Piece and lot count - what does it mean?

[nerdsforprez]

WARNING!

WARNING!

This is a long post. Read at your own expense. Grab popcorn, coffee,soda, whatever you need to stay awake. Take your time, several days if

needed, to read the whole thing before responding.

Also, couple of things that will help you as you read this post. First, APPL stands for Average Pieces Per Lot. If a set or MOC has 1000 pieces

and 100 lots then there are on average, then... 10 pieces per lot.

The data set I used for the following is something I compiled on my own. If there are any interested parties I have no problem sharing it. I apologize up

front if I have misconstrued the data at all. I took the values of piece count and lot count from Bricklink. Also, from memory on some sets

regarding piece count. Funny how some things just seem to stick with you. I recognize that there are many more sophisticated methods for examining the below: I chos

I chose the below because of its simplicity, and thus maximizing the availability of others to join in the fun.

This post has been percolating around in my mind for a while, ever since I read The Mathematics of Lego by Dr. Samuel Arbesman.

http://www.wired.com...matics-of-lego/

Some of the ideas in this post were discussed in Dr. Arbesman in his article, but some are not. Some of the ideas are also borrowed from an

article that Dr. Arbesman himself referenced; http://www.ncbi.nlm....pubmed/12381294 ; which is absolutely

fascinating. Sometimes I wonder if we fully realize how far-reaching the influence of Lego really is. I think that it is fascinating that Lego

sometimes acts as a microcosm for phenomena that occur in real life.

Dr. Arbesman discusses the non-linear relationship between the total number of elements and total number of lots in a set. Obviously, there is a

positive relationship; as the number of total elements increase so do the total number of lots (most of the time). However, this relationship is

non-linear because the steepness of slope in this relationship is different for smaller sets compared to larger sets; which emulates real, true

life-phenomena.

Dr. Arbesman makes his statements based on a data set of all genres, or most all genres, of Lego. I re-examined not his data set, but my own, randomly

pulling sets from a variety of genres, but mostly Technic, Star Wars, Town/City, and other general system sets. Although I saw the same

relationship as Dr. Arbesman, any purported relationship really fell apart when dealing with very large sets, or sets with specific themes. Here are

at least two reasons why (there are likely many more):

(1) System sets, or sets like Creator sets, don't necessarily need to have a function. They are either purely artistic or meant to emulate

something in real life, but minus the function. This can create problems when looking at the variables of interest in Dr. Arbesman's article. Best

way to describe it is to provide examples. Case in point: Lego 3450. Statue of Liberty. 2882 pieces but only 49 lots. That is, on average,

nearly 60 pieces per lot! I am sure there are many, many more examples (think of any mosaic project) but this is one that comes to mind. Sets like

these will really mess with the data. Comparing sets that are too different from one another will lead to an apple and oranges comparison but not being

aware of it.

(2) Sets that offer lots of playability may not really be one set at all. Case in point, set 10188 is actually many different builds, right? To

say the set has 3803 pieces, and 438 lots, divide the two and come up with an average piece per lot value would be incorrect, right? One would really

have to deal with each little room as its own set in terms of lot and element count. Too complex though. It was not done in Dr. Arbesman's data,

and therefore really skews the data. Sets also that have lots and lots of accessories (I will use 10188 again as an example) also will skew the data,

because they artificially inflate the individual lots value. The accessories are not needed for the build, but included in the lot count.

So, to rectify the two above issues, I thought it would be fun to examine total element count and lot count in ONLY Technic sets/MOCs. I think that

doing so fixes the above problems, perhaps not totally but in my mind satisfactorily because:

(1) Technic models add functionality, which by nature, maintains some sort uniformity in the sets of interest. We are not comparing sets that are

so different as say, Lego 3450 and 10188.

(2) Technic models don't artificially inflate individual lot values by adding lots of accessories, which a lot of sets in other genres do. As

mentioned, for small sets this really is not an issue, because there are not many accessories to be had if the set itself is small. But for large sets,

it is a real issue, and that is why the relationship between the two variables of interest pretty much dissolves when dealing with large sets.

So, that is a long introduction to what this post is really about; but, there you have it. I wanted to examine the relationship between total

number of Technic elements in Technic sets/MOCs and their relationship with individual lot counts. Below is a picture of a simple scatterplot of these

two variables. The picture below that gives best of fit lines, with a logarithmic function barely beating out a standard function as the best line

of fit for the model (R - squared values of .83 versus 90 respectively).

