[jghub]

The difference in usability is most apparent during context switching and burst activity.

The Problem with Heuristics: Most tools use simple counters and multipliers. If you spend 10 minutes performing a repetitive task in a temporary directory (e.g., a "one-off" burst of cd actions into a build folder), a heuristic model can "overlearn" that path. This often clobbers your long-term habits, making your primary project directory harder to reach until you have manually "re-trained" the tool.

The Usability of the Power-Law Model: Because sd calculates the score by convolving a fixed window of history (the "Attention Span"), it distinguishes between a long-term habit and a recent fluke more effectively.

Stability: Your main work directories remain at the top of the results even if you briefly go "off-track" in other folders.

Decay Precision: if you look at the README of the project, the current chosen default exponent of the power-law decay p=9.97 -- which just means that if you include the 1000 last cd actions into ranking computation that the 500th of those (in the middel of the window) gets a weight of 1/2^9.97=1/1000 -- this effectively means that only any visit to the considered dir within last 500 contributes to the score (while the window width controls how long the cd remains within "attention span") and only the last 100 or so really influence the scor. so that is by default (can be altered by user easily) much "steeper" than a linear or simple exponential decay. It prioritizes what you are doing right now without forgetting what you do consistently.

Zero Maintenance: You rarely have to "purge" or "delete" paths from the database because the math naturally suppresses "noise" while amplifying "signals."

In short: The math matters because it reduces the number of times the tool teleports you to the wrong place after a change in workflow.

The difference in detail behaivour boils down to: sd does log the individual cd event history, so nows something about _when_ each visit has happened not only how _often_ it has happened plus when the single most recent one did (which to the best of my understanding is what z/zoxide do). So there is more information to utilize for the ranking. And I believe the difference in behaviour is notable and makes a difference.

the rest is matter of taste: sd does allow to alter ranking transiently in running shell if you note that your current task requires shortly to emphasise or de-emphasise recency importance (alter power exponent) or you want smaller or larger attention span (alter window size). I rarely need/do that but it happens.

last not least sd also provides an interactive selection facility to pick any dir currently within attention span (i.e. "on the dir stack"). if you have fzf installed it uses that as UI for this selection, othrwise falls back to simply index-based selection in terminal. Again, I used this not too often, but sometimes one does want that (e.g. if simply not remembering the path but having to read it to remember it...)

[cap11235]

Is this not just equivalent to clearing out zoxide's db periodically?

[jghub]

Not really, because zoxide's "aging" is a global multiplicative downscale of cumulative scores. It doesn't solve the problem of "Historical Rigidity."

In zoxide, every visit you have ever made contributes to a monolithic frequency score. Because the "aging" is a global multiplier (0.9), it preserves the relative proportions of your history. If "Project A" has 1000 visits from three months ago, its score can remain so high that it still outranks "Project B," which you started this week and visited 50 times. This is why zoxide provides a manual remove command -- users sometimes have to intervene when the "ghosts" of old projects won't stop winning matches. I have never felt the need to do something like that in sd (although the option is there, mostly as a historic artifact).

In sd, the ranking is based on the density of visits within a fixed window (the "Attention Span").

If you haven't visited "Project A" in your last ≈1000 moves, it has exited the window and is ignored for ranking purposes (as long as a pattern match is found elsewhere on the stack -- otherwise fallback logic kicks in and "Project A" is still discoverable). So it doesn't matter if you visited it 1000 times earlier in the year; it no longer occupies your "attention." Conversely, if you've visited "Project B" 50 times in the last two days, those visits occupy a high-weight portion of the power-law curve.

sd essentially uses a sliding window weighted summation approach. It prioritizes what you are doing now without being weighed down by the "debt" of what you were doing months ago. This provides "Zero Maintenance" because the math naturally suppresses old signals as they exit the window, whereas cumulative models might eventually require manual pruning to fix a sluggish ranking.