In the mad dash back last week to type in the last couple paragraphs I ended up forgetting something that I had wanted to include. Since the local theatre version of Kiss Me, Kate, managed to run right up to the 11:00 hour, I had forgotten my notes about the show which I wanted to include in lessons for a team. Well, I’ll note it this week, but part of my notes are how I almost forgot to do this.
There’s two obvious hooks for this particular musical to show up in quiz bowl. The first is the straight ahead “musicals by Cole Porter” of which this is probably the easy part, depending on which high schools are doing Anything Goes in your area. The other common hook is the “musical adaptations of Shakespeare” angle which this covers reasonably well. But there was a third hook which I noted during the performance, but because I had silenced and stashed my phone, I forgot to write down during the performance.
In the musical, the name of the second female character lead is the non-Superman affiliated Lois Lane. And this was something that kept rattling in my mind as “were I writing a question about this, I’d have to put in something about this, with distinguishing this from the other character with this name.” Because I had stashed the phone, I kept doing that every time I saw the character on stage, and never acted upon the impulse to write it down. So until I sat down tonight and started this, I had the entire week with this flicker in the back of my head of something I was supposed to do but forgot. Normally I do pack a small sheet of paper and a pencil with me at all times, but I forgot for this trip out. If I had managed to do this, I would have saved myself a lot of irritation this week.
“Name’s the same” questions are quite common in quiz bowl, but moreso in circuit competitions, because you need the space to describe both instances of the name. It is a very flexible construction, allowing you to bridge categories, or even construct entire bonus questions on the concept. As a coach, you need to teach your players to be aware of the construction, and how it can be used, and confused, or even in the hands of an inexperienced writer, combined. One of my earliest packets ended up sliding credit for “A Traveler in War-Time”, an account of an American author in Europe during WWI, to his more famous namesake, an author who won the Nobel in Literature, but was more known as a British Prime Minister. This was cleaned up on edit, before it was read, but it was quite embarrassing to me. And yes, your team needs to know there’s more than one Winston Churchill.
The good news about musicals is that theatre kids overlap significantly with quiz bowl kids, so it’s unlikely you’ll have to do any study sheets for this category for high school. In fact, it’s probably the rare subcategory that skews easier for high school than the writer and editor expect. But that also means that your theatre kids are going to be local experts in this category. You will want to make sure that before they graduate, they are passing that information on to the younger members of your team, and those that don’t have experience with the category. Whether that is achieved by your local experts writing their own questions or study guides for the team, or through pointing out things for those that come after them to watch, you want to make sure the knowledge they have is not lost when they leave the team.
[Not sure if I’m happy with how this turned out. There’s a point in here about pyramidality happening as a natural consequence of the process of writing and reading, but it’s probably too academic for the new book.]
I was reading a thread about the length of questions and as it is wont to do, it morphed somewhere in the middle into a critique of how questions seem to violate pyramidality when the length gets too short. In here, I saw the word that baffled me for a minute, until I realized the implication of what the use of that word meant for their view of the process of question answering. And with that I had a small revelation that people don’t see all the things I’ve seen, and so I should explain the problem here.
The word chosen to describe the process providing clues to answer questions was ‘stochastic’, and while I think they got the context right in not choosing to use the word ‘random’, I felt like they were missing some points about how one could be even random in choosing clues, and still manage to end up with a pyramidal result. Stochastic is defined as:
of or relating to a process involving a randomly determined sequence of observations each of which is considered as a sample of one element from a probability distribution.
and it is this sequence that is where I found a problem. It gives to my mind the false impression of a set of clues that while relating to the answer, are not considered in any sort of relation with each other. That is there’s a certain probability that a player will answer correctly given each individual clue. While that may be appropriate for someone who is a new player, or inexperienced, or has little memory of previous questions, once a player realizes that clues can eliminate possibilities, and build on previous clues to reach an answer, it’s no longer an appropriate model for how questions will be answered. Rather than considering a probability distribution function running the length of the function, we should consider the cumulative distribution function running the length of the question.
A Cumulative Distribution Function (CDF) is what you get if you sum a Probability Distribution Function (PDF) from one end. Essentially it’s the integral from negative infinity to x of PDF(x). If we model it assuming the question’s probability of a correct answer is zero prior to any part of the question being asked, it’s the integral of the PDF from 0 to t where t is the amount of the question already asked. Each clue then adds a probability that it will be answered, and the sum of those probabilities indicates the probability that the question has been answered correctly. That should be an increasing probability throughout the question, which is what pyramidality should predict.
The reason these are not perfectly analogous is because as a question is read, the clues in a question are not independent events affecting probability. Each previous clue affects the probability of a subsequent clue causing a correct answer to be given, both in reducing the answers that could be the correct one, changing subsequent clues’ effectiveness, and in causing answers to be given, which changes who is eligible to answer, and what answers they could give.
It’s an imperfect analogy, if every player was listening to every clue, and keeping all of that information in their front brain, considering each clue consciously, and reacting to clues, instantaneously, that situation would resemble a cumulative distribution function. The fact that all of those factors are never exercised simultaneously keeps it from being an easily considered perfect state, but even without those conditions, it more resembles a CDF than a simple PDF.
Now there is a slightly stochastic problem where the sequence of clues would affect in which order it could be answered among a group of people: For instance if a question about a city like Vienna covered the arts, the geography, and the historical events of the city in that order, it would benefit an arts player over a history player, but were it written in the reverse order of clues it would reverse the benefit. The thing is that both patterns would be pyramidal. (An interesting question for research would be "do writers tend to approach multidisciplinary questions in a particular order of disciplines, similar to how English speakers order classes of adjectives to describe an object?" If this were true, there would be an exploitable advantage in studying one subject’s clues over another.)
The problem with considering the rules of pyramidal questions as applied to a cumulative distribution function is that it becomes trivial to achieve pyramidality with that framework. The only requirement to satisfy pyramidal structure is that you add no clue such that there is no possible person who would use that clue to answer who had not already answered based on a previous clue or clue(s). [as an example: a clue that someone is a Marylander, having already mentioned they lived in Baltimore.] And even clues like that, which restate a premise, are barely seen as clues at all, or restatements of previous clues.
Pyramidality is a powerful organizing principle of question writing, but we run afoul of its effects when we miss that it has elements of being a self-organizing principle of writing. Where we assume it’s a mark of higher sophistication in writing, we miss that it can result from the simple act of reading clues orally in sequence. Understanding it in terms of a CDF instead of a PDF brings us closer to seeing how it can happen as a natural consequence.