Tag Archives: teaching

Stop Ignoring Impact Multipliers

I love to play board games, especially in this golden age we’re in. Every once in a while, I learn a new way of thinking from a board game. In this post, I’d like to share one general lesson that I learned from one of my favorite strategic board games, Navegador. This lesson actually succinctly encapsulates key messages from several of my recent blog posts, among other thoughts I’ve had recently.

Navegador is an exploration and economic-themed game designed by Mac Gerdts. Throughout the game, players representing different nobles in Portugal during the Age of Exploration accumulate a combination of five scoring opportunities: sailing to new lands, buying colonies, and building factories, churches, and shipyards back in Lisbon. The scoring varies by player, though: At the end of the game, each of these five achievements score a varying number of points depending on how many of another component called “privilege tokens” that each player has. For instance, factories are worth 2 points plus one additional point for each factor privilege token you have, to a maximum of 5 points. So a player with nine factories and one factory privilege token will score 27 points, while a player with only six factories but all three factory privilege tokens will score 30. The story in the game is that each player is winning influence with the government that will make their factories that much more valuable.

An illustration of Navegador scoring: the five columns represent colonies, factories, exploration, shipyards, and churches, respectively. For instance, this player has two churches (the gray buildings at the bottom), which are each worth 3 + 2 = 5 points. If you want to practice counting their full score, I think they have 89 points shown here (including 2 points for their money).

This scoring system naturally encourages everyone to specialize in one or two of these five tracks, accumulate as many of those along with all three privilege tokens of that type. For instance, we might describe someone as pursuing the “shipyard strategy” if they try to buy as many shipyards as possible and make them as valuable as possible (shipyards score 3 points plus 2 for every shipyard privilege token, maxing out at 9 points each!).

However, when new players play, it can be very easy to simply overlook the privilege tokens. They don’t really help players’ economic engines, and also have a steep price tag of costing a worker (the story is that you’re sending one of your employees to work in the government, where they can make things go even smoother for you). They also are clearly a long-term strategy, so new players can easily get stuck in early game habits that don’t often accumulate privilege tokens. When it comes to the end of the game, they can’t catch up and don’t end up getting the full value for everything they’ve gotten.

How does this lesson generalize? The key is that I’ve realized that many opportunities we have in life have a similar sort of “scoring rule,” where the effectiveness of what we’re doing tends to scale as the product of multiple features. Let’s just take a look at some of my recent blog posts…

Teaching valuable material effectively

Last week, I wrote about an oft-neglected component of teaching: curriculum choice. One could phrase the two components here as teaching valuable material, and teaching it effectively. If the material we are teaching is valuable, but we cannot usefully communicate it, then our effort is wasted. This was probably the strongest criticism of the “Common Core” movement — teachers weren’t properly trained to teach the material, even if it was a more helpful for students. But more frequently, I see the reverse: We’ve become very effective at teaching material that quite possibly will be useless to our students. By focusing only on effective teaching, we ignore the impact multiplier of the choice of curriculum.

As another example, in the same post, I pointed to the analogy of GiveWell, an organization that seeks to evaluate charities for the good they actually do, not just whether dollars donated are going to direct work. Yes, it’s important for an organization to minimize overhead costs, but it’s also important for them to be doing actually useful work to the people they’re trying to serve. If either is zeroed out, their mission fails.

Let’s study algorithms people actually use

I noticed exactly the same pattern in my research options in applied math. So many fields of research try to learn incredible amounts of detail about models that have very little to do with reality. This is the same error: Effectiveness of applied research is proportional to both our ability to answer questions and those questions actually being relevant in practice. It’s difficult to find research where both are promising (it’s taken me nearly five years just to find that intersection!), but it’s important if our research is to be noticeably better than useless.

Who even reads this stuff?

As another recent example on my mind, I have been part of the team putting together the MIT Et Spiritus, a student journal of Christian thought. This week, we were very excited to publish our third issue. We’ve spent the entire semester writing, editing and laying out the journal, poring over everything from the big picture to word choices to captions on the pictures. Naturally, it can be tempting to just relax after finally finishing.

But that would be to miss a crucial impact multiplier: distribution. It’d be completely useless to publish a journal and not get it out to anyone, wasting all of our hard work. And especially with these early issues, without much of a following, we really need to get word out about the journal and establish an audience who will come to us wanting the next issue when it comes out.

Perilous Proselytism

Speaking of Et Spiritus, I had the joy of editing an excellent examination of evangelism by sophomore Ryan Robinett that went by this title (it starts on page 10 in the PDF). In his article, Ryan describes some of his experiences with evangelism, both positive and negative, and how he is still motivated by the beauty of the gospel despite the difficulties. To pick a couple of the best quotes from the piece, Ryan “fears embodying the callousness, arrogance, and intellectual dearth that is stereotypically trademark of evangelism.” But at the same time, he “has had the joy of seeing the gospel catch the wonder and the hope of others.” It’s for this reason that he presses on, while also being completely aware of the pitfalls that come with proselytism.

I think this approach is exactly right. Even if you aren’t a Christian, you’ve probably considered our perspective that absent intervention, our close friends are going to hell. Of course we want to do something!

