moon, and PoF) to the nearest degree.
I do not use any rounding whatsoever and this can make a difference in the final selection of horses.
For example, 7.5 rounded + 7.5 rounded = 16 and not 15.

When I have to make any assumptions, or wilfully ignore what Sepharial said, I do so by considering what Sepharial would have done today and with the tools that we have at our disposal.
However, as in this case, Sepharial may have a good reason for rounding to the nearest degree other than making the maths simple.

Where we have variants, as in this case of whether to round or not, I suggest considering the logic of the context.
Another approach would be to back-test each variant and see which performs best.

Sepharial describes the formula for PoF in the usual way

From the longitude of the Moon (expressed in signs and degrees) adding 12 signs if necessary for subtraction, take the longitude of the Sun and add the longitude of the Ascendant.
The result is the longitude in signs and degrees counted from Aries 0, of the Part of Fortune, called Fortuna.

However, in his only worked example where his calculation of PoF can be checked, he clearly is using the 1st Cusp and not the ASC as the reference point.

I have assumed that this is his intention and use the 1st Cusp in determining the PoF.
But I think it is quite reasonable to calculate the PoF in the normal way and consider the worked example as a mistake on Sepharial's part.
The difference between the two is the difference between the ASC and the 1st Cusp.

So here we have another possible variant.

Sepharial in the Eclipse method is not surprisingly silent on night racing and whether the PoF formula should be reversed at night.
Although I expect he may have expressed a view on this elsewhere.
I used to reverse it, but since reading Frawley's Sports Astrology have changed my mind and use the daytime formula only.
Again another variant for you to make your own choice and possibly back-test.


PoF 159.2661047844 or 9?16 Virgo.

Find the Significator ie. the object nearest a Cusp

PoF is the Significator.

This is quite simple to see on the chart I have included.
But I am not aware of any usual house method corresponding to Sepharial's equal houses but based on the MC (and not the ASC).
And if you cannot plot arbitrary points such as PoF based on the 1st Cusp, you may have to resort to the maths.


Find the Measure

The Measure is the distance of the Significator to the nearest Angle.
But do this for the non-significators too as this will help determine whether to "flip" or not, later.


Measure of Significator (PoF) = 33.844637728716
Measure of Sun = 41.378343803184
Measure of Moon = 7.533706074467

Scale (of the race) = 13
For this I assume weights carried are used ie. including any jockey allowances rather than the published weights.
I do not know what information was published in Sepharial's day but I assume that as today the published weights were the weights as per the race conditions plus any penalty incurred but not including jockey allowance.

Again, another possible variant for your decision and possible back-testing.

Calculate the Proportions

The first is Measure * (Scale / 2) / 90
The second is (Scale / 2) - the first

Proportions: 2.4443349470739 4.0556650529261

Sepharial rounds the first proportion to 2 and half the scale - 2 = 4.5 which rounded is 5 for the second proportion.

Another variant, to round the Proportions or not.
Your choice. I do not round.

Direct or Converse

In his main body of text, Sepharial says:

When the Significator is supported by either of the other factors (Sun Moon or Fortuna) by those factors indicating the same weights or horses, then it is a sure winner.
But when both the other factors (NEITHER being the Significator) show the same weights as one another, and different weights to the Significator, then they act together and instead of destroying the significance of the other factor or Significator they reverse its terms so that we have to apply the measure from the nearest angle to the bottom weight instead of to the top and the converse measure to the top weight instead of the bottom.
If we call the short measure A and the long measure B, then in normal cases A is applied
to the top weight and B to bottom weight to get the INDICATED weights.
But in converse or abnormal cases, B is applied to the top and A to the bottom.
But in no case do we ever take the measures from any other than the prime factor which is the Significator.

In his worked examples he says something different:

The Moon and Fortuna are not here pulling together but at a considerable angle, but near enough to indicate the same horse. In order to produce a reversal of the Measure of the Significator the other two factors must be the same or nearly the same distance from THE SAME ANGLE as one another, and though they agree together they must not agree with the Significator.

Ignoring the "sure winner" for the moment, to decide whether we use Direct or Converse Proportions, we must calculate the Proportions for each non-significator.
And this is the only time I do any rounding.
I calculate the relevant Proportions and round them.
If both non-significators have the same Proportions and these are not the same as the Significator's Proportions, we may flip the use of the Significator's Proportions.
I say "may", because you may take the view that the SAME ANGLE noted in the worked examples is an afterthought.

I do use the same angle but this is possibly another variant for your choice and back-testing.

Looking at my chart it is reasonably clear, in this case, that the Sun and Moon Proportions will be quite different without doing the maths.
But even when this is the case you will likely need to do the maths if you want to find "sure winner"s which we have ignored for now.

Sun Proportions = 41.378343803184 *(13 /2) / 90 = 2.988435941341067 and subtracting this from 13 /2 = 3.511564058658933

Moon Proportions = 7.533706074467 *(13 /2) / 90 = 0.5441009942670611 and subtracting this from 13 /2 = 5.955899005732939

Significator Proportions: 2.4443349470739 4.0556650529261

Rounding these Proportions they are not the same for each non-significator, so, in this case we are Direct and not Converse.
If they had been the same we would also check that the applicable Measures were to the same angle.

