I wouldn't put too much store in mechanistic predictions like that, particularly when I wasn't referring to density but quantity per se. Considering the invulnerability of much of the Germans' defensive works to all but the heaviest artillery, the Entente artillery superiority is more of a 'superiority'. Note also that German artllery had a much simpler task. This makes the British successes on the Somme all the more notable.
All predictions are necessarily mechanistic, but my way of predicting is more in line with accepted theory (e.g. Lanchester equations) than simply regarding friendly losses as a function of friendly strength.
Your way of factoring in artillery versus defensive works is IMHO not accounting sufficiently for that the main contribution of artillery is not in destroying such defensive works, but in suppressing them, which of course necessitates good synchronisation between different artillery and infantry - essentially a qualitative factor. But it is certainly correct that prepared defenses work as a force multiplier. The exact balance of these effects (arty superiority vs. advantage gained by defensive works) depends of course very much on the specific values for a large number of variables (exact numbers of guns andnof shots of each type, exact number and distribution of defensive works). It cannot be solved by mere generalisations but requires some serious numbers crunching.
I am not convinced the task of the German artillery was simpler. On the one hand troops attacking are out in the open and thus more vulnerable to shell effects. So if the British were more on the attack than the Germans, they were more vulnerable to this.
On the other hand the defending artillery faces some control challenges that the attacking artillery does not, namely determining the precise location and, more important, time, of the attack in order to make its fire effective. Note that at least in the case of the German artillery the reality of position warfare violated some crucial assumptions for its defensive use, namely that during the approach phase of an enemy attack it would have enough time to adjust its fire and then fire for effect while the enemy is . As the first lines of both sides infantry positions were often located quite close to each other once trench warfare had set in, this assumption was no longer valid. This reduced effective time for artillery fire considerably, all the more, as (again good staff work on the attacking side assumed) strong preparatory fire of the attacking side can shield the beginning of its attack from observation by the defending side, at least to some degree, by blinding observation posts or by destroying communications.
(I have read a good deal of WW2 German artillery accounts. In nearly all instances of large enemy attacks the wire communications between forward observers and either command points or battery positions were destroyed immediately by enemy preparatory fire and fire control depended largely on radio communications between observers, commanders and battery positions. In WW1 however, exactly this radio communication was missing).
The attacking artillery can draw precise schedules that synchronize its actions with those of the infantry. Normally these schedules cannot precisely anticipate the flow of events and thus are somewhat off in later stages of the attack, but with some good staff work they should work at least during the initial stages, and as long as the troops were relatively close to the own position, was was probable for many of the engagements during the Somme attack, which was after all fought in a rather restricted area.