What Does Braveheart Have To Do With an Upcoming Workshop in Stirling, Scotland: July 1-4th? Everything
I was born in 1975 which means that on May 24th, 1995, I was 19 years old. Why is that date relevant? Because that is the day the greatest movie of the story of Scottish independence ever made was released in America — Braveheart. Therefore it goes without saying seeing as how I am a a white American male drawn randomly from the Generation X distribution, this is one of my favorite movies of all time. So imagine to my chagrin when over time I started to hear dissenters telling me that it was grossly inaccurate.
Why am I bringing this up? Because I am wanting to share with you that from Monday July 1st to Thursday July 4th, I am going to be leading a four day workshop on causal inference at the University of Stirling in Scotland for the Scottish Graduate Programme in Economics in Stigling itself. The course will cover the following:
Foundations of causal inference: potential outcomes, treatment effects, selection bias and randomization
Unconfoundedness: directed acyclic graphs (DAGs