The Callahan prior: How perceptions affect choices

I think a lot about perception. I’ve written about it here before . I talk about it on twitter a lot. The question of perception looms large for me, both in my thinking about how to understand history and my thinking about how to understand hockey.

When it comes to making choices perception is a huge factor. As human beings we create patterns in the world, pulling order out of chaos. We create these patterns by digging to find out the causes of events, and this shapes our perceptions of the people and processes we encounter. Much of this is hidden even to ourselves, even while it’s happening. But these patterns become the framework into which new experiences are integrated, so they’re hugely important in decision-making.

In terms of history, my questions are about how the words we use to explain the world shape (or expose the shape of) the possibilities we see. Perceptions of race, of gender, of class, of education, of religion all shape how we understand citizenship, for instance. Can women be citizens if they are dependent on men? Can freed slaves be citizens if they’re used to dependency?

The perception that African Americans were prone to criminal acts was used repeatedly throughout the eighteenth and nineteenth century to deny both freedom and citizenship to African Americans. This happened despite the fact that the people making these arguments witnessed numerous acts of obedience by slaves on a daily basis. It happened in the face of relatively prosperous black-owned business and not infrequent interaction with respectable freedmen and women.

The wills of slave owners in the United States were replete with bequests to beloved and well-respected slaves, but the perception continued that by their nature, slaves could not be law-abiding or self-sufficient if freed. If you asked a white American adult in 1820 whether black men and women could, as a group, become respectable members of society, you’d overwhelmingly get an answer in the negative, despite the examples to the contrary that they could point to.

It’s a problem of perception. The framework of racial thought at the time didn’t have a hook for the competent, self-disciplined black man or woman, despite constant exposure to such. This framework begged for evidence of criminality among blacks, so every instance of petty theft or violence or drunkenness or licentiousness was added to it, reinforcing the structure and solidifying perceptions.

Yet the knife didn’t cut both ways. Examples of criminal behavior by whites did not lead people to the conclusion that white people as a race were rife with criminality. The details of white criminality were hung on a different framework, one of what we would today call class (with a mixing of ethnicity and religion). This was a framework that had room for the respectable poor, however, and Americans granted citizenship rights to the white poor long before they were willing to contemplate it for even the black middle class.

It has, of course, long been established that we as humans discount those bits of evidence that threaten our established perceptual frameworks. We do this actively, searching out explanations that allow us to maintain our perceptions long after they’ve ceased to be truly functional. The more emotionally involved we are in those perceptions the more we fight for them. In fact, the more emotionally invested we are the more we need our perceptions to be proven right. The proof becomes its own reward.

In Bayesian statistics, these perceptual frameworks are called “priors,” (or “prior probabilities“) and it can take a lot to truly bring down a strongly held prior.

Let’s say, for instance, that you are 95% certain that your boss doesn’t like you. Evidence that this is true will be readily accepted while evidence that it isn’t will be discounted. If you discover that your boss called a co-worker at home just to chat the night before but they’ve never called you, you could easily see that as evidence that your boss socializes with others but ignores you. If you then discover that the call was to plan a surprise party for your birthday, with a 95% prior, it would take a really, really good party to convince you that your boss truly does like you. It might drop it down to 75% (called a posterior probability) or even 50% if there was a bouncy house, but it won’t erase the prior.

If, on the other hand, your prior is weakly held–say you’re concerned that your boss doesn’t like you but not sure, for a prior of about 30%–the birthday party could very well convince you that your boss likes you rather well. The probability might change from “30% sure boss doesn’t like me” to “30% sure boss does like me.” And at this point you start going back over your past interactions with your boss seeing new evidence of favor that you discounted before, shoring up your posterior, which becomes the prior for evaluating new evidence.

This process is a fundamental facet of human nature. It’s not a bad process. But knowing whether you’re coming into a situation with a strongly held prior belief can help you take a second look at evidence. Self-awareness helps us make better decisions.

So what does any of this have to do with hockey? Well perception influences how we evaluate players and the contracts they sign. And they can do so silently. For instance: Beloved captain Martin St. Louis has demanded a trade. Steve Yzerman, as GM for the Lightning has arranged one: Ryan Callahan. Is the trade a good one?

We start out needing this trade to be good. We estimate it rather generously with “I’m pretty sure this will be a good trade.” 60%

We marshal evidence over time:

  • A disgruntled captain is bad for the team.
  • A 29-year-old player is better than a 38-year-old player.
  • They’re both captains, so there’s no step down there.
  • Callahan scores 6 goals to St. Louis’s one.
  • Callahan brings heart.
  • Callahan brings leadership.
  • Callahan is leaves it all out there, plays hard, works hard.
  • Callahan wants to be here.

All of these bits of evidence are added to the framework, each shoring up its little bit of the prior. At the end of it all, the posterior is that the trade was probably good. But there’s more evidence to come:

  • Callahan is re-signed by the team for $5.8M cap hit for six years.

Now we’re all in on this being a good trade, and in the absence of objective evidence that it is, we gather subjective evidence.

  • Leadership matters tangibly and will make a good team better. (a perceptual prior in and of itself.)
  • The salary cap will rise, so this won’t be as bad of a hit in years to come.
  • The GM agrees with me.
  • The coach agrees with me.
  • Other fans agree with me.

With each bit of evidence that sticks to our framework, the perception solidifies, even in the face of evidence to the contrary. Even as we watch the team buy out a different player signed to just such a deal to play just such a role, the strength of our prior perceptions prevents that evidence from moving the needle very much. And we end up with a stronger belief than what we started with.

One of my personal priors is that leadership doesn’t lead directly to results on the ice and that teams should pay more for results on the ice than for good feelings in the locker room. Another one is that leadership is identified in hindsight not in foresight, so it’s impossible to plan for it. I have lots of evidence for these, and they are, by now, fairly strongly held beliefs. That evidence may not convince other people, however. That’s life.

But this does help explain how people can split into camps over things like contracts. Perception matters very much to us as human beings, and we’ll fight for it rather than have to re-establish new understandings of the world every day.