There seems to be a whole metagame in TF2 revolving around hat crafting. Lots of people trade for craftable hats, craft them together, and hope to strike gold by crafting a hat more valuable than the two they used to craft it. I've always wondered how likely it actually is to end up crafting a valuable hat, if it's even worth doing or not, how often I would have to craft hats to break even, and what price I'd need to buy the hats at in order to have a high enough chance of making a profit, but I've never found a good resource on the subject except some generic guides saying it's good to buy at or below 1.33 ref.









In light of this, I decided to do my own analysis, the results of which I've posted here. The following content will fit into five main sections:

Description of the process I followed for analysis Assumptions A generic, static statistical overview of hat crafting profitability A summary of the results from the parameterized simulations I ran Conclusions First things first. I needed to find a list of all the craftable hats in TF2 and the accepted values associated with them. The list of hats I parsed from the TF2 wiki and the prices I queried from backpack.tf (11/30/2012). That left me with a list of 306 craftable hats and their maximum associated current prices. I performed some basic probability analysis on this and then ran a large number of simulations with different parameters to see how things were likely to occur in reality.





I will be making some assumptions about pricing in the rest of this article. I will usually specify those assumptions where they are being made, but in general, when not specified I am assuming the following:

Buds are worth 27 keys

Keys are worth 2.77 ref

Craftable hats are worth 1.33 ref and you purchase them for 1.33 ref

It costs 2.66 ref (2 craftable hat purchases) to craft a hat The last two of the above parameters are varied throughout the simulations to account for the possibility of being able to buy craftable hats at lower than 1.33 ref. Additionally, I assume that hats are crafted via the rebuild headgear option rather than the fabricate new headgear option because it is about .33 ref more cost effective.





On to the basic static analysis. From the prices I scraped from backpack.tf, only 182 hats have a maximum accepted value of above 1.33 ref. Making the above assumptions, this means only 54 hats are actually profitable to craft. Furthermore, each headgear rebuild has a 17.65% chance of crafting a profitable hat. You may at this point be thinking that because some hats are so valuable, this sort of chance is still good. However, if you were to craft each hat exactly once at the above price assumptions, you would spend 30.15 buds but gain only 25.35 buds (a loss of 4.8 buds). We can see from this that hat crafting is all about luck in crafting valuable hats and not crafting run of the mill hats; however, since this is all a game of chance with opportunity for significant payoff with enough luck over time, we don't know much more than we did before other than that each individual craft has a low probability for payoff.





It remains to be answered how crafting large numbers of hats and playing with the buying price influence your overall probability of making a profit. Additionally, it is also still unclear how much profit you are likely to make if you happen to be luck enough to make a profit. This is where the previously mentioned simulations come in. I built a program to perform specified numbers of random hat crafts under a parameterizable set of conditions and then perform statistical analysis on the results to determine overall profitability across a different metrics. This, in my mind, is the ultimate answer to the following questions:

How likely is it to make a profit crafting hats?

How much does lowering my buying price increase my chance of making a profit?

How much does increasing the number of hats I craft increase my chance of making a profit?

And ultimately, should I get into crafting hats for profit? I used this program to run simulations of all scenarios possible given the following parameters: Buying craft hats at 1.33 ref, 1.22 ref, 1.11 ref, and 1 ref Running the same exact scenario simulation 10 times, 100 times, 1,000 times, 10,000 times, and 100,000 times. This parameter gives us a wide variety of sample set sizes to account for the randomness of hat crafting and give us as accurate of a prediction as possible. You can think of it as having several of your friends all buying at the same price and crafting the same number of hats. Each of you may gain or lose value through the experience, and people would be able to learn a bit about whether hat crafting can be expected to be profitable or not by taking metrics from your experience such as minimum profit, maximum profit, average profit, and percentage of your friends that made any profit at all. Crafting 1, 5, 10, 25, 50, 75, 100, and 500 hats during each round of the simulation. If I were to continue the previous analogy, you and your friends would each craft 1 hat, pretend like it never happened, craft 5 hats, reset, craft 10 hats, and so on all the way up to 500 hats each. I should specify that crafting a hat in my simulation is as simple as adding to the total accumulated cost whatever 2 times the craft hat purchasing price is and adding the value of a randomly selected hat from the previously mentioned list of 306 hats to the total accumulated value gained. This may not be exactly in conformance to how TF2 crafts hats (i.e. crafting the hats you used to craft in the first place, etc), but given the number of times each simulation is run, this variance is insignificant. Additionally, I do not account for the fluctuation in prices of certain hats around the release of new items since crafting only when new hats are released and aiming for low craft numbers is a different business model than hoping to profit from optimal buying prices and crafting volumes.

