WEBVTT 00:00:00.000 --> 00:00:02.470 align:middle line:90% [SQUEAKING] 00:00:02.470 --> 00:00:03.952 align:middle line:90% [RUSTLING] 00:00:03.952 --> 00:00:06.916 align:middle line:90% [CLICKING] 00:00:06.916 --> 00:00:21.258 align:middle line:90% 00:00:21.258 --> 00:00:23.300 align:middle line:84% RICHARD DE NEUFVILLE: Richard de Neufville again. 00:00:23.300 --> 00:00:26.350 align:middle line:84% The previous segment that I prepared for you 00:00:26.350 --> 00:00:29.570 align:middle line:84% is to describe what the flow of averages is. 00:00:29.570 --> 00:00:32.830 align:middle line:84% But now, we're talking about why it is important. 00:00:32.830 --> 00:00:36.910 align:middle line:84% And it's important because the standard practice that 00:00:36.910 --> 00:00:40.640 align:middle line:84% evaluates the performance of a system, under the most likely 00:00:40.640 --> 00:00:44.170 align:middle line:84% or the average conditions, gives you the wrong answer. 00:00:44.170 --> 00:00:47.650 align:middle line:84% If you do that, the result is the wrong estimates 00:00:47.650 --> 00:00:50.440 align:middle line:84% of the performance of any particular design, 00:00:50.440 --> 00:00:53.740 align:middle line:84% consequently the wrong ranking of the alternatives, 00:00:53.740 --> 00:00:56.500 align:middle line:84% and consequently the wrong choice of design. 00:00:56.500 --> 00:01:02.350 align:middle line:84% That is, unless you really look at how the system performance 00:01:02.350 --> 00:01:04.720 align:middle line:84% occurs over the range of possibilities, 00:01:04.720 --> 00:01:07.840 align:middle line:84% the ranges of demands, the ranges of performance, 00:01:07.840 --> 00:01:09.280 align:middle line:90% and ranges of prices-- 00:01:09.280 --> 00:01:12.610 align:middle line:84% unless you do that, you get the wrong answers. 00:01:12.610 --> 00:01:14.110 align:middle line:84% Mathematically, they may be correct, 00:01:14.110 --> 00:01:15.735 align:middle line:84% but they're not what's going to happen. 00:01:15.735 --> 00:01:17.900 align:middle line:84% And you get the wrong choice of design. 00:01:17.900 --> 00:01:19.850 align:middle line:84% That's why you should care about it. 00:01:19.850 --> 00:01:24.620 align:middle line:84% That's why you should not be a victim of the flaw of averages. 00:01:24.620 --> 00:01:28.120 align:middle line:84% So just let me put it in-- to show you how this works, 00:01:28.120 --> 00:01:30.830 align:middle line:84% to give you a concrete, a specific example, 00:01:30.830 --> 00:01:34.850 align:middle line:84% let's suppose we have a very simple measure of performance, 00:01:34.850 --> 00:01:39.030 align:middle line:84% which is that this f of x is equal to x squared plus 2, 00:01:39.030 --> 00:01:42.380 align:middle line:84% and that x can have-- with equal probability, 00:01:42.380 --> 00:01:46.240 align:middle line:90% it can be 1, 2, or 3. 00:01:46.240 --> 00:01:50.800 align:middle line:84% So on average, the average value of x is 2. 00:01:50.800 --> 00:01:54.370 align:middle line:84% If we evaluate this function using that average value, 00:01:54.370 --> 00:01:59.860 align:middle line:84% we get x squared is equal to 4 plus 2, result 6. 00:01:59.860 --> 00:02:05.260 align:middle line:84% But that's not what the average value of that is. 00:02:05.260 --> 00:02:08.740 align:middle line:84% If we calculate it with x is equal to 1, 00:02:08.740 --> 00:02:11.080 align:middle line:90% we have 1 plus 2 is equal to 3. 00:02:11.080 --> 00:02:14.800 align:middle line:84% If x is equal to 2, it's 6, but if x is equal to 3, 00:02:14.800 --> 00:02:18.760 align:middle line:84% it's 9 plus 2, 11, all with equal probability. 00:02:18.760 --> 00:02:24.310 align:middle line:84% And the average value of this is 3 plus 6 plus 11, divide by 3, 00:02:24.310 --> 00:02:25.870 align:middle line:90% which is 6 and 2/3. 00:02:25.870 --> 00:02:29.680 align:middle line:84% And it's not the 6 that is the value 00:02:29.680 --> 00:02:31.700 align:middle line:90% we calculate using the average. 