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Counting is hard

Posted by ricardo on Jan 9th 2025

[contains large tables, charts & GIFs for your viewing pleasure. some may take time to load.]

[Update Jan 31, 2025: In our new post: Phthalates and EVOO(O), we go over our updated drop weight calculation. Thus, the drop weight information contained in this post has been deprecated.]

[Updated on Jan 11, 2025: Added the VK2:EVOO ratio of 1:14.138 in the summary.]

(yes, thats an ai generated graduated cylinder with an inverted meniscus)

We were warmed by the emails received from you all regarding our decision to refund orders due to a drop discrepancy. Thanks so much for your support and suggestions!

We apologize for the error and for taking so long to get back with you about our findings. I didn't think our foray into getting more consistent drops needed this much experimentation...

Our hope is that you'll glean an understanding of why it took so long and the logical steps we took in order to reach our conclusion. If not, please  let us know how we could have done better!

To recap: Since Dec 31, 2024, we've been constantly experimenting how to consistently calculate the number of drops in our VK2 in EVOO product. We thought we had it down before, but could not reliably replicate it. It's been a series of interesting twists and turns (and dumbfounded expletives).

Why should counting drops out of a dropper be so hard? Physics.

Sugary Summary:

Per usual, my assumptions bit me in the ass as I realized that:

  1. All drops out of a dropper are not created equal. We found that the average drop weight of VK2 + EVOO Solution is LESS than the average drop weight of only EVOO by ~4.3%. Who would've thought that?
  2. Not scraping the dropper on the side of the bottle before dispensing leads to slightly bigger drop weights, ~2.8%.
  3. Drops poured are much heavier (36.7%) than dispensing drops from the dropper.
  4. All drop weights dispensed at varying bottle fill levels are NOT alike.
    1. When the bottle is <50% full, drop weights are ±1% off from average.
    2. From ≥50% full to <75% full, drop weights are ~3.2% LIGHTER than average.
    3. At ≥75% full, drop weights are ~3.3% HEAVIER than average.
  5. The number of drops dispensed per segment affects drop weight. "Segment" refers to each time you take the dropper out of the bottle, dispense X drops, and put the dropper back into the bottle. Meaning, if you took the dropper out, dispensed 5 drops, then put the dropper back in the bottle, that would be a 5-drop segment. The average weight of all the drops in the segment varies by the number of drops, in this case 5, that you dispense in each "segment." The average drop weight starts ~6% heavier than average in a 1-drop segment, then gradually lowers until it ends up ~1% LIGHTER than average at 10, 15, and 20-drop segments.
  6. The speed (and thus precision) at which you dispense drops affects the drop weight. The faster you dispense, the heavier the drop, where the fast vs slow average drop weight is ~9% heavier.

We felt that the best way to get consistent repeatable results was to:

  1. Unequal drops: Focus testing on VK2 + EVOO Solution.
  2. Scrape the dropper on the side of the bottle's mouth before dispensing.
  3. Pour Drops: We will no longer count pour drops, but to use the residual weight in the bottle ÷ by the average drop weight to calculate the remaining drops in the bottle.
  4. Drop weight at different bottle fill levels: It looks like all of the values would somewhat average out over the lifetime use of each bottle, so we'll use the average.
  5. The drops per segment variation gets sticky as this depends by your use case, so we think it's best to incorporate varying drop-count segments in our baseline testing and use the average.
  6. Drop speed: Using the slow drop speed allows us to get consistently repeatable results.

After incorporating the above lessons learned, we did testing on 4 bottles. 3,262 drops later and with the help of Dr. algebra, we came up with the following ratio to bottle each individual ~2 mg of VK2 per drop bottle with going forward:

  • 1.756 grams of VK2 powder
  • 23.07 grams of EVOO

Importantly, using this method you should definitely get at least 2 mg of VK2 per drop no matter how fast you squeeze the dropper.

If you would like to read on, grab a coke or 5:

Fail #1: All drops are created equal.

I assumed (assumptions always bite you) that all drops dispensed were of the same weight and volume. I mean, that's what a dropper is used for right?

Alas, assumptions and stupidity die hard. I started out just dropping EVOO to get a baseline hoping it would dovetail into testing the VK2 + EVOO solution (it didn't). See table below:

Fail #2: No need to scrape!

Obviously (in hindsight), when putting the dropper into the bottle and removing it, there will be a thin film of liquid on the outside of the dropper.

Let's see if there's any significant dribble on the outside of the dropper that we have to worry about. Note, my hand is not on the bulb, but on the rim of the cap. No squeezing here, I promise!

VK2 + EVOO Solution Dribbled Drops at 50% and 90% filled bottles:

Looks like it. With a 50% filled bottle, there's at least 2 drops. And with a 90% filled bottle, at least 5 drops. I think if we waited longer, more drops would slowly dribble off.

But, are these drops significant enough to even matter? As in, how much do these drops weigh vs "normal" drops? See table:

In the table above, we only used EVOO, however I think the results are indicative that there's a potential non-negligible amount. If you think otherwise  please let us know.

