A mathematical question on calculating "bang for the buck"

[Radium_Angel]

Another user posted a question about scrapyard wars and it got me to thinking about calculating "bang for the buck"

Let's say, for example, I buy a 100$ used PC. I run some benchmarking programs and they return a nice round number of 1000.

 

Would it be safe to then assume that for every dollar I spent on the original PC, I got 10 points in benchmarking?

 

Let's say then, I spend another 100$ upgrading the PC and re-run the benchmarking program and get 4000 points.

Would the math run as 200$ (100$ originally spent to buy it and the additional 100$ spent upgrading it) per the 4000 points (4000/200=20 points per dollar spent)

or would it run 1000/100$ (the original money spent and benchmark results)= 10 points per dollar spent, PLUS 3000/100$ (the improved performance as a result of the additional 100$ spent=30 points per dollar spent) then added to the original 10 points, making for a total of 40 points per dollar spent.

 

The reason I ask this is the concept of "bang for the buck", and where the most improvement would come, per dollar spent, in upgrading an old PD.

Or is my thinking all wrong here? (I was never very good at math)

[fUnDaMeNtAl_knobhead]

I think that the term bang for the buck wasn't supposed to be defined objectively. I think that it was supposed to be subjective or not meant for calculations. For ex RTX 2080 vs RTX 3070 at MSRP which is very rare the 3070 is better bang for the buck but how do you do that for a case or long term bang for the buck.     TLDR I don't know but I think that the mathematical calculations was just to prevent confusion and subjective judgement.

 

 

P.S i am not good at math either

[Kilrah]

Depends what matters to you, the performance you got for the total paid or the increase you got e.g. thanks to an upgrade.

[Radium_Angel]

30 minutes ago, Kilrah said:

Depends what matters to you, the performance you got for the total paid or the increase you got e.g. thanks to an upgrade.

My thought was to host a contest (local to my circle of friends) to go out, buy a used PC (and show receipts) for as little as possible, then spent, again, as little as possible, on parts to improve it, and the winner would be the one that showed the most improvement per dollar spent.

I'm trying to calculate (or determine how to calculate) how to do that. The fastest PC wont necessarily be the automatic winner.

[Chris Pratt]

There's a number of things wrong here. For one, component performance is not linear, i.e. if spending X gives you Y performance, spending 2X doesn't mean you get 2Y performance. While there's exceptions to every rule, it's generally asymtopic. As you go from zero cost up, performance dramatically outpaces the extra investment until you start hitting the high end where cost then dramatically outpaces any increase in performance. The best value or "bang for the buck", therefore, generally lies in the midrange.

 

Second, components do not work in isolation. The reason it's called a system is because they all interact with each other. A good CPU can be hamstrung by bad RAM, for example. The value of the system lies in the combination of parts, so you can't just look at two systems with the same CPU, for example, and say one is a better value than another because it costs less. It might cost less for a reason, and the difference in cost may actually add a significant performance boost to the second system, that outpaces that difference.

 

Finally, value is somewhat subjective and depends on the workloads. For example, I purchased a 5900X, because for me, it was an excellent value. I do a lot of multicore heavy workloads, and dollar for dollar, there's nothing right now that matches the 5900X for those workloads. If you were just building a system to play CS:GO, the 5900X would be a horrible value, though.

[IPD]

You're in the ballpark.  "Bang for the buck" is a nebulous idea.  In the example you give, I think it's more like:

 

-Upgrade A costs $200 and will give a 3000 increase.

-Upgrade B costs $25 and will give a 1000 increase.

-Upgrade C costs $2000 and will give a 10,000 increase.

 

From these 3 alone, upgrade B will give the most "bang for the buck" even though the performance increase is lowest. 

 

So you aren't really factoring in the original equipment--unless you are replacing all of it.  Potentially, an upgrade could get you 90% of the performance of an entirely new build--but only cost half as much.  At that point, you'd be comparing the cost of the new built (all required to get the max performance) or the cost of the upgrade (only the upgraded part counts).

 

You have to be careful here, or you end up in the realm of Parmenides' Fallacy; where you compare current against previous...rather than current against another possible (current) outcome.  "Bang for the Buck" then, should be taken as meaning "given all possible (acceptable) choices, which one will deliver the highest return yields for the lowest cost"?

[IPD]

2 minutes ago, Radium_Angel said:

My thought was to host a contest (local to my circle of friends) to go out, buy a used PC (and show receipts) for as little as possible, then spent, again, as little as possible, on parts to improve it, and the winner would be the one that showed the most improvement per dollar spent.

I'm trying to calculate (or determine how to calculate) how to do that. The fastest PC wont necessarily be the automatic winner.

That's pretty easy.  You just establish what your benchmark will be, and then divide that by the total cost/s.

[Radium_Angel]

1 minute ago, IPD said:

That's pretty easy.  You just establish what your benchmark will be, and then divide that by the total cost/s.

My thought was to run the benchmark on the initial system, then do the upgrades and compare the final benchmark.