00:02:31.700 --> 00:02:33.880 align:middle line:90% So the point is very simple-- 00:02:33.880 --> 00:02:37.600 align:middle line:84% that if you don't use the whole distribution, 00:02:37.600 --> 00:02:39.890 align:middle line:90% you'll get the wrong answer. 00:02:39.890 --> 00:02:44.530 align:middle line:84% Now to be fair, there is an example, a counter-example. 00:02:44.530 --> 00:02:47.860 align:middle line:84% That is, if the situation is totally linear-- 00:02:47.860 --> 00:02:52.450 align:middle line:84% so I have an equation like the function is x plus 2, 00:02:52.450 --> 00:02:55.750 align:middle line:84% and you have 1, 2, or 3 with equal probability-- 00:02:55.750 --> 00:02:59.560 align:middle line:90% in that case, they are the same. 00:02:59.560 --> 00:03:02.140 align:middle line:90% But the world is not linear. 00:03:02.140 --> 00:03:04.780 align:middle line:84% The world is, in fact, our systems, 00:03:04.780 --> 00:03:08.260 align:middle line:84% are almost always guaranteed to be non-linear. 00:03:08.260 --> 00:03:09.910 align:middle line:90% There are step functions. 00:03:09.910 --> 00:03:15.380 align:middle line:84% That is, we build one plan, and then we build another plan. 00:03:15.380 --> 00:03:19.870 align:middle line:84% So the capacity goes from this level in a step function 00:03:19.870 --> 00:03:20.860 align:middle line:90% to another level. 00:03:20.860 --> 00:03:22.870 align:middle line:90% There are changes in prices. 00:03:22.870 --> 00:03:24.730 align:middle line:90% There are economies of scale. 00:03:24.730 --> 00:03:26.570 align:middle line:84% There's all kinds of things that happen. 00:03:26.570 --> 00:03:28.370 align:middle line:90% The world is not linear. 00:03:28.370 --> 00:03:32.140 align:middle line:84% So in general, the flaw of averages 00:03:32.140 --> 00:03:35.650 align:middle line:84% holds and you get the wrong answer if you use, 00:03:35.650 --> 00:03:39.280 align:middle line:84% if you base your calculations on, the average or most 00:03:39.280 --> 00:03:40.850 align:middle line:90% likely value. 00:03:40.850 --> 00:03:44.590 align:middle line:84% So what are the practical consequences? 00:03:44.590 --> 00:03:46.780 align:middle line:84% Since the world is not linear, unless you 00:03:46.780 --> 00:03:49.300 align:middle line:84% work with a distribution, you get the wrong answer. 00:03:49.300 --> 00:03:50.710 align:middle line:90% It's as simple as that. 00:03:50.710 --> 00:03:57.100 align:middle line:84% Any calculation done based upon a single expected trajectory 00:03:57.100 --> 00:04:01.840 align:middle line:84% of demand, or costs, or performance, 00:04:01.840 --> 00:04:05.390 align:middle line:84% rather than the distribution, gives you the wrong answer. 00:04:05.390 --> 00:04:08.410 align:middle line:84% The answer from a realistic distribution 00:04:08.410 --> 00:04:11.350 align:middle line:84% of what might happen differs from the result 00:04:11.350 --> 00:04:13.610 align:middle line:90% you get from the averages. 00:04:13.610 --> 00:04:15.400 align:middle line:90% So why is that? 00:04:15.400 --> 00:04:18.310 align:middle line:84% Because very often, the gains when things go well 00:04:18.310 --> 00:04:23.920 align:middle line:84% do not balance off the losses when things do not. 00:04:23.920 --> 00:04:28.180 align:middle line:84% | have a visual example here that may be interesting to you. 00:04:28.180 --> 00:04:30.820 align:middle line:84% Here is a story of the drunk walking down 00:04:30.820 --> 00:04:32.050 align:middle line:90% the middle of the road. 00:04:32.050 --> 00:04:34.610 align:middle line:84% On average, he's in the middle of the road. 00:04:34.610 --> 00:04:38.710 align:middle line:84% The cars pass and don't hit him, but on average, he 00:04:38.710 --> 00:04:42.190 align:middle line:84% is hit by a car, in fact, and is dead. 00:04:42.190 --> 00:04:46.530 align:middle line:84% Do not be a victim of the flaw of averages. 00:04:46.530 --> 00:04:58.000 align:middle line:90%