(sorry for the bad pic quality - I upload from mocpages and they have always been behind the curve in terms of technology. If anyone needs clarification,I can try to answer any questions) So, we can therefore say that, although lot counts increase with set size, it is to a much lesser extent with larger sets than with smaller sets. Thismakes sense, especially if you read the article mentioned previously: http://www.ncbi.nlm....pubmed/12381294As systems increase, so does their tendency to repeat themselves, or what can be referred to as "redundancy" in a model. Now, redundancy is usually abad word, but in this case, not really. Redundancy can add to efficiency; which is the very thing that I want to discuss. Cities with many, many gasstations (redundancy) lead to efficiency in traffic. In biology, systems (animals, plants, etc.) that have many, many cells (again, redundancy) areusually more efficient than smaller systems (think of the metabolic rate of an elephant versus a mouse; that is why their life spans are so ridiculouslydifferent). But what does all this mean for Lego sets? If you look at the graphs below, those models that fall above the curve have lower averagepiece per lot (APPL) values than their relative (the term relative is important here, because when using the curve we are comparing small sets tosmall sets, medium to medium, etc.) counterparts. Those that fall under the curve have higher APPL values. The further a dot is from the curve the moredistinguishing they are; either for having low or high APPL values. The question I would like to put forth to the forum is "What do these valuesmean in terms of the sets/MOCs we love so much?" Does a low AAPL value set mean that it uses more unique parts than one with a high AAPL? Is this somecrude measure of UNIQUENESS for our sets? Is a set that has an AAPL of 10 "uniquier" than one with say, a AAPL of 15? (assuming both were more or lessthe same size?). Or... do large APPL values simply mean that a set is more EFFICIENT in its use of parts than a set with a small APPL? I am NOTtrying to use these questions as a way to judge MOCs or sets, there are so many more variables that better depict elements of a quality in a MOC or setthan what I am discussing. I just think that it is an interesting idea, and would like to know more thoughts from others. Many may be thinking. What the heck is this guy talking about??? Perhaps a couple of examples will help. Below are circled two sets that are amongthe most beloved Technic sets; old or young (notice that I say "among" - I get that there is much subjectivity here). Notice how they are both wellbelow the curve, meaning they have a lot of redundancy, or repeating pieces in their build. These sets have very high APPL values relative to theirsize group. Can anyone guess which ones they are?

If you guessed 8288 and 42009, both cranes, you guessed right (if you can guess what set is to the left of the 8288 set, GOLD STAR for you!). And they both scream redundancy in part usage right? In fact, that was one of the criticisms of 42009; lots and lots of pins. 8288 has lots and lots of liftarms for a set with only 800 parts. So, are these high APPL values reflective of redundancy or efficiency? Dr. Arbesman would argue both. As a system (or Lego set) gets bigger, it gets more redundant,and therefore more efficient (I get there are many definitions of "efficient" here; in this application we mean efficient from a productionstand-point, not a functionality standpoint. TLG loves sets like these if they sell. Not a lot of molds have to be used and/or created for a set withhigh APPL; and we all know that is really where TLG loses money. In the making of new molds). What do you think though? As I mentioned, I think itis no coincidence that two of the highest APPL values are also two Technic fan favorites; but this could also be to the fact that we all just lovecranes. That is why I am directly stating that I don't think that APPL values have really anything to do with popularity or skill in which they arebuilt, but I do think they are curious phenomena to discuss. So what about low APPL values? Remember we are talking about values relative to set size. An APPL of 8 for a set or MOC that is 3,000 pieces isentirely different from the same value for a set of say, only 300 pieces. Do low APPL values mean that a set is unique? Does it mean that elementsare used in a unique and creative way? Or something that I have not mentioned? Some examples of sets with low APPL values would be set the twosets circled below:

Can anyone guess which two these are? Guess the first one (not gonna tell you) and the second (furthest to right) is the 8110 Unimog. Relatively a lot of lot counts for a limitednumber of pieces. What does this mean? Does this confirm or change anyone's previous perception of the Unimog (or the other set that I will notmention)? Lastly, keen viewers will notice that I have included sets that do not reflect any known official Lego sets. These are a variety of MOCs fromwell-known builders. I selected the sets in a somewhat random fashion, and with the help of rebrickable.com and some very kind and helpful, talentedbuilders (Thanks Sheepo and Crowkillers!)These MOCs from left to right are:

