Not that this is not an interesting question, its main problem, (and there are several), is that it asks for particulars with respect to the general rather than asking for particulars about something in particular. This creates a logical fallacy.
Yes, Starbucks® house blend is always processed as what the industry calls a gravity feed or gravity fed brew, just as you suggest. Also, as you suggest, certainly it can be expected to yield an average “per serving” caffeine content or level. Unfortunately you do not specify what would be meant by serving size in terms of, say, ounces. This is a problem for your question because a *blend” in the coffee business invariably means that two or more different kinds of beans are in use (such as the original mocha java). Each bean type will have its own properties, including caffeine content. This itself makes it impossible to answer a per bean question, especially since it’s a Starbucks® trade secret how many different types of beans are in their house blend and, more importantly, what the proportions are. There’s just no telling.
Lab tests could be performed (and most certainly have been performed) on gravity fed servings (of some predefined size) of Starbucks® house blend which would provide, of course, an average caffeine content per serving. From knowledge of the weight in grams of the grounds used (on average) to produce each such serving, one could easily extrapolate what this means for caffeine content on a per bean basis, because the weight in beans is no different than the weight in grounds, and because, as you point out, an average bean count per volume grind can be surmised (indeed with even greater precision than you chose to offer). One would just have to qualify the results in the aforementioned ways, meaning that no one bean could be expected to yield precisely these results, akin to each family having 2.5 children on average.
Buried within your question, and part of what makes it an interesting one despite the rather sketchy feel of your mathematics, is the matter of how much of the essence of the bean gets extracted when processed under gravity feed alone. I like it that you find this relevant, because it more than most certainly is. The caffeine content in an average coffee bean stated in milligrams can only be arrived at (and published accordingly) based on chemical analysis of the bean in full, that is, many beans in full. And since not even the most efficient brewing systems, (using steam and mechanical pressure in combination with a delicately fine grind), can extract 100% of the beans essential oils, it is hardly reasonable to think that nothing more than boiling water poured over a much coarser grind under the mere force of gravity has any hopes of doing much more than scratching the surface in this same regard. In short, I think your numbers significantly overestimate how much of the bean’s caffeine makes it into your cup under, that is, the conditions you prescribe. Rather than half I would guess it’s no more than 20%.
To test this, spread your used grinds out, allowing them to dry. Then reduce them to an espresso grind, and process them in you home espresso machine to see just how strong the results are compared to a normal espresso –just be sure and use the house blend, which sounds ghastly, as your control rather than a true espresso blend/roast. Additionally, if my estimates are correct, the whole batch of used grinds should yield about 3 cups of coffee similar in size and strength (though not very good to the taste) to the one you produced when gravity fed, or slightly less when one bears in mind what oils may have been lost to evaporation (drying). Now, I said 20%. So you may be asking why I didn't say your used grinds should yield 4 cups of coffee, since 4 out of 5 is 80%. The answer is based on the fact that we cannot reasonably expect a total 100%, for reasons outlined above. If the best system can extract only 90% of a grind's essential oils, for example, the loss of an initial 20% leaves only 70% to be collected. That's a bit more than 3 times 20% or, that is, 3 times your original cup. Subtract for oils lost to drying and that ought to about do. (Almost pedantic, I agree, but such is the nature of the question.)
The following statements represent a substantial edit based on subsequent concerns expressed by the author of the original question and are in no way intended to deviate from granting satisfaction to a question asked in earnest.
A white paper which somewhat covers this topic, as submitted by the question’s author within the Comments section of this answer, can be found here. I say somewhat because as studies go it has multiple and serious problems, not the least of which is the extent to which it spreads itself a bit thin. It attempts to cover too much subject matter in one paper, often making it difficult to read an interpret. It initially establishes a baseline caffeine content for coffee by selecting both major varieties (arabica and robusta), grinding them down to a powder, and then submitting them to lab tests. From here the study proposes to explore the extent/rate of caffeine extraction from coffee powder under one of two broad conditions, either soaked or percolated. Afterwards it proposes to explore the caffeine content of three local varieties of instant coffee with the apparent purpose in mind of determining whether the labeling is accurate. The interspersion of this last portion of the study goes a long way toward gumming up meaning along the way, as anyone who reads the study will discover.
