Benefit: Suppose that in a clinical trial running one year, 80% of patients on drug A benefit from the drug, and 82% of patients on drug B benefit equally. Now drug B is better by 2%, but what does that mean? If we treat 100 patient on each drug for one year, we expect 80 "benefactors" from Drug A and 82 benefactor from drug B, a difference of two patients saved every year for every 100 treated, or one saved for every 50 patients treated (for one year).
A shorter way to calculate this is NNT = 1/(0.82-0.80) 1/(0.02) = 50 patients "needed to treat" for one to benefit. Make sure to subtract the smaller probability from the larger, or you up with a negative number.
Cost: Now suppose that drug B costs $10,000 per year, compared to $1000 per year for drug A; Is drug B worth ten times the expense? NNT helps answer that question. Consider that treating 50 patients for one year (the NNT) would cost $250,000 on drug B and and $50,000 on drug A - a difference of $200,000 for one life saved each year. Now is drug B worth the cost? If the benefit is strong, like not dying, then it may be worthwhile. It certainly is if you are the 1-in-50 patient, but you can't know that is advance. Also, resources are limited. It is not good practice to make patients pay large expenses, or tie-up hospital resources, for treatments with very little benefit.
If anyone is wondering, this is not Obama-Care Death-Panel stuff, this is a serious sort of decision that determines what doctors call "Best Practice".
Well so far this has been pretty boring, but now we can take the idea behind NNT and turn it into a statistic for games.
If we replace the probability a treatment will be effective with the probability of a successful "to-hit" roll, we get a measure of Number or rolls Needed to Hit (NNH). This is now the number of to-hit attempts you will need to make, with some higher probability of success, in order to hit one more target on average. In the sniper rifle example from the previous comments, the difference between 80% and 82% means one more hit out of every 50 shots fired. This 2% gain could be useful from the perspective of a first-person-shooter game, or even critical to ensure taking out an important target, but on a larger scale other things could matter more. For instance, if the more accurate rifle weighs more, or costs more, and this is reflected in game usage and costs, then 2% gain in accuracy might not be worthwhile.
9 comments:
I've think you will find that what I've written in my latest blog will amuse you somewhat, even if my facility with the maths is far below yours.
Hey! You forgot the link!
I understand the concept better now. The cost ratio benefit of the improvement may not make it worthwhile. The US Department of Defense may come to that conclusion based on the slight advantage and the cost to gain it versus budget considerations.
The Scope would be also discussed in places like Soldier magazine for example. The individual Sniper would disagree with DOD, of course. As said before on the ground any advantage no matter how slight is welcome.
The hitch is, the individual Sniper is right from his/her perspective as well as the DOD being right from theirs. This scenario occurs often actually, and interestingly both sides have in the past (probably still do) inferred that the other doesn’t understand the practicality of the situation. Which reinforces stronger, the idea of different perspectives and interpretations based on the same data. As Dan said a patient might have a slightly different outlook on the data presented in the medical example as well based on their outlook.
For purpose of my games, the distinction, even though slight, is important even at the larger unit scales. They are important because they are part of a larger whole. If you gain a 2 percent advantage on every weapon or technology in a Division sized unit, that advantage cumulatively can be significant. Not meaning cumulative mathematically, just conceptually.
Think of a track and Field event. If I ran, jumped, and threw, just slightly longer, faster and higher then my opponents, cumulatively those slight differences mean the difference between Gold vs. Silver or a win vs. a loss.
Now you've got it, and you are right too. When it comes to highly skilled specialists in important rolls, they should have the best equipment for the job.
Thinking with my keyboard --> If there was some piece of equipment that would improve your entire force by 2%, that would be amazing. This wouldn't happen by giving high-tech sniper rifles to every soldier though.
Also, maximizing a strength may not be as important as minimizing a weakness. Better sniper rifles might not be the best force to improve the force as a whole.
No there’s not any one thing that will improve a force on its own. That’s why all the little things are important. Take an old PC wargame Operational Art of War. In the manual it gives the values assigned to individual weapons within each unit. Most Units in the game are Division level some lower. This database lumps many slightly different, and sometimes vastly different weapons into one. For example all 75mm Anti Tank guns are lumped together, though historically they were quite different and individually representing them would not have been at all difficult technically. The result is these differences generate skewed results in combat. The differences in some of these generalized categories may be slight but that doesn’t mean they aren’t significant and when put together with other differences it makes quite a difference. The 75mm Tank mounted weapons of the Soviets verses the 75mm Tank mounted weapons of the German had differences. These may seem slight when looking at the numbers. But differences on the Steppes of Russian meant then Soviets were at a major disadvantage that effected many results of battles even at Division level and higher. By not specifying these small advantages the game does not yield even close realistic results.
Thanks for this Post DC! I find it really helpful in the current reproductive health rights debate my country is going through. Particularly the Ethical aspects of "Best Practice".
Thanks Nikolas. I don't get much chance to talk about serious topics like ethics here. People like games because they pose interesting and difficult problems, but the same skills are used in solving real world problems (maybe I should have said that the other way around).
Almost forgot! Nikolas is a prolific blogger on games on other topics. Be sure to check out Game in the Brain and Gamer's Mind.
thanks for the plug :D
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