1 - Porsche 997 GT3 by Crowkillers

2 - Vampire GT (Black) by Crowkillers

3 - Black Muscle Car by Crowkillers

4 - Lambo Aventador LP 720-4 by Stefan Birkefeld

5 - Cadillac Eldorado by Martijn Nab

6 - Land Rover Defender by Sheepo

7 - Volkswagon Bus Type 1, Manual by Sheepo

8 - Mustang GT, Manual by Sheepo

9 - Volkswagon Bus Type 1, RC version by Sheepo

10 - Mustang GT, RC, by Sheepo

11 - Wing Body Truck by Madoca

12 - Terex RH400 Mining Excavator by Sheo

13 - Tractor Truck by Lucio Switch

Edited February 2, 2016 by nerdsforprez

[dr_spock]

Where is the executive summary?

[JGW3000]

You really have too much time on your hands (I guess I do too, for reading through and checking the linked papers ). Best fit might be an exponential function to account for the apparent asymptotic behavior - as the sets get larger, the number of new lots to choose from becomes smaller and smaller.

From a TLG perspective, replacing one unique part/lot combination with two or more parts from larger lots already included in a set makes sense, as less production resources are required. A classic industrial engineering scenario - do we spend more on parts and material but save even more on logistics and manufacturing;, this then would help explain some of the seemingly odd part and color choices in official sets. You would think that MOCs usually do not have this restriction; however, when I build a MOC and I am guessing many of us are of the same mindset, one goal is to use parts on hand, and not have to continue to buy more parts/lots, so I am always substituting parts I don't have for ones I do - which is one of the beauties of the LEGO system. (now I guess I really do have too much time on my hands ).

Edited February 2, 2016 by JGW3000

[mediumsnowman]

This is really fascinating data, though I have no idea what anyone could do with it.

[brunojj1]

Maybe some interesting questions are raised here stimulating some thinking and eventual conclusions. First I´m not sure which point of view you are looking from –the business company, customer or independent scientist. If to assume one of them, so probably there would come up several pros and cons to make solid conclusions. Such terms as efficiency supported by redundancy seem to be contradictory for an average guy like me, but I try to understand that the scaling exponent follows some natural laws. If a system gets more complex it has to increase efficiency, but usually it doesn´t happen proportionally and more redundancy occurs automatically. One thing you can say for sure that it´s getting more complex and more efficient for sure with time. The development of computers or electronic systems can be predicted by mathematics. Despite of this I hope the robots won´t overtake our world soon!

My personal thoughts are that the data don´t say anything conclusive to me as a normal Lego customer or regular MOD/MOC builder. Would I prefer to buy a set because of its higher part count and higher parts differentiation even if the two factors are not proportional? Not always, but mostly Yes. Is this set the one I prefer to play with because it has a lot of different parts or functions? Yes and No because some are good to handle and some are not. The overall design and looks are as important to me and I simply don´t like Star Wars or Bionicles, no matter how high the differentiation of used parts may be or price per piece. Would I build my MOCs faster or more efficiently, reduce total part counts if I would have more different parts available? Don´t really think so, depends more on developing skills like training on a chessboard.

Maybe the profit oriented companies can do something with this sort of data, and I´m sure they do their own research similar to this primarily for higher efficiency in doing business – an aspect I don´t care about as a customer. I spend too much money on this anyway ;-)....

Sorry if I couldn´t understand all of this stuff but thank you for your research!

[nerdsforprez]

Sorry if I couldn´t understand all of this stuff but thank you for your research!

No, no..... please don't look at it this way. I am not trying to "flex" any muscles.... really I am not. I just think it is an interesting phenomena and like to try and find trends that play out in a little children's toy but that we also actually see in real life. Your comments are greatly appreciated and valuable.

In fact, your insight of looking at it the problem from the viewpoint of a scientist, businessman, etc. is exactly on point. In fact, I mentioned in the article that the "efficiency" really is only defined by a business model (making of less molds etc.). Unlike things like biological organisms where redundancy equals to more efficient creatures I don't think you can make that same argument for Lego. If not thinking from a business perspective, what the heck does "efficient" mean for a Lego model? One that uses less battery power for PF components. Or less manual power to turn all functions?

Again, I am just curious about others thoughts. And as mentioned int he article, I agree with you that I don't think you can use the data to judge on the worthiness of a MOC or whether or not to buy a set based on the data in the article. There are way too many other factors that likely play a much more significant part in making such decisions.....