Below are the most in results of each set of simulations. After the results I will summarize the results of all the simulations and discuss my conclusions on hat crafting profitability. I am including only the 100,000 x runs below because the lower numbers, while sometimes interesting, are more prone to the 1 hit wonder hit or miss sort of statistics which does not help us make a general prediction and the higher numbers were all very similar to each other.

========================================================================



PRICE ASSUMPTIONS:

Buds are worth 27 keys. Keys are worth 2.77 ref. Craftable hats are worth 1.33 ref ref and you purchase them for 1.33 ref. It costs 2.66 ref (2 craftable hat purchases) to craft a hat.

GENERAL ANALYSIS:

Of 306 total craftable hats, 182 are valued above 1.33 ref (backpack.tf max prices as of 11/30/2012 1:26:33 PM EST). Assuming a cost of 2.66 ref to craft, 54 are profitable to craft. This means each headgear rebuild has a 17.65% chance of crafting a profitable hat. If you were to craft each hat once at 2.66 ref, assuming keys at 2.77 ref, you would have spent 30.15 buds and gained 25.35 buds (a loss of 4.8 buds).

SIMLUATION RESULTS:





After running 100,000 simulations in which 1 hats were crafted at a cost of 2.66 ref in each simulation, 17,851 simulations were profitable (17.85%) with a minimum profit of 0.11 ref, an average profit of 0.85 ref, and a max profit of 1.04 keys

After running 100,000 simulations in which 5 hats were crafted at a cost of 2.66 ref in each simulation, 19,013 simulations were profitable (19.01%) with a minimum profit of 0.55 ref, an average profit of 4.13 keys, and a max profit of 2.07 buds

After running 100,000 simulations in which 10 hats were crafted at a cost of 2.66 ref in each simulation, 16,584 simulations were profitable (16.58%) with a minimum profit of 0.48 ref, an average profit of 8.75 keys, and a max profit of 4.66 buds

After running 100,000 simulations in which 25 hats were crafted at a cost of 2.66 ref in each simulation, 18,821 simulations were profitable (18.82%) with a minimum profit of 0.15 ref, an average profit of 2.18 buds, and a max profit of 12.93 buds

After running 100,000 simulations in which 50 hats were crafted at a cost of 2.66 ref in each simulation, 17,334 simulations were profitable (17.33%) with a minimum profit of 0.2 ref, an average profit of 4.68 buds, and a max profit of 25.85 buds

After running 100,000 simulations in which 75 hats were crafted at a cost of 2.66 ref in each simulation, 18,075 simulations were profitable (18.08%) with a minimum profit of 0.5 ref, an average profit of 6.52 buds, and a max profit of 38.78 buds

After running 100,000 simulations in which 100 hats were crafted at a cost of 2.66 ref in each simulation, 17,557 simulations were profitable (17.56%) with a minimum profit of 0.92 ref, an average profit of 8.61 buds, and a max profit of 51.7 buds

After running 100,000 simulations in which 500 hats were crafted at a cost of 2.66 ref in each simulation, 21,555 simulations were profitable (21.56%) with a minimum profit of 0 ref, an average profit of 35.9 buds, and a max profit of 258.52 buds









PRICE ASSUMPTIONS: Buds are worth 27 keys. Keys are worth 2.77 ref. Craftable hats are worth 1.33 ref ref and you purchase them for 1.22 ref. It costs 2.44 ref (2 craftable hat purchases) to craft a hat.

GENERAL ANALYSIS:

Of 306 total craftable hats, 305 are valued above 1.22 ref (backpack.tf max prices as of 11/30/2012 1:30:57 PM EST). Assuming a cost of 2.44 ref to craft, 68 are profitable to craft. This means each headgear rebuild has a 22.22% chance of crafting a profitable hat. If you were to craft each hat once at 2.44 ref, assuming keys at 2.77 ref, you would have spent 27.65 buds and gained 25.35 buds (a loss of 2.31 buds).