Further, If the bottle is above ~1/3 full, at least some of the dropper will be immersed in solution resulting in dribbled drops. Meaning, roughly 2/3's of the normal use of the bottle will have some amount of dribbled drops coming off the outside of the dropper as you use it.

Maybe we can mitigate the dribbled drops by scraping the dropper on the bottle before dispensing. So what method of scraping should we use? And is there really a significant difference between the styles versus not scraping?

Here are the 4 types of scraping  we came up with: No scrape, normal scrape, round scrape, and tip dipping.

See graphic below of the 4 styles using VK2 + EVOO Solution:

And now for the results (using EVOO only):

Oddly, normal scraping produced the lightest drop in EVOO even versus just tip dipping.

We decided to use the normal scraping method because its more user friendly and easier to get consistently repeatable results.

With that being said, we also tested it using VK2 + EVOO Solution:

Yep, there's still a difference!

Fail #3: Poured drops out of the bottle are probably the same as drops from the dropper.

WRONG! See table:

But that 36.7% heavier? Never would've thought...

Fail #4: All drops dispensed throughout the bottle are cross-my-fingers equal.

No, they aren't.

I'll let the chart tell the story (377 drops):

As expected, when the bottle is full (75 - 100%), drops are heavier compared to average, as there are more dribbled drops to fall down off the dropper. But I didn't' expect the 0 - 24.9% quartile to be heavier than the average, as when the bottle is only 1/4 full, the dropper isn't immersed in solution, meaning no dribbled drops. The middle 2 quartiles' drops being lighter than average is also quite interesting, since they will have dribbled drops.

Fail #5: Drop count dispensed per segment doesn't matter.

It matters. To clarify, by "segment" I mean each time you take the dropper out of the bottle, dispense X drops, and then put the dropper back into the bottle, counts as a segment. In other words, a 10-drop segment is when, you'd take the bottle out of the dropper, dispense 10 drops, and put the dropper back in the bottle. Hope that's clear. Sorry I couldn't think of a better word. Put in a third way: As you vary the number of drops per segment, the average weight of all drops dispensed in that segment also varies.

See graphic (377 drops):

Curiously, dispensing 1 drop per segment is the heaviest...then the weights gradually creep down to -1% vs the average.

(Note that in total there were 7x 1-drop segments, and 6x 20-drop segments, meaning that only 7 drops make up the 1-drop segment average, while there are 120 drops that make up the 20-drop segment average. This skews the average heavily in favor of what the higher drop-count segments. Confused? ya sorry...)

 

Fail #6: Drop tempo, who cares.

The drops care. The rate at which you dispense the drops plays quite a big role in the weight of the drop. Which makes sense, since you can practically use a dropper as a squirt gun if you smash the bulb fast enough. The slower you go, the more careful and thus precise you can be.

See results in chart below (789 drops):

A Fast Tempo was me trying to go as fast as possible while still getting drops to come out (instead of a stream).

Medium, is what I'd call a normal pace for someone who is used to using droppers. Meaning momentarily pausing after each additional increase in squeeze pressure to let each drop dispense out of the dropper.

Slow, is a methodical pace where you are slowly increasing the pressure on the dropper and stopping when a drop is about to dispense, waiting for the drop to fall, then slowly increasing pressure again for the next drop.

A 9.19% (5.33 + 3.86%) difference between slow and fast is quite large. Definitely unexpected.

Analysis and Conclusion

Ok, if you've stuck with me this far, thank you for your time and interest. Let us know if you have any  questions or comments.

Now, what does this all mean or how do we make use of the data?

  1. Different liquids = Different drop weights: We will only use VK2 + EVOO solutions that closely resembles our target vitamin gram per drop ratio to do testing.
  2. Dropper scraping types: Regular scraping of the dropper on the side of the bottle's mouth is our best shot at producing consistently repeatable results (i haven't said this enough, have i?).
  3. Weight of Poured drops vs Dropper drops: We will no longer count poured drops as "drops" since they are much heavier than drops out of the dropper. We will use the leftover weight of solution in the bottle divided by the average weight / drop to calculate how many "dropper drops" are left in the bottle.
  4. Drop weights at varying bottle fill levels: It looks like over the lifetime of the bottle, each drop will average out to, well the average (duh). So, I don't think its something that we need to place much emphasis on.
  5. Drop weights at varying drop-count segments: To recap, one "segment" refers to each time you take the dropper out of the bottle, dispense X drops, and put the dropper back into the bottle. The average weight of the drops dispensed per segment varies by the number of drops, X, that you dispense in each "segment". I think the best way to incorporate this, is to use varying drop-count segments in our baselines so that it is included in the drop weight averages.
  6. Drop Tempo: Slow and methodical is again what we can consistently replicate, and that's how we will dispense and measure drops going forward.

What does this mean for you, our customers?

Well, we need to use our analysis from above to establish a baseline to calculate how we will bottle the VK2 + EVOO Solution moving forward.

See the 3 tables below using the following methods concluded above.

  1. VK2 + EVOO Solution
  2. Regular dropper scraping
  3. Not pouring drops
  4. At varying bottle fill levels
  5. At varying drop-count segments
  6. At a slow methodical drop tempo

With a baseline average drop weight of 0.0287 of VK2 + EVOO Solution, we then need to address which unit of measurement to use: weight, volume, or a mix of both.

Given the above variables we measured, and the fact that we are doing everything manually besides using a digital NTEP certified scale, we feel its best to keep everything in the same unit of measurement: grams.

Why not continue to use volume/milliliters for EVOO? Using  pipettes and graduated cylinders isn't as straight forward as using a digital scale to measure weight.

First, we have to make sure that the pipette or graduated cylinder is level, then make sure that when we read the volume our eye-line is level with the graduated markings on the glass container, finally we need to eyeball the solution's  meniscus against the graduated markings to make sure its at the desired level. All in all, there are too many variables that can hinder attaining consistently repeatable (precise) results.

Note that we do not make a large vat of VK2 + EVOO solution and then pour it into each bottle. After we steam sterilize each bottle and dropper, we first place the specified VK2 powder weight in each individual bottle, followed by the EVOO. You are getting the exact amount of VK2 powder in every bottle.

Now that we will have the baseline drop weight and know our unit preference, below is the calculation we will use to bottle 2 mg of VK2 / drop bottles moving forward:

target VK2 mg/drop: 2.03 (1.5% buffer over 2 mg)
target VK2 g/drop: 0.00203 
VK2 powder grams to add: 1.756
est'd VK2 EVOO Solution grams/drop: 0.0287
calc'd Drop Count:
	=1.756 g ÷ 0.00203 g/drop
	= ~865 drops
calc'd Total Solution grams:
	= 865 drops • 0.0287 g/drop
	= 24.826 g
calc'd EVOO to add grams:
	= 24.826 g - 1.756 g
	= 23.070 g

From now on, each bottle will receive 1.756 grams of VK2 powder and 23.07 grams of EVOO. Which is quite interesting, because based on our previous EVOO tests, 23.07 grams of EVOO is roughly 25.30 ml EVOO, which is very close to the 25 ml we were using previously.

A more important thing is: because the slow-tempo scraped average drop weight is the lightest compared to other variables, no matter how quickly you squeeze the dropper, you will get at LEAST 2 mg of VK2 per drop.

[Update on Jan 11, 2025] I don't know why it didn't occur to me earlier, and you may have figured this out already. The ratio of VK2 to EVOO in weight would be 1.756 : 24.826 or 1 : 14.138. Meaning, for every 15.138 units of VK2 + EVOO Solution, you'd get 1 unit of VK2 and 14.138 units of EVOO. The ratio is unit agnostic, as in the unit can be milligrams, grams, kilograms, ounces, pounds, etc so long as you use the same unit of weight for both VK2 and EVOO.

Did this make sense to you? Do you have questions/concerns/comments/likes?  Please do let us know!

The genius in you has probably wondered about some other factors that we could've accounted for like: temperature, different EVOO brands/batches, dropping angle, etc. We will need to revisit different EVOO brand/batches very soon, as we have found another USDA organic (if that matters to you) EVOO that also solidifies at refrigerator temperatures and will keep the blog updated as we hit that point. As for the other factors, we felt that they didn't require the attention as the ones analyzed in this post. If you feel otherwise,  let us know!

Thanks again for your time. Hope this was helpful. For your time and patience, please use code countingishard at checkout :) it expires at the end of Jan 2025.

Product Pipeline:

We are working on the following:

  1. Super Concentrated ≥98% purity Vitamin K2 in EVOO -  Just bottled what should be a 6 mg/drop solution, if nothing precipitates out, I will do a drop test and strive for 10 or 12 mg/drop next. When we get to what we think is a maximum level, as you've read above, we will advertise it as grams of VK2 in grams of EVOO :)
  2. Vitamin D3 ≥98% purity powder in EVOO (w/ COAs) - Samples are coming in and being sent to labs for testing. (Hat tip to John in NZ!)
  3. Micronized Eggshell Calcium: Unfortunately, this is going to be delayed for awhile as the company who we were going to use for jet milling has said in their experience, it probably won't reach our intended size target. We need to find a different mechanical way of milling the eggshells now, but that may introduce metallic contaminants that we were originally trying to avoid. We will keep looking.
  4. (not a product) Distilled vs Reverse Osmosis (RO) vs Filtered & Softened vs Plain Well Water testing - We sent off the last batch of water samples to the lab for testing 154 parameters and will write a post about it once we get all the information back:
    1. General (all) - 113 parameters
    2. Radon (Distilled & Filtered/Softened only) - 1 parameter
    3. PFAS (Distilled & Filtered/Softened only) - 40 parameters
!