You really have too much time on your hands (I guess I do too, for reading through and checking the linked papers ).

My wife would agree with you Edited February 2, 2016 by nerdsforprez

[Zerobricks]

So if I get this correctly, the bigger the model, the less relative percantage of the unique lots number it has. A small model with 200 parts may have relativly much higher percantage of new parts and lots than a big 2000 part one. Also I did notice Lego does seem to sometimes reduce number of different parts when needed, for example using 2x 2x4 plates instead of one 4x4 etc, which makes sense when thinking of optimising packaging process.

Edited February 2, 2016 by Zblj

[nerdsforprez]

So if I get this correctly, the bigger the model, the less relative percantage of the unique lots number it has. A small model with 200 parts may have relativly much higher percantage of new parts and lots than a big 2000 part one.

Exactly. Yes.... you got it. Which makes complete sense. To me the interesting thing is that Nature has a way of imposing limits on things. In terms of Lego, the limitations of Lego production is not just a reflection of a money grubbing, complete business-ideology. I think the efforts of TLG to limit the molds they create is not JUST an attempt to maximize their bottom line. It is easy to point that finger. I think it resembles something more innate to Nature which is essentially, a competition of resources. Limiting the types of bricks in a set, but perhaps not so much the overall amount of bricks leads to the relationship that we see in the graphs I posted. Again I encourage people not to interpret this as a diabolical Lord Business-scheme concocted by TLG --- but simply a reflection of Nature's imposition on us as humans as she has a limited amount of resources and requires us to compete for those resources.

For Technic sets..... redundancy is destined. Here is why. We tend to focus on overall elements in a set.... right? (especially with the omnipotent BWE to come out that nears 4,000 pieces!!) Kinda like any statistic or figure you have heard of the wonderment of the human brain. 100 BILLION neurons right? Astounding number. But..... whether talking about Technic sets or the human brain the individual elements that make up both (neurons versus Lego pieces) are only half the story. Think about all the connections! For Technic.... think of all the connections in a build of nearly 4,000 pieces! Those connections have one thing in common for Technic. Pins or axles. Something has to connect them. Because the amount of connections that exist between pieces increases exponentially as piece count increases, so will the elements used to connect Technic pieces. TLG group has a very limited number or connectors and pins (relatively speaking), so those pins, axles, etc. increase at an exponential rate relative to the overall size of a build. Redundancy..... defined. However, in becomes increasingly efficient in terms of a system that competes for resources. Just like the human brain. Each neuron has several dozen to several hundred connections to other neurons...... and there are only a few types of connections. Again..... redundancy. In fact.... redundancy epitomized. If you think that 100 BILLION is a difficult figure to wrap your head around..... try to think of that number where EACH individual figure is multiplied by a factor of either several dozen or several hundred. Funny.... I have lectured on this before. I have had those in the audience who pridefully claim they can wrap their head around 100 billion but never never have I had someone say they can wrap their head around the latter number in question. Funny how we can wrap our head around individual elements but not the relationship or connections they have with other elements......This astronomical number creates a degree of efficiency not paralleled in all the animal kingdom. Fun stuff to think about on a Tuesday afternoon.... (for some of us )

[JGW3000]

I stand corrected, I had thought the function was in the form exp(1/x) or exp(1/(1-x)), but it is most likely a natural log function, ln(x), with no asymptotic limit apparent - maybe if enough sets in the 8,000-20,000 part range are analyzed, we will see a limit. (Now back to work, but lunch first )

[brunojj1]

Exactly. Yes.... you got it. Which makes complete sense. To me the interesting thing is that Nature has a way of imposing limits on things. In terms of Lego, the limitations of Lego production is not just a reflection of a money grubbing, complete business-ideology. I think the efforts of TLG to limit the molds they create is not JUST an attempt to maximize their bottom line. It is easy to point that finger. I think it resembles something more innate to Nature which is essentially, a competition of resources. Limiting the types of bricks in a set, but perhaps not so much the overall amount of bricks leads to the relationship that we see in the graphs I posted. Again I encourage people not to interpret this as a diabolical Lord Business-scheme concocted by TLG --- but simply a reflection of Nature's imposition on us as humans as she has a limited amount of resources and requires us to compete for those resources.

