Distribution In, Distribution Out

A common catch-phrase at school is: “Point Estimates are for Suckers”.  The reason they say this was highlighted by something my Decision Modeling professor said in our last class: “A point estimate is basically a 0% confidence interval.”  For those of you that don’t have a background in statistics, what this basically means is that we can gauge the likelihood that the true value of something we are trying to estimate lies between two values.  This is called a confidence interval.  So, a 90% confidence interval means that we are 90% sure that the true value lies between the two ends of that interval.  For instance, I could say that I am 90% confident that the gas mileage of my car lies between 20 mpg and 35 mpg.  Basically, this is a calculus equation finding the area under the curve for a given range of a given distribution.

If, however, we posit a guess of an exact amount (say, 28 mpg in my example) we have selected a range that has a length of zero.  The area under the curve for a single point is infinitesimally small: the value under that point approaches zero.  In that way, our confidence that our point-estimate is right is 0%; our confidence that the real value is something else entirely is near 100%.

Which is all an argument for using distributions and meaningful confidence intervals in our modeling instead of pure point estimates when dealing with inputs for which we cannot and do not know the exact value.

The folks who are forecasting revenue at work struggle every day to deal with this problem: they get input from the sales and channel representatives who supposedly know the likelihood that this deal or that deal will succeed.  If it succeeds, we’ll get a certain amount of revenue (an amount that, itself, ought to be a distribution).  If it fails… we’ll get none of that potential revenue.  How ought they forecast revenues, then?  If they could model the inputs – the likelihood of sealing a deal, the value of that deal – as uncertainties and distributions, then they could generate distributions at the end that give a range of likely revenue scenarios.  I wonder if providing confidence intervals like this would make decision-making at higher levels in my company better.

Anyway, that’s the update from Decision Modeling for this week. 

This week, I need to spend a little more time really focusing on my career planning.  I’ll report on how that goes, as time permits.  As for writing… well, my brain has been just dry this past week.  We’re almost halfway through the semester, and my brain just needs a recharge break before writing ideas start percolating again.

Update from PM Class

It’s time for my weekly update from the Project Management class, for want of anything better to talk about.  Which, this week, is a pretty big want.  In other words, there wasn’t much interesting about the most recent PM class.  This class we had a guest speaker who talked a lot about Microsoft’s Project Portfolio Server program.  I wasn’t really inspired by it.  Certainly, it made organizing large numbers of projects into a single view easier, and easier to do some cursory analysis on them.  But, with the analytics essentially obscured to the user, I didn’t feel confident that it was a good platform for decision analysis when considering multiple projects against constrained resources.  What I’m learning in my Decision Modeling class is much better for that, I think – and there, defining the parameters becomes a much more transparent process.

We also were given our group assignments, and I’m still waiting on feedback from my boss about whether there’s a project here at work that we can use.  If not, one of the other group members may have a project.

Tangentially related, as I was thinking about projects – both for this class and for the Decision Modeling class – I came up with what I think may be a great project idea for Decision Modeling.  In that class, we’ll need to model a complex and non-trivial decision with lots of constraints and uncertainties.  I don’t know all the details of the project’s requirements, but I was reflecting on the A & M Kerfuffle when this idea struck me.  I left a comment on John Scalzi’s blog a few days ago (scroll down to comments #43 and #44) about one of the factors that I thought was entering into the psychology of consumers regarding e-book prices (one which I hadn’t seen really brought up much, that being that physical books, even having the same content as e-books, can be valued higher simply because they have physical, concrete, and tactile existence).  Later, I thought about my comment, and thought: “Stephen, you’re smarter than that.  There’s more that enters into pricing, and perception of price, than any one factor.  It’s a complex interplay of Supply, Demand, Break-even, Equilibrium, and Consumer Psychology, all in one package.  Heck, it’s a complex, non-trivial nut to crack.”  That’s when I thought: “Complex!  Non-trivial!  Nuts-to-crack!  These are the features of the sorts of problems that I’d want to use my new decision modeling ninja skills on.”  Besides that, the prof had mentioned finding a project about which we were interested.

