Nothing Ever Reads Zero

A player looked at a dozen results, saw the same number every time, and asked the obvious question: does anything ever land close to zero? The number was right. The scale we printed next to it was a lie.

Every combination shows a distance. The card said:

distance from midpoint: 0.724 units (0 = exact center, ~1.4 = unrelated)

Which sounds like 0.724 is mediocre, drifting toward the bad end of a scale that runs to 1.4. Read a dozen of those and you conclude the recommender is sloppy. That is exactly what happened, and the report was reasonable: everything is around 0.7, nothing is near 0.

What the number is

Every game is a 1024-dimensional unit vector built from its genres, its Steam user tags and its store description. Combining takes the midpoint of two of them and normalizes it, then ranks real games near that point:

mid = (A + B) / |A + B|
distance = |C - mid|          # both unit vectors

So 0.724 means the result sits at cosine 0.738 to the ideal point. That is not a bad answer. But you cannot tell that from a caption claiming the scale bottoms out at zero.

Worth being precise about one thing the figure implies and the engine does not do: the winner is not simply the nearest game to that point. Nearest means maximising the sum of the two similarities, and a sum rewards lopsidedness, so a game very close to one input and mediocre to the other beats a game that is decently close to both. That is the "it just gave me more of the first game" complaint, expressed as arithmetic. Ranking blends the minimum of the two similarities with their geometric mean instead, so a result has to earn both. For the pair above that costs a little distance: a game 0.007 nearer the midpoint lost because it leaned too hard on one side.

Seeing it

Below is the real thing: actual vectors, flattened from 1024 dimensions to three. Drag to rotate, scroll or pinch to zoom. The faint line joins the two inputs, the square is their exact midpoint, and the dashed line to the lime point is the distance being reported.

Zero is unreachable

A distance of 0 needs a game sitting exactly on the midpoint. Nothing does, and not because of tuning. Two editions of the same product, Shadowverse CCG and Shadowverse: Worlds Beyond, are 0.448 apart. The closest unrelated pair we could find anywhere in the catalog, Slay the Spire 2 and Astrea: Six-Sided Oracles, is 0.414.

If two versions of one card game cannot get below 0.45, no midpoint of two different games reaches 0. With 146,288 games spread through 1024 dimensions, the space is overwhelmingly empty. The endpoint we printed was not merely rare. It was unreachable.

The reported 0.724 was not a poor result drifting toward 1.4. It was the median.

Why 0.7 turns up so often

Because that is what the inputs are. Across 400 random pairs of popular games, the correlation between how similar the two inputs are and how close the result lands is r = −0.56:

291 of 500 pairs land in that middle band, and that band averages 0.735. Two games chosen because both are fun are usually only loosely related, so the honest answer for the point exactly between them is that nothing sits there. The distribution of results is mostly a picture of what people drop on the board.

Search deliberately and it moves. Drawing pairs from each game's own neighbourhood instead of at random found 0.226 for Project Zomboid plus Mesorift Survival, and 0.265 for Balatro plus Black Jacket. Tight numbers exist; they just require inputs that already agree.

Would more signal help

This was the first instinct: embed more fields, get tighter answers. It does not follow. A random direction in the same space has nothing within 1.338, so a typical result at 0.73 is already finding something far better than chance. What lowers the number is denser catalog coverage in that region, or inputs that are alike, and adding dimensions spreads the same 146,288 games thinner and pushes distances up rather than down.

What changed

Not the model. The caption now carries anchors from the observed distribution rather than the theoretical ends of the formula, and the phrase links here so the answer to midpoint of what is one tap away:

distance from the mathematical midpoint: 0.724, typical for a combo
                                          0.315, tight, closer than most combos get
                                          0.904, very loose, little lives between these two

The bit that generalises

A scale's endpoints should be reachable. Ours were mathematically correct and practically fictional, and the gap between those two things is where the misreading lived. Nobody misread the number; they read it against the only reference we gave them, and that reference had never once been observed.

Worth noticing that this was not caught by any probe or invariant. It took someone looking at a dozen results in a row and finding the sameness suspicious, which is a thing internal tests are particularly bad at noticing.