SIMLUATION RESULTS:





After running 100,000 simulations in which 1 hats were crafted at a cost of 2.44 ref in each simulation, 21,063 simulations were profitable (21.06%) with a minimum profit of 0.22 ref, an average profit of 2.41 ref, and a max profit of 2.12 keys

After running 100,000 simulations in which 5 hats were crafted at a cost of 2.44 ref in each simulation, 28,374 simulations were profitable (28.37%) with a minimum profit of 0.1 ref, an average profit of 3.44 keys, and a max profit of 2.11 buds

After running 100,000 simulations in which 10 hats were crafted at a cost of 2.44 ref in each simulation, 21,114 simulations were profitable (21.11%) with a minimum profit of 0.22 ref, an average profit of 8.09 keys, and a max profit of 5.25 buds

After running 100,000 simulations in which 25 hats were crafted at a cost of 2.44 ref in each simulation, 23,316 simulations were profitable (23.32%) with a minimum profit of 0.22 ref, an average profit of 1.9 buds, and a max profit of 13.13 buds

After running 100,000 simulations in which 50 hats were crafted at a cost of 2.44 ref in each simulation, 21,243 simulations were profitable (21.24%) with a minimum profit of 0.44 ref, an average profit of 3.86 buds, and a max profit of 26.26 buds

After running 100,000 simulations in which 75 hats were crafted at a cost of 2.44 ref in each simulation, 22,301 simulations were profitable (22.3%) with a minimum profit of 0.5 ref, an average profit of 5.83 buds, and a max profit of 39.39 buds

After running 100,000 simulations in which 100 hats were crafted at a cost of 2.44 ref in each simulation, 22,538 simulations were profitable (22.54%) with a minimum profit of 0.22 ref, an average profit of 8.04 buds, and a max profit of 52.52 buds

After running 100,000 simulations in which 500 hats were crafted at a cost of 2.44 ref in each simulation, 22,369 simulations were profitable (22.37%) with a minimum profit of 0.99 ref, an average profit of 38.75 buds, and a max profit of 262.59 buds









PRICE ASSUMPTIONS:

Buds are worth 27 keys. Keys are worth 2.77 ref. Craftable hats are worth 1.33 ref ref and you purchase them for 1.11 ref. It costs 2.22 ref (2 craftable hat purchases) to craft a hat.





GENERAL ANALYSIS:

Of 306 total craftable hats, 305 are valued above 1.11 ref (backpack.tf max prices as of 11/30/2012 1:35:52 PM EST). Assuming a cost of 2.22 ref to craft, 76 are profitable to craft. This means each headgear rebuild has a 24.84% chance of crafting a profitable hat. If you were to craft each hat once at 2.22 ref, assuming keys at 2.77 ref, you would have spent 25.16 buds and gained 25.35 buds (a gain of 1.8 keys).

SIMLUATION RESULTS:





After running 100,000 simulations in which 1 hats were crafted at a cost of 2.22 ref in each simulation, 39,286 simulations were profitable (39.29%) with a minimum profit of 0.11 ref, an average profit of 1.17 keys, and a max profit of 5.2 keys

After running 100,000 simulations in which 5 hats were crafted at a cost of 2.22 ref in each simulation, 23,885 simulations were profitable (23.88%) with a minimum profit of 0.22 ref, an average profit of 1.99 keys, and a max profit of 6.21 keys

After running 100,000 simulations in which 10 hats were crafted at a cost of 2.22 ref in each simulation, 22,152 simulations were profitable (22.15%) with a minimum profit of 0.4 ref, an average profit of 7.39 keys, and a max profit of 4.31 buds

After running 100,000 simulations in which 25 hats were crafted at a cost of 2.22 ref in each simulation, 25,045 simulations were profitable (25.04%) with a minimum profit of 0.74 ref, an average profit of 1.89 buds, and a max profit of 13.33 buds

After running 100,000 simulations in which 50 hats were crafted at a cost of 2.22 ref in each simulation, 24,708 simulations were profitable (24.71%) with a minimum profit of 0.22 ref, an average profit of 3.97 buds, and a max profit of 26.67 buds

After running 100,000 simulations in which 75 hats were crafted at a cost of 2.22 ref in each simulation, 24,826 simulations were profitable (24.83%) with a minimum profit of 0.05 ref, an average profit of 5.73 buds, and a max profit of 40 buds

After running 100,000 simulations in which 100 hats were crafted at a cost of 2.22 ref in each simulation, 24,996 simulations were profitable (25%) with a minimum profit of 0.28 ref, an average profit of 7.77 buds, and a max profit of 53.33 buds

After running 100,000 simulations in which 500 hats were crafted at a cost of 2.22 ref in each simulation, 25,341 simulations were profitable (25.34%) with a minimum profit of 0.06 ref, an average profit of 37.95 buds, and a max profit of 266.67 buds













PRICE ASSUMPTIONS:

Buds are worth 27 keys. Keys are worth 2.77 ref. Craftable hats are worth 1.33 ref ref and you purchase them for 1 ref. It costs 2 ref (2 craftable hat purchases) to craft a hat.