Our focus will necessarily be on those portions of the study which work with actual coffee grinds (which it calls grains), that is, in the form of coffee powder. Here’s a quick overview of the two methods explored.
For the soaking substudy the focus is on ‘how long’ the powder is soaked at 100°C. This same substudy then devolves into measuring results based on water temperatures lower than or equal to 100°C, that is, by increments of ten. This makes possible a number of comparisons. For example,
…by soaking at 60°C for 15 min, approximately 90% caffeine has been
freed from coffee powder when contrasting to that of 90°C.
This is obviously to say that when using the soaking form of brewing on coffee powder, 15 minutes of water at 60°C pretty much does as good a job as 15 minutes of water at 100°C. The very next sentence of text says it as follows,
Therefore, hot water (not boiling) was effective enough for extracting
caffeine from coffee powder.
The investigators decided to use only the hottest of water (100°C) in determining the rates of caffeine extraction from coffee powder in percolating, but decided to limit the scope of their study to only robusta varietals. They do not say why the put this limit in place. Even though robustas have a caffeine content on average higher than the arabicas by weight, it appears that the rate of extraction as a function of percentage was not expected to vary much if any, or at least not when all of their other terms are adhered to.
The next thing the investigators decided to do is percolate the same batch of coffee five times, each time measuring the amount of caffeine extracted as a percentage of the whole. Unfortunately, they did not set things up in such a way as to reflect real world conditions. For example, real world conditions would not normally employ coffee in powder form. It also wouldn’t use so small an amount of coffee (a mere 5g, which is less than a fifth of an ounce), so small an amount of water (a more 30 mL, which is about 2 tbsp), or so large a coffee to water ratio (1g/6mL) compared to something more like 1g/16mL both at home and elsewhere. The setup details are found in the fourth paragraph of the section titled “Materials And Methods”. The results however are presented below in snapshot form, and deserve to be discussed one statement at a time.
The first statement here makes it clear that percolation is only 90% as effective (at extracting caffeine) as soaking for 15 minutes at 100°C. Later evidence suggests that this statement was made in error.
The second statement represents the cumulative, and will be referenced again shortly in association with the graph the authors included.
The third and fourth statements operate in conjunction. The first states quite unambiguously that percolating 5g coffee powder with 30mL boiling water can extract a maximum of 59% of the caffeine contained by the powder. The second statement compares that rate of extraction to a 66.0% maximum to be had by the soaking method (as defined). We note how well this corresponds to the opening statement of the paragraph, as 0.59 is roughly 90% of 0.66, with the latter representing the words “nearly two thirds”. But since problems later emerge with that opening statement, the validity of this statement too is brought into question.
The nature of the fifth statement is not inherently clear. It could be pointing up a matter of not quite diminishing returns or, that is, a claim that further efforts at percolation can, at least for a while, be expected to extract small but not negligible quantities of caffeine. Or it could be intended to say that further percolations could be expected to yield nothing other than neglible results. This absence of clarification is among many similar examples which greatly detract from the paper’s effectiveness, starting with the very opening statement of the paper’s abstract, (which be assured contain no typos),
The stimulating effect of coffee is mainly depended on caffeine
availability in products.
The sixth and final statement lies well outside the scope of our general ability to explore. However, what we can benefit from is a view of the graph that the authors provided in support of this excerpt.