You are saying do it as a ratio of initial benchmark vs final, I was questioning if going by dollars spent would give me more accurate "bang for the buck" answer...

[Chris Pratt]

5 minutes ago, Radium_Angel said:

My thought was to host a contest (local to my circle of friends) to go out, buy a used PC (and show receipts) for as little as possible, then spent, again, as little as possible, on parts to improve it, and the winner would be the one that showed the most improvement per dollar spent.

I'm trying to calculate (or determine how to calculate) how to do that. The fastest PC wont necessarily be the automatic winner.

You'd have to pick a specific task. In the Scrapyard Wars episodes, there was always a particular game or games they would have to compete in at the end. It's a very different thing to say go out and build the best gaming machine versus go out and build the best machine for video editing or programming. Heck, it's a very different thing to build a rig for playing FPS versus playing RPG titles. The winner would have to be one that excels that that particular specific task while spending the least money.

[Moonzy]

Both are right, but one is judging purely on the upgrade alone, the other is your overall spending

 

That's why LTT used to do "full system cost fps per dollar" on their GPU videos because, yea, a 3060 is 80% the performance of a 3070, but it costs 70% as much, so it's way better value than the 3070 by itself

 

But if you factor in other PC costs, the 3070 may end up being more fps per dollar spent on the entire PC

[Radium_Angel]

3 minutes ago, Chris Pratt said:

You'd have to pick a specific task

Which is exactly what I don't want to do, hence the thought of an "overall" benchmark score.

Going after a single specific task is too easy, the overall "most improved" would require much more thought, IMO.

 

 

[Avocado Diaboli]

Since you're pretty much just calculating the coefficient of money spent vs performance achieved, you could say that it's a valid metric of calculating "bang for the buck" and also determine the point of diminishing return. It just depends on how you define performance. If you buy a part for performance specifically because of a benchmark and not some real-world task, then the "bang for the buck" coefficient is only applicable to said benchmark. It all depends on your intended use case and also how far you need to take those calculations.

 

If you need to render a lot of videos and have the following scenario:

 

PC 1 costs $1000 and renders the video in 60 minutes = 1000/60 = $16.6 per minute in rendering time.

PC 2 costs $2000 and renders the video in 45 minutes = 2000/45 = $44.4 per minute in rendering time.

 

PC 1 has better bang for the buck for rendering videos (in isolation) because you only spend roughly a third of the amount per minute of rendering time.

 

Of course, this only matters if you render 1 video and then throw out the computer, which you probably won't do. The more expensive PC can render more videos per day. If we take that aforementioned video and say every video that has to be rendered takes the exact same amount of time to render and the earnings of all the videos are identical:

 

PC 1 renders 24 videos per day, 720 videos per month or 8640 videos per year.

PC 2 renders 32 videos per day, 960 videos per month or 11520 videos per year, so 33% more videos than the cheaper machine.

 

You spent 100% more on PC 2 for 33% more earnings over PC 1. So now the balance has to be between spending $1000 on a machine vs. how much you earn more from it. If a video brings in $1 in earnings, at the end of the year the numbers look like this:

 

PC 1 earns $8640 from rendering videos

PC 2 earns $11520 from rendering videos

 

I'd certainly buy PC 2 and eat the $1000 if it means I get $2000 more net revenue from it over the cheaper machine, even though on paper, its specs would indicate that it's not twice as fast for twice as much spent. In the end, a calculation like this needs a ton of variables to be accurate. 

[Radium_Angel]

39 minutes ago, Avocado Diaboli said:

In the end, a calculation like this needs a ton of variables to be accurate. 

Yes, this is why I raised the original question, how to calculate this type of info.

I can see now why the LTT Scrapyard wars would only concentrate on FPS, as opposed to an all over improvement, because that sort of thing is hard to calculate as you have mentioned.

 

May have to rethink this....

 

[suedseefrucht]

18 hours ago, Radium_Angel said:

for every dollar I spent on the original PC, I got 10 points in benchmarking

Like people said before, the performance for dollar is not constant over the range of benchmark points.

I think, what really helps us evaluate systems is making a table with the bechmark score in one column and the system's total price in the other column.

And if someone gets the same or a better score with less money, the line will be overwritten.

With that table you could see, how much money people needed to spend to get to a benchmark score.

 

But think about Fast & Furious 8's cuba race. If you max out the bang for the buck, your system will probably not live that long.

[varrys]

An issue is if every person starts with a different system. Someone using a 2008 system may have a hard time finding parts, and sometimes legacy stuff costs more. Compared to someone using a 2015 system who can find more parts to work with.

 

But if you can solve the starting equipment issue (maybe dictate a cap on money spent on original system and give a year range for manufactured?), I would think you run original system. Then upgrade and run the benchmark again. What is the percentage improvement? That's your first variable.

 

Then take the total amount spent on upgrades. That's your second variable. I would focus specifically on upgrade cost if the systems are near each other in starting specs, but maybe do full cost if you can't get people to use systems near the same year/specs.

 

So it's percentage improvement divided by money spent.