GENERAL ANALYSIS:

Of 306 total craftable hats, 305 are valued above 1 ref (backpack.tf max prices as of 11/30/2012 1:40:16 PM EST). Assuming a cost of 2 ref to craft, 76 are profitable to craft. This means each headgear rebuild has a 24.84% chance of crafting a profitable hat. If you were to craft each hat once at 2 ref, assuming keys at 2.77 ref, you would have spent 22.67 buds and gained 25.35 buds (a gain of 2.68 buds).





SIMULATION RESULTS:





After running 100,000 simulations in which 1 hats were crafted at a cost of 2 ref in each simulation, 29,906 simulations were profitable (29.91%) with a minimum profit of 0.33 ref, an average profit of 1.97 ref, and a max profit of 1.78 keys

After running 100,000 simulations in which 5 hats were crafted at a cost of 2 ref in each simulation, 23,393 simulations were profitable (23.39%) with a minimum profit of 0.65 ref, an average profit of 4.48 keys, and a max profit of 2.71 buds

After running 100,000 simulations in which 10 hats were crafted at a cost of 2 ref in each simulation, 25,027 simulations were profitable (25.03%) with a minimum profit of 0.5 ref, an average profit of 7.52 keys, and a max profit of 4.39 buds

After running 100,000 simulations in which 25 hats were crafted at a cost of 2 ref in each simulation, 25,381 simulations were profitable (25.38%) with a minimum profit of 0.26 ref, an average profit of 2.29 buds, and a max profit of 13.54 buds

After running 100,000 simulations in which 50 hats were crafted at a cost of 2 ref in each simulation, 24,452 simulations were profitable (24.45%) with a minimum profit of 0.66 ref, an average profit of 4.12 buds, and a max profit of 27.07 buds

After running 100,000 simulations in which 75 hats were crafted at a cost of 2 ref in each simulation, 24,786 simulations were profitable (24.79%) with a minimum profit of 0.15 ref, an average profit of 6.4 buds, and a max profit of 40.61 buds

After running 100,000 simulations in which 100 hats were crafted at a cost of 2 ref in each simulation, 24,708 simulations were profitable (24.71%) with a minimum profit of 0.68 ref, an average profit of 8.74 buds, and a max profit of 54.15 buds

After running 100,000 simulations in which 500 hats were crafted at a cost of 2 ref in each simulation, 25,765 simulations were profitable (25.76%) with a minimum profit of 0.52 ref, an average profit of 41.14 buds, and a max profit of 270.74 buds



========================================================================









The above simulation results allow us to draw a few conclusions.

Buying craft hats at 1.33 ref gives you roughly a 20% chance of making an overall profit no matter how many hats you craft, but having a long string of luck in your crafting and crafting several hundred hats returns a very significant profit. Buying hats at 1.22 ref gives you roughly a slightly higher chance of making an overall profit across all volumes of hat crafting in the low to mid 20s percent range. However, at this price it seems better to craft only a few hats and get out while you're ahead similar to 1.33 rather than craft for volume since your profit margin on most hats is still low if it exists. Buying hats at 1.11 ref does not differ much from buying at 1 ref but both have significantly higher changes for overall profit in the high 20s to mid 30s percent range. If you decide to craft hats and are haggling with someone over this different in price, it doesn't make much of a difference in the long run. Crafting a hat here and there is not a reliable way to make a profit in the long run. While you may craft a valuable hat, it's very likely that its value won't exceed the value of all the hats you've crafted at a loss in the process. Hat crafting in general is definitely a high risk high reward business model. A streak of luck can bring in several hundred buds worth of profit, but the vast majority of times any profit made will be negligible if it exists at all. The people who make a large profit off crafting a few hats are statistical anomalies. That being said, you have a significantly higher chance of making money crafting hats than you do uncrating an unusual. If crafting is going to be profitable, the profit margin has to be higher because the chance for success is so low. This means crafting low craft numbered items around the times new hats are released is a much better business model than just crafting hats and hoping for profit to come from a few valuable crafts. Bottom line, considering that it is very difficult to buy craftable hats for less than 1.33, it doesn't seem worth it to me to try to craft hats for profit unless you really like to take risks. My approach (excluding going for low craft numbers) would be to craft a few (less than 10) and if I get lucky, be happy, and if not, cut my losses.





Preface: as stated later on, I am ignoring the business model of waiting for updates and crafting low number high value hats since the risk reward tradeoff is much different than it is on an average day of hat crafting.