We know from the way the tests were set up that we’re dealing here with 5g of coffee powder. We also know from the excerpt’s second statement, as well as what we can see in this graph, that the total percent caffeine is not likely to reach much more than 3.5%. After five percolations we see a cumulative total only slightly higher than “3.15% on dry weight”, where each new round of percolation extracts at least some significant percentage of caffeine. But we’re also witnessing a precipitous drop ending in .23% and .16% respectively. Coupled with plain old common sense, this makes it clear that at best we’re to expect, say, another set of .11%, .08%, .06%, and so forth on down to ostensibly zero. So again, one cannot help but emerge clear on the fact that there’s little more than 3.5% total caffeine to be realized, as 3.15 + .11 + .08 + .06 + .04 + .03 + .02 + .01 = 3.5 on the conservative side. And since percentages are not a function of any other measure, this necessarily means that any unit of robusta contains about 3.5% caffeine.
It is unfortunate that the authors did not entertain of an arabica as well, since the Starbucks® house blend is most certainly comprised of arabicas. Nonetheless, if we’re careful with the numbers that the authors provide in tables 2 and 3 (their labels), we can make an extrapolation. On average the extraction for arabica is 58.17% that of robusta, all other things being equal. Applied to the known caffeine content for robusta, we can see that the caffeine content for arabica would be right at 2% (because 2 is about 58% of 3.5). We cannot speak to which robusta or which arabica the authors used in their study. So there’s quite a limit when it comes to how confidently one can toss those numbers about. But it at least provides the beginnings of an authoritative framework.
So beyond this, what’s the takeaway? I see a couple of things which deserve place in answer to the original question. The first is this. Normal forms of brewing are entirely inadequate when it comes to extracting all of the caffeine from coffee. For the soaking method, as revealed in tables 2 and 3, the robusta never yields more than 2.08% compared to the fuller 3.5% known to be contained therein or, as the authors later state, a little less than two thirds total caffeine content. (In truth, this is a mistake on their part as 2.08 is a little less than two thirds of 3.15 rather than two thirds of 3.5, making it clear that they failed to include in their calculations the remaining but not insignificant percentages which would have followed from percolations number 6, 7, 8, etc, … by which therefore this approximately 66% extraction is more reliably 59% or, that is, the same as what we find in one round of percolation.)
At this point and for so many now obvious reasons, it’s hard to see this study as something less than fundamentally flawed. But even if we treat of some of its core assertions as reliable, we still run into insurmountable difficulties when it comes to applying its findings to the question at hand. The authors used a robusta bean in powdered form for their percolation study and “determined” that a first pass releases at most 59% of total available caffeine. (Since they never state what that total is known or measured to be, we cannot check their numbers.) The at most part plainly suggests an average or typical yield somewhat lower, probably closer to 50%. If we allow, as the authors seem to imply, that the extraction rates for the arabica they had on hand would not be significantly different from that of the robusta they actually used [for their multiple percolation study], and if we allow that a blend of arabicas will yield in liquid form a close approximation to what the average arabica would contain in caffeine content, and finally if we allow that we’re percolating with an arabica in powder form rather than a normal grind and at an exceedingly strong coffee to water ratio of 1g/6mL, we are then perhaps able to say that an extraction of half of the available caffeine can be expected on a normal single pass of percolation? Problem is, that’s a lot of conditions to cede or adhere to in order to draw that conclusion. And that’s just for coffee in powder form. Bump that up to a standard grind and there’s just no telling how different the outcomes may be. In short, this leaves us not terribly far from where we were before reviewing this study.
What we can say however, in a reasonably common sense enough way, is this. To successfully extract most of the essential oils from coffee is to also extract most of its caffeine. The tests that I encouraged the performance of (using the grounds once, drying them, reducing them to an espresso grind, and then processing them incrementally), were very much intended to take advantage of this obviation. As the strength of the outcome diminishes in terms of both color and flavor, so too the percentages of extraction. But again, if from those grinds you can draw a yield of three more cups of coffee equal in both darkness and intensity of flavor to the original cup (mixing the three together to form an average), you will have sufficed to confirm what I continue to expect in the way of caffeine content for your original cup. A French press won’t work because it actually calls for an even coarser grind than is typical of the conditions by which you framed your question, much less the powder used in the lab tests you subsequently cite.