I’ve already reached out at work on that project, too, to see if there was a complex decision problem requiring ninja-level-analysis there.  And that will take precedence if I find one.  But I’d be much more interested in exploring the complex problem of e-Book pricing, if nothing at work pans out.  If I proceed with it, I’ll next have to consider how I’d frame the question, and what, precisely, I’m trying to “decide” and from who’s perspective.  Probably, I’d think that both Amazon’s and Macmillan’s positions on the issue are well vetted within their organizations, so the tack I’d have to take would be: from an author’s perspective, what is the ideal e-Book price?

If this goes forward…

STAND BACK!  I’ll be doing SCIENCE!

Modeling as Art

Just a short update from the grad school trenches for today.  Decisions Modeling continues to be one of my favorite classes from the MBA program so far.  And I continue to realize that this is largely because I am a nerd (and also because the professor is really great). 

I did struggle a couple times in the last DM class to stay awake, right at first.  I’d had a long day at work, and the previous two nights I’d been up way to late working on homework for class.  I felt awful about it because I sit very close to the front and center.  I managed to pull myself out of it, though, and focus in on the class.  A good amount of the class was building more Excel and Modeling “ninja” skills, as the prof calls them.  Much of class was spent looking at random number and distributions and other skills related to sensitivity analysis.  We talked more about objective functions and constraints in linear programming models, and how very robust models can flip the two on their heads, solving the same problems using different approaches.  I asked whether we might see situations where we would find it useful to spend the time solving the problem from opposite directions and the professor answered, emphatically, that YES, very complex and difficult problems can benefit from taking multiple approaches to them.

Meanwhile, one of the benefits of the @Risk add-on is that we can define an entire distribution within a single cell (and reference that distribution in our formulas which will generate distributions for answers).  We can also define a distribution based on empirical, observed data.

So, yeah, no cool writing thoughts to glean from all this.  But, the deeper we get into this modeling stuff, the more I am coming to realize that spreadsheet modeling is really working art with numbers.  The professor has said over and over things like “there’s an art to this”.  And I can see that he’s right.  That’s the reason I like this stuff.  I’m a very creative type who happens to have a very logical and mathematical mind.  This sort of modeling appeals to both those halves.  That’s also why I like writing so much: a well written story or novel operates within a very structured environment, and the way language works is has an emergent internal logic and consistency.  Creating something new within that structure, using sound logical principles, is very gratifying.

Happy writing…  or modeling.

Making Models

Another update from Decision Modeling.  I’m really enjoying this class.  Yes, it’s a lot of hard work.  But the professor is really good, and I enjoy the topic.  This week, we started learning about modeling “risk profiles” in your spreadsheets, and adjusting for risk in a way that’s more nuanced and robust than what is normally used. 

See, most B-schools tout the praises of NPV-analysis and business decisions that have the highest EMV – and these are important and useful tools.  But they are, in reality, pretty limited, because they make an assumption that we can afford to lose however much there’s a chance we might lose.  It’s not very robust.  Real people – and real businesses – may not be that tolerant of risk.  Using Risk Profiles and another trick called Risk Utilities allows us to be more nuanced in the way we approach decisions in which risk plays a significant factor.  We also learned a little about how to use a package called @Risk (an Excel add-on) to help with this analysis.

Finally, we learned more about general Excel modeling tips and tricks.  As much as the former part of class was interesting, this was, for me, the best part. You see, I love writing.  Writing is a deep-seated need, for me.  I love drawing.  And though it seems wholly unlike those creative activities, I love making models in Excel.  In part, that’s because I’m a nerd.  But more than that, it’s because I feel like making models in Excel is a creative challenge.   It’s still a creative activity, bounded by logical constraints.  Trying to solve a problem on how to do something in Excel is like trying to solve a puzzle.  When I come up with a creative and elegant solution, it gives me a feeling of pride and pleasure.  Learning more tricks of the trade only better equips me to tackle bigger, more mind-boggling problems.  Put it another way, it’s like playing with Legos, but the Legos are numbers and Excel formulas (FYI, I’m a grown man, and I still love Legos; please send more). 