For Technic sets..... redundancy is destined. Here is why. We tend to focus on overall elements in a set.... right? (especially with the omnipotent BWE to come out that nears 4,000 pieces!!) Kinda like any statistic or figure you have heard of the wonderment of the human brain. 100 BILLION neurons right? Astounding number. But..... whether talking about Technic sets or the human brain the individual elements that make up both (neurons versus Lego pieces) are only half the story. Think about all the connections! For Technic.... think of all the connections in a build of nearly 4,000 pieces! Those connections have one thing in common for Technic. Pins or axles. Something has to connect them. Because the amount of connections that exist between pieces increases exponentially as piece count increases, so will the elements used to connect Technic pieces. TLG group has a very limited number or connectors and pins (relatively speaking), so those pins, axles, etc. increase at an exponential rate relative to the overall size of a build. Redundancy..... defined. However, in becomes increasingly efficient in terms of a system that competes for resources. Just like the human brain. Each neuron has several dozen to several hundred connections to other neurons...... and there are only a few types of connections. Again..... redundancy. In fact.... redundancy epitomized. If you think that 100 BILLION is a difficult figure to wrap your head around..... try to think of that number where EACH individual figure is multiplied by a factor of either several dozen or several hundred. Funny.... I have lectured on this before. I have had those in the audience who pridefully claim they can wrap their head around 100 billion but never never have I had someone say they can wrap their head around the latter number in question. Funny how we can wrap our head around individual elements but not the relationship or connections they have with other elements......This astronomical number creates a degree of efficiency not paralleled in all the animal kingdom. Fun stuff to think about on a Tuesday afternoon.... (for some of us )

This sounds kind of religious and I disagree on nature (small n) doing or imposing anything on us, but you can believe what you want and I don´t want to argue on this basis because this is not the right place to discuss about things like that. There are of course laws in nature such as in physics or mathematics, usefull to understand and to implement on trivial things like Lego. There is no diabolical business scheme, it´s simply a question of reason in order to save money and be competitive on the market. The efficiency is given deliberately, on purpose and by correspondent design (with the help of smart computers of course).

Not to be theoretical, here is a practical example: recently I bought the 42042 crawler crane. It features a really intelligent design, nice building techniques and a bunch of blue parts – a WHOLE bunch of 15L beams and NOT ONE single 13L beam! I realized just yesterday that it´s very sad if you´d like to have some in your stock for example to build a MOC and be variable and not be limited by this sort of redundancy. The whole color coding issue with fancy colorful axles, rare and unbelievable expensive axle connectors at specific angles in specific colors can drive you mad sometimes. It´s not nice at all.

So don´t be angry about me, but I (Edit: totally) disagree on your viewpoint. Anyway I like this product like you do and appreciate especially the constantly growing part diferentiation which allows us to have fun by creating new unseen unlimited varieties of sticking parts together . Cheers!

Edited February 2, 2016 by brunojj1

[JGW3000]

...a WHOLE bunch of 15L beams and NOT ONE single 13L beam!...

Exactly the point - by getting the 13L beams out of the design, presumably replaced with 15L beams, the cost of material goes up a little bit, but the savings in terms of logistics and production capacity more than makes up for that increased production costs.

[nerdsforprez]

This sounds kind of religious and I disagree on nature (small n) doing or imposing anything on us, but you can believe what you want and I don´t want to argue on this basis because this is not the right place to discuss about things like that. There are of course laws in nature such as in physics or mathematics, usefull to understand and to implement on trivial things like Lego. There is no diabolical business scheme, it´s simply a question of reason in order to save money and be competitive on the market. The efficiency is given deliberately, on purpose and by correspondent design (with the help of smart computers of course).

Not to be theoretical, here is a practical example: recently I bought the 42042 crawler crane. It features a really intelligent design, nice building techniques and a bunch of blue parts – a WHOLE bunch of 15L beams and NOT ONE single 13L beam! I realized just yesterday that it´s very sad if you´d like to have some in your stock for example to build a MOC and be variable and not be limited by this sort of redundancy. The whole color coding issue with fancy colorful axles, rare and unbelievable expensive axle connectors at specific angles in specific colors can drive you mad sometimes. It´s not nice at all.

So don´t be angry about me, but I (Edit: totally) disagree on your viewpoint. Anyway I like this product like you do and appreciate especially the constantly growing part diferentiation which allows us to have fun by creating new unseen unlimited varieties of sticking parts together . Cheers!

No problem whatsoever. I actually think I may have used some poor word choice. Especially if my thoughts came across as religious.