Yet if we just do anything, we’re ignoring a crucial impact multiplier: What’s actually effective? Even more than that, some of the things we do are actually counterproductive! (You definitely don’t want to be getting more factories if they’re worth negative points!) As David Kinnaman and Gabe Lyons write in unChristian,

In our research with some of the leading “mass evangelism” efforts, we found that often these measures create three to ten times as much negative response as positive. In other words, imagine your church is considering mailing Bibles or videos or other Christian materials to homes in your community. Our research shows that the “collateral damage” of doing so — those whose impressions of your church and of Christianity would be more negative as a result — is significantly greater than the positive impact on those who will respond favorably to those efforts. (unChristian, p69)

Kinnaman and Lyons go on to describe how the vast majority most people who come to faith list relationships as being a key factor, not mass media like radio, television, or tracts.

Where does that put me as a Christian blogger? Do I even have the hope of bringing someone to faith through my posts? These are important questions, and I’m not really done wrestling with them. I have noticed that the more explicitly Christian a post is, the more it seems to only get attention from Christians, which limits my ability to communicate important truths about my faith to those on the outside. Still, I think many Christians and seekers alike struggle with some of the topics I’ve tried to address already (e.g. gay marriage, abortion, miracles, or faith), and I only hope that what I write can help to explain my perspective.

Armchair policy experts

The more I look, the more I see myself sharing the exact same message post after post. Even my post on taking a week off from politics back in March falls into this category. As I reflected back then,

And yet, as I noticed, very little good had come out of all this attention, both mine and others. The levers of democracy in this democratic republic of ours only operate every couple of years. Sure, we could call our representatives, but I live in Massachusetts. Besides, has anyone ever heard of diminishing marginal returns? They’re already getting dozens of faxes a day, let alone letters, e-mails and phone calls.

Despite that, I still spend hours every week reading about politics, trying to stay as informed as possible on whatever the latest Trump scandal is about. But why does this matter if I’m not doing anything about it? Having a precise understanding of all of the Trump associates that have been traced back to Russia doesn’t matter unless it’s somehow going to affect my decisions in the future. It’s not all of our jobs to be millions of little citizen investigators, as tempting it is to want to understand the truth.

I’m definitely part of the problem, but I’ve recently noticed a pattern on some of the discussions that I’ve engaged in on Facebook. My friends and I will frequently debate the fine details about alternative proposals we might bring to solving a few of the most obvious problems with the world, all of this with no actual plan to make any of our ideas come to fruition. In just the last month or two, we’ve collectively written 51 comments debating whether various news reports had sufficient sourcing to be believable, 86 comments on the best way to reduce the miscarriage rate, and a whopping 218 comments on precisely how much people should be compensated for being involuntarily bumped from a flight. Okay, those weren’t the only topics discussed, but you probably get the point.

I don’t necessarily regret these discussions, since they’ve been congenial and fun (and at least have served as good examples of convergent discussion on Facebook in that regard). But speaking to myself probably more than anyone else, I think we might put a bit too much effort into them given the completely zeroed out impact multiplier of actually doing anything with the conclusions we come to.

How to properly weigh various impact multipliers

Another board game I love features one somewhat interesting but unfortunately rarely useful impact multiplier example. In the game of Dominion, duchies always cost $5 and are worth 3 points. Dukes are another card that you sometimes play with; they also costs $5 but give you one point per duchy you have. A natural question arises: if you’re going for a duke-duchy strategy, what order should you buy them in to maximize your points at every step?

This is pretty easy to work out, although the answer isn’t immediately obvious. If you have n duchies and m dukes, your score is mn + 3n, or (m+3)n. That’s the exact same product structure as before! Therefore, you should buy a duke if m+3 < n, i.e. you have at least four more duchies than dukes, and you should buy a duchy if m+3 > n, i.e. you have at most two more duchies than dukes. If m+3 = n, either works. (Of course, in reality, the piles are limited and you might have an idea of when the game will end, so you might want grab that fifth duchy before the first duke, especially if multiple players are going for this strategy.)

In general, let’s say that effectiveness depends on several (positive) multiplicative factors: m_1*m_2*m_3*…*m_k. The effect of increasing m_i by one is equal to the product of the rest of the terms, or in other words, the current effectiveness divided by m_i. That means that the most important factors to improve are those that are currently the weakest, on the scale of plausible changes we could make. Another way of putting this is that we should focus on the percentage improvement we’re making in each of those relevant factors. Of course, this is equivalent; currently low values will be much easier to improve on a percentage basis.

This rule of thumb can actually be somewhat useful in practice, beyond the artificial constructs of board games. In my recent research, I’ve been trying to demonstrate that certain techniques are both theoretically and empirically justifiable — both of which are necessary to be able to say anything new. Depending on how much progress I’ve made in each (and how much I would additionally expect to make in an hour), I try to gauge which of the two objectives I need to work on next, at least without alternating too much.

But beyond that rule of thumb, I hope this post and all of the ones I’ve referenced have inspired you to look for those hidden impact multipliers in your life, especially those which are particularly low at the present.

If You Want to Speak Last, Speak Best

Previously in this leadership series: How Not to Delegate. My examples in this post are typically drawn from Christian leadership, but the message also applies more widely to other instances of collaborative leadership, group discussion, and public speaking.

Four months and seven years ago, I was a high school senior visiting colleges. Out of laziness, I had only applied to three, and was pretty set on attending Caltech. I came to Caltech’s Prefrosh Weekend mostly to solidify that decision and get to know the campus a bit better before I would arrive.

My host’s roommate found out that I was a Christian when I listed that I like to listen to Christian music on the interest sheet which they used to match us with hosts. He told me that he’d recently been attending a Friday night bible study and invited me to come along. Read more of this post