Sometimes, I just wish I had the guts to ask permission, at work, to be in charge of building the budget and forecast models in Excel, from scratch.  I’ve no doubt I could do it – it would be a long-term project, certainly, but I have the skills.  And I’ve learned enough about good “modeling hygiene” (as the Decision Modeling professor likes to put it) to make it a really robust and flexible and reasonably realistic model.  I can’t say for sure it would be terribly easy for non-excel jocks to use, but my experience building that character sheet for my modified D&D game system I mentioned last week suggests to me I have the ability to make components of the overall model easy for non-gurus to enter information.  Ultimately, though, I realize such a model is really too much for Excel.  I’d want something that works like Excel, but in reality it would have to be a database, and what individual departments would have, rather than an Excel spreadsheet, is some sort of application (that looks and works something like a well-modeled Excel spreadsheet might) that gives them access only to that part of the database that directly concerns what they can control.

My current company is trying to roll-out such a database application, using an Excel add-on that makes Excel act as the front-end of the database, called Hyperion.  We’ve been using it in Finance for the last year, now, and we’ll soon be rolling this out across the company.   The problem is, while Hyperion (with the add-ons to it that we’re using) does the interface and database part that is necessary, it has no inherent business model on the back-end.  Which means that when we enter data into the database, it’s just numbers without meaningful context.  There’s no part of it that says “if I spend money here, then this measurable result will happen here” (the sole exception to this being our Headcount model, and though I helped build parts of that model, I don’t get to be the guy on the team that does the ongoing management of the model).  This lack of a connection between inputs and results means that when we make a decision on one aspect of our business, we have absolutely no basis for understanding what the ramifications of that decision will be on other measurable business metrics, aside from some heuristic models in the heads of various grand high muckity-mucks that may or may not be reflective of reality.

It’s exactly that kind of problem I’m learning to address in my Decision Modeling class.  Now, somehow, I have to convince the grand high muckity-mucks that I’ve got the skills needed to make this thing work and make their jobs easier.  The Decision Modeling prof calls these our ninja-skills and we, the students, are ninjas in training.  I kind of like being a ninja, I just wish I wasn’t so stealthy.

In Which I Learn to Excel

I wrote about some of my trepidation going into my first Decision Modeling class, but after my third session of that class, I have to say my impressions are very positive.  It’s clear there’s a reason this professor is so well-renowned at my university.  Sometimes, a reputation like that is a set-up for a disappointment, but in this case that reputation is well-deserved.

No doubt the course has been challenging, so far.  There’s been a lot of material to read.  And there’s a lot of ground to cover.  But what’s been great, for me, is how much I feel like I’ve learned in just a few short weeks of class.

Going into this class, I was already something of an Excel expert.  I knew most of the tricks and the shortcuts, and I could really hammer out some impressive spreadsheet models, given enough time.  I once redesigned the game system of the 3rd Edition of D&D to make it better fit the story of the novel-in-progress (maybe that little side project was one reason progress on my novel slowed down?) and built a fully customizable spreadsheet model of a character sheet for my revised system that would automatically calculate every detail and crunch every number.  That’s not a unique feat, by any means, but it’s still a tough one.

And yet, by the third class, I’ve learned some impressive new tricks for Excel that I’m sure are really going to help me not only in my current job, but in jobs to come.  And the practice I’m gaining in thinking about problems and how to model them in order to better understand them is really going to improve my ability to perform well in any business capacity.  It’s making me rethink the way I think about problems.

In a funny side-story related to this, I found myself making some notes  on the background of my novel-in-progress, and I was trying to reason through a problem in the background in which something didn’t quite make sense.  I realized, as I was writing these notes, that I was approaching the problem in a very logical, systematic way that reminded me of the way we were learning to approach problems in the modeling class.

Which isn’t to say that I consider Decision Modeling to be an especially useful skill for writers, but I’m glad I’m able to take inspiration from such a peculiar source.  And I do feel confident these are skills that will help my career in general.  I look forward to further classes in this subject.