Purple Star Astrology Statistics: 20,000 Charts Analysed
Structural analysis of 20,000 Purple Star Astrology charts: how often a palace holds no star, why only nine patterns exist, and where the Body Palace falls.
Most writing about Purple Star Astrology explains what the twelve palaces mean and what each star stands for. That is the necessary starting point, but it leaves a different kind of question untouched: what does a chart actually look like, in the aggregate? How often does a palace come up empty? How many distinct chart shapes are even possible? Those questions have definite answers, and they can be checked rather than asserted.
So we ran our own chart engine over twenty thousand birth moments and counted. This page reports what came back. Nothing here is a reading, and nothing here is a prediction — it is the structure of the chart itself, described in numbers.
What was counted, and how you can check it
The sample is twenty thousand charts, generated from birth dates spread evenly across 1900 to 2030, with the hour drawn from all twenty-four across the sample. The engine is the same one that powers the chart tool on this site, driven through its full calculation path rather than a shortcut. The pseudo-random sequence uses a fixed seed, which means the same twenty thousand charts come out in the same order every time anyone runs it. If you rebuild the sample, you get the same percentages printed on this page.
One limitation is worth stating plainly, because it changes how the numbers should be read. This is a sample of birth moments drawn evenly from a date range — it approximates the spread you would see across a population, not the set of all charts that could theoretically exist. Where the two differ, this page says so.
Only structure is counted: which stars occupy which squares, and which squares end up holding none. Interpretation is a separate layer, and this page does not go there.
A chart with no empty square is the exception
Fourteen main stars are distributed across twelve squares, and they do not divide evenly. The result is that **82.16% of charts have at least one square with no main star** — 16,431 of the 20,000. A chart with every square occupied accounts for 17.84%.
This runs against the impression you get from beginner material, where the empty palace is treated as an oddity that needs explaining. In fact it is the ordinary case, and it is the fully occupied chart that is comparatively rare. Any approach to reading that treats an empty square as a warning sign has the base rate backwards before it starts.
The number of empty squares is never odd
The counts come back in three values and nothing else: no empty squares (17.84%), two empty squares (65.72%), four empty squares (16.43%). No chart in the sample has one, three, or five.
That is not a statistical tendency — it follows from how the stars are placed. The fourteen main stars are laid out in two families whose positions are locked to each other: one group is anchored by the position of Zi Wei, the other by Tian Fu, and the second is a mirror of the first. Counting the two together, the squares they leave bare come in pairs. A quick way to see it is to enumerate the twelve possible positions of Zi Wei and lay out the chart for each; the empty squares always appear in twos.
Practically, this means the question 'is my empty palace unusual' has a short answer: roughly two charts in three have exactly two empty squares, so two is the normal state of affairs.
There are only nine empty-palace patterns
If the empty squares always come in pairs, the next question is where those pairs can sit. Laying out all twelve possible positions of Zi Wei and recording which squares stay bare produces exactly **nine distinct patterns** — not dozens, not a continuum. Twelve positions collapse to nine because three pairs of positions share the same layout.
The patterns are shown below, with the bare squares shaded. Some consist of two squares sitting side by side; others are separated. One pattern leaves four squares bare, and two of the twelve positions produce no empty square at all.
The consequence for reading is concrete. When you look at a chart with two empty squares, you are looking at one of a small, closed set of shapes — the same shapes that appear in every chart anywhere. There is no such thing as an unusual empty-palace arrangement, only one of nine.
Which palace goes empty is fair. Which branch does not.
Split the same data two ways and a striking asymmetry appears. Count empty squares by **palace name** — Life, Siblings, Spouse, Wealth and the rest — and the frequencies come out nearly flat: every palace lands between 16.18% and 16.88%. No life area is more likely than any other to be the one left without a main star.
Count the same empty squares by **branch** — the twelve earthly branches that fix each square's position — and the spread opens up five-fold, from 6.13% to 32.31%. Some branches carry an empty square roughly one time in three; others barely one time in sixteen.
The two results are not in conflict, and the reason they differ is the useful part. Palace names are assigned relative to the Life Palace, which is fixed by birth month and hour — quantities that are spread fairly evenly across a population. Branch positions, by contrast, are pinned to the position of Zi Wei, and Zi Wei's position varies unevenly across birth moments.
So if you are asking 'could my Wealth Palace be the empty one', the answer is that Wealth is exactly as likely as any other palace. The unevenness shows up in a different coordinates system, one that readers rarely think in.
The Body Palace has six possible seats, not twelve
The Body Palace is the one component of the chart that does not get a square of its own; it borrows the square already occupied by another palace. What decides which one is the birth hour, and only the birth hour — not the month, not the day, not the year.
Twelve double-hours map onto six seats, because the hours pair up: the two hours six apart in the cycle land on the same seat. So the Body Palace can sit with the Life Palace, or with Fortune, Career, Travel, Wealth, or Spouse — and nowhere else. The sample confirms it, with each of the six appearing in 16.36% to 16.98% of charts.
This is worth knowing before you read anything into the Body Palace's position. The range of places it can appear is half the size you might assume, and the reason is arithmetic rather than symbolic.
Where the numbers land for the Life Palace
The Life Palace draws most of the attention, so it is worth separating out. **16.21% of charts have no main star in the Life Palace.** That figure sits close to the 16.4% you would get if the empty square were equally likely to fall on any palace, which is consistent with the near-uniform result in the previous section.
When the Life Palace does hold a main star, it usually holds one. The fourteen main stars each turn up alone in the Life Palace between 3.92% and 4.50% of charts, with Seven Killings the most frequent single occupant and Great Yin the least. Across the whole sample there are 39 distinct Life Palace configurations — some single stars, some pairs, and the empty case.
Malefic stars are a separate layer, since they sit on top of whatever main stars are present. **42.48% of charts carry at least one malefic star in the Life Palace**: one star in 35.57% of charts, two in 6.46%, three in 0.44%. A reader who treats a malefic in the Life Palace as a marked chart is describing close to half of all charts.
Only twenty-four star pairings exist
When two main stars share a square, which two can it be? The sample returns 24 combinations, and every one of them shows up in roughly 16% to 18% of charts.
That narrow spread is the tell. If pairings formed freely from fourteen stars, there would be dozens of possible pairs appearing at very different rates, with most of them vanishingly rare. Instead the pairings are fixed by the placement rules, so they arrive as a closed set — the same 24 pairs, again and again, at similar frequencies.
The chart is sometimes described as if its contents were drawn from a wide pool. Structurally, it is much narrower than that.
What this data does not say
Every figure on this page describes structure. None of it says anything about whether a configuration is favourable, and it should not be read that way. An empty square is a statement about stars, not a verdict on the life area it represents.
There is also genuine disagreement within the tradition about how to handle an empty palace once you start interpreting — whether to borrow the opposite palace's stars, to read across the three-fang structure, or to treat the square as a place where the surrounding configuration speaks louder. That disagreement is about reading method. The arithmetic above is not in dispute, and the chart tool on this site computes it the same way every time.
The honest summary is this: the chart's shape is far more constrained than it looks, most of what feels unusual is ordinary, and the numbers to check that impression are right here.