Trust me..... I am likely the least religious person you will ever meet. And I agree.... not the place to discuss it on this forum. I will say this, however.... I use capital "N" for nature not because I endow it with some personal identity or form, but because, regardless of its origin or source, nature serves a great purpose for me. I find it amazing....and therefore it deserves my respect.

Let me explain it this way...... (and hopefully you get my humor here and that I don't really take myself too serious) You have build a rendition of the BMW M4. I think that it is simply astounding. It captures my interest and I think it is a wonderful build in Lego Technic. If I were to describe model to someone... I may choose to capitalize whatever word I use to describe it. And I may choose to do this NOT because I am trying to say anything about its source or try to given some title of divinity or personal identity.... I only capitalize whatever word I use to describe it because it is something I respect. I don't care if it was built by something of intelligent design (which it was) or a bunch of monkeys sitting in a room for a million years building with Technic that by random chance happen to stumble across the exact configuration of Technic pieces to mimic your car. I don't care. I really don't. It is awesome ...... end of story, and IMO deserves respect and awe. That is how I feel about nature..... end of story. No intention or reference to a source whatsoever. Perhaps the phrase "imposition on us as humans" was too strong...... I simply wanted to allude to the fact that in nature there are limitations and those limitations are felt by us everyday and I think are reflected in many different ways.... including in the topic of discussion in this thread.

[rollermonkey]

Being a 43 year old in college as a STEM major, sadly my first reactions are:

You didn't label your axes

No legend included in the last image.

I'm not really surprised that the lot counts taper off, TLG makes a finite number of part types, but total part count can comparatively 'approach infinity'. (There are several billions of bricks in existence, but I'd be surprised if there is more than a couple thousand possible lots.)

Edited February 3, 2016 by rollermonkey

[zux]

I find this idea very interesting. It was good that example with 42042 was mentioned so that it makes some things clear to me. Especially why certain choices are made.

However I'm more interested in investigating the rest of the dots in your graphs. Do you mind sharing the data? Or at least graphs with all dots labelled?

[nerdsforprez]

There is no way to label all the dots.... it would be too messy and..... well, that would mean that I really would have too much time on my hands

Send me a PM and I can share it via email.

[Nick Barrett]

Hmmm... I'd be interested to know if Technic sets have higher or lower APPL values than system sets - I suspect the former and not just because of the accessories you mention. The fact that you can take the pieces of a handful of sets at random and make pretty much what you want with Technic, but not necessarily with System, would seem to bear this out. Designing out the use of a liftarm size you don't have is easier than, say, a missing curved slope piece or window frame.

[Bublehead]

I think this kind of ties into why TLG supplies spare parts in the set for the smallest (therefore equating to easiest to loose) pieces. The cost of the extra parts are outweighed by the increase in customer satisfaction (or actually lack of disappointment) a customer would experience by completing the model without having to interact with TLG’s customer service department. The savings is two fold, there is the savings on time and materials for the CS representative who doesn’t have to field the complaint, get the missing part, and ship it to the customer, plus the less physical and harder to determine actual value of  “customer satisfaction” of completing the model without any hassle.  Somebody in TLG has gone through these calculations and made a business decision based on the benefits v.s. costs.  So figuring out things like how do we reduce other set costs but not noticeably affecting the customers desire to purchase have to be considered, I just don’t know what the granularity is of these calculations.  I would think they would be as high as the automotive industry where cost savings of fractions of cents per part is a very big deal.  When you use 1000 screws per vehicle to assemble it, and you make 100,000 vehicles a year, that’s 10,000,0000 screws and if you can save a penny per screw on costs, that’s a savings of a million bucks a year.  Now We have all heard that TLG is the largest maker of tires (tyres) in the world so I’m figuring their numbers are in the automotive ranges and they DO care about every little part in every set. No decision is a small one in their world. When they worry about millimeters of thickness of a part just because it MIGHT break when taking it apart, the cost of changing the mold, the increase in plastic per part, etc.. all of these factors are thought about during the development of new parts. Would make sense they are tracking every element of a set during development, and even revisiting older elements when they are up for use in a new model.  I am sure the pains that @nerdsforprez went through to look at slicing and dicing TLG data is only a small exercise in the way they actually slice and dice their own data. And if TLG is not doing this, one would wonder why not?