Now let us see if we have a "sure winner".

The Sun's Proportions, rounded, are 3 and 4.
The Significator's Proportions, rounded, are 2 and 4.

The fact that one adds up to 7 and the other to 6 is attributable to rounding errors.
Both add up to 6.5 without any rounding.

Just to remind you:

When the Significator is supported by either of the other factors (Sun Moon or Fortuna) by those factors indicating the same weights or horses, then it is a sure winner.

So regardless of whether the Proportions and weights agree, the best way is to see if the indicated horses agree.
The indicated horses may agree even when the indicated weights are not the same.
For example, a top indicated weight of 135 and a top indicated weight of 137 will find the same horse where there are runners carrying 140, 136, and 133 lbs.

For the Significator we are looking for indicated weights of 131 and 124.
For the Sun we are looking for indicated weights of 130 and 124.

In the worked examples Sepahrial says:

Same day at 2.15, the Sun was Significator and its distance was 34/56.
It was supported by the Moon and Fortuna so far as the light weight was concerned and they all pointed to BLUE DANUBE who won.

This seems to suggest that if either the heavy weight indicated horses or light weight indicated horses agree we have a "sure winner".
And in the case of this race Gild Master is the "sure winner".

Sepharial only talks about indicated horses in his worked examples and says:

Note: Always follow the horse nearest the indicated weight.

I take that mean to if you have top indicated weight of, say, 132 and a bottom of, say, 124, then using this race's carried weights, the bottom indicated horse is nearer to its indicated weight than the top indicated horses to their indicated weights.
And thus the bottom indicated horse is the selection and the others are disregarded.
This, to me, follows the logic in the Blue Danube statement, but it could be construed to mean follow the horse(s) nearest each indicated weight.

Another variant for you to decide and possible back-testing.

In this race we use the Proportions in a Direct fashion and not Converse.
So we take the first Proportion of the Significator from the top weight and add the second to the bottom weight to get our indicated weights.
But if we are working in Converse fashion, we take the second Proportion of the Significator from the top weight and add the first to the bottom weight to get our indicated weights.

I think it is useful, for me at least, to list all the variants I have identified (and I may have missed some) in reading Sepharial's words and second-guessing his intentions.

• Objects (Sun, Moon and PoF): precise longitudes or rounded to the nearest degree
  PoF: 1st Cusp or ASC as reference point
  PoF: Daytime only formula or day and night
  Weights: Carried or Published
  Proportions: precise or rounded to the nearest lb
  Angle: use the same angle when deciding whether Converse or not
  Nearest Weight: use the nearest of both or each

The first option of each of these variants is the one I use in my implementation.
As we have 7 (and possibly more) variants, we have 42 permutations which could be back-tested.

I have tried to keep this as simple as possible and apologise for failing to do that!

Amazing post, skyrack!

You have put a lot of work in.

Thank you so much.

Thanks skyrack.

I shall read your post with great interest and see if I am calculating in the same way as you.

The house system used is available in some computer packages. Solar Fire calls it "MC on 10th".

The Bangor 4:05 should be interesting. I believe the Eclipse and Addey methods both select 'Heist'.

Addey - Mars
Eclipse - 11.8 (horse carries 11-7)

My implementation is lagging behind what I wrote this morning.
In particular regarding "sure winners" and Blue Danube.

So until I bring it up to date, my implementation may be misleading.

But I have It's A Mans World.

Have you found this race to be Converse?

skyrack wrote:My implementation is lagging behind what I wrote this morning.
In particular regarding "sure winners" and Blue Danube.

So until I bring it up to date, my implementation may be misleading.

But I have It's A Mans World.

Have you found this race to be Converse?

I think you are right. Rounding up, it's A Mans World at 11-10.

Be interesting to see which method prevails.

Thanks for correcting me, skyrack.

This is what I have:

There Is No Point (IRE) 166
Too Scoops (IRE) 166
Court Dismissed (IRE) 165
It's A Mans World 164
Heist (IRE) 161
Watt Broderick (IRE) 158
Good of Luck 158
Hairy O'malley (IRE) 151

Scale: 15
Sepharial PoF: 166.12696708213
Signifier: Moon
Measure: 28.104294630689
Certain
Proportions: 2.3420245525574 5.1579754474426
Indicated: 163.65797544744 156.15797544744

array (size=8)
'It's A Mans World' => float 0.3420245525574
'Court Dismissed (IRE)' => float 1.3420245525574
'Watt Broderick (IRE)' => float 1.8420245525574
'Good of Luck' => float 1.8420245525574
'There Is No Point (IRE)' => float 2.3420245525574
'Too Scoops (IRE)' => float 2.3420245525574
'Heist (IRE)' => float 2.6579754474426
'Hairy O'malley (IRE)' => float 5.1579754474426

Selections:
It's A Mans World

But as I say, I have some updates to do to bring it into line with my post this morning.

If you have anything different from my Signifier, Measure, Proportions and Indicated let me know please.

There's an interesting race on the card at Doncaster at 18:15 this evening.
My selection is Sound Reflection - 5th sextile to Taurus Moon - reflections are ruled by the Moon, of course, and the glyph of the Moon herself is one of a convex or concave nature - i can never remember which is which. I think this selection is backed up by the Moon's yin or passive/female nature.