[pleegwat]

Another possible reason for spares is inaccuracy of the dispensing system. If a set has 17 beams of length 15, it is easy to imagine these are counted out. If it has 100 black pins though, they may very well dispense them by weight instead - and target a bit over because of inaccuracy.

Though that would not explain having a spare for a 1x1 round tile with a print on it which only has 4 copies in the BOM. So the cost of dealing with customer complaints is likely also a factor. Or there's additional considerations.

[bonox]

On 2/3/2016 at 4:09 AM, nerdsforprez said:

. I have had those in the audience who pridefully claim they can wrap their head around 100 billion but never never have I had someone say they can wrap their head around the latter number in question. Funny how we can wrap our head around individual elements but not the relationship or connections they have with other elements.

I think context can help or hinder a lot here.

The concept of a hundred billion for example. I've shovelled a lot of sand in my life, by hand and with machinery. I also live near a beach and enjoy walking up and down the beach a lot. A back of the envelope calculation suggests a number of grains of sand of that rough order of magnitude on the kilometer or so long beach that I frequent. A feel for how much volume is involved and the size of the component parts means I can comprehend a number of that size, at least in terms of a visible collection of items.

If you turn around though and say that the same number of molecules exist in just a tiny drop of water lapping at the edge of that same beach, then i've completely lost any meaning of the size of that number.

I can get the same kind of thing with lego relationships: I've got a feel, having built a thousand different technic contructions, of the number of possible pinned connections between liftarms and assorted connectors. At the same time though, i've got no idea of the concept of how many ways you could assemble an assorted pile of liftarms and pins in exactly the same way that I can't wrap my head around the mathematical analyses that determine the number of ways you can put six 2x4 bricks together. 
 

I know what the number means - I don't know what the range of constructions would look like.

In a similar fashion i'm fascinated by the idea of a simple computer screen. Rewinding a few years ago and 320x200 monochrome pixel screens were common and you can print all sorts of readable stuff on it. In theory, you could use those 64,000 dots to manufacture any book, music script etc that ever has been written or ever will be written. The number of relationships isn't all that many, since the usable results will probably have similar kinds of relationships (ie you won't have many pieces of text where pixels are unconnected to a least a few other pixels of the same colour), but the scope of what you can potentially generate just makes my mind explode. You could write a simple piece of code to build all the possible combinations of dots, but if you didn't throw any away by focussing on meaningful relationships between adjacent pixels (a bit like the relationship between liftarms), you've got a 64000 factorial problem which makes the total number of possibilities greater than a number with approximately 280,000 digits!!!

Expand the same pixels to 256 colours, and the scope has broadened by many orders of magnitude, but the principle is still the same - and if I can't deal with the scope of every book that will ever be written, I really can't cope with the scope of every photo that will ever be taken or every image that will ever be painted by somebody and if you stack multiple images together, every piece of news video that people will ever experience too!

edit: thread necromancer not withstanding of course....

Edited August 8, 2018 by bonox

[bonox]

And if you look at those relationships, while there is an unfathomable (at least to me) bigatude to the number of relationships between lego parts, looking around at people's MOCs, there seems to be a lot of similarity going on. The same collection of parts and relationships bas resulted in 20,000 cars, 200 cranes, two birds and one ship in a bottle 

 

[nerdsforprez]

I am bumping my own topic.  Inspired by @Erik Leppen's most recent post about the upgrades he is planning for 42083 I wanted to look at the APPL value for the set (again, Average Pieces Per Lot - the idea being the higher the APPL value the more redundant the pieces.  Example - Lego 8288 had 800 pieces but only in 79 lots. An exceptionally high APPL value for a set of 800 pieces). 

The value was actually not that bad.  Just over 11 - which, as an absolute value is high but relative to a set with nearly 4000 pieces it is not high at all.  Therefore, not that redundant.

But I thought better of it and I realized that with the increased focus on color vomit in sets nowadays I think this renders my data and whole theory useless.  Color vomiting dilutes the relationship between piece and lot count because color variation, especially compared to like pre-2015 when there was not so much color variation/vomit, will artificially inflate the denominator in my formula.  Essentially, this counts different colored pieces as unique when they are not; i.e.e functionally the same.   So sadly, I don't think the Bugatti's value of just over 11 counts much here.  If I thought there was more value to this project I might do a recount but count similar pieces just in different colors as the same (like a 1x5 lift-arm for example in different colors) but then I would have to re-do my whole data for comparative purposes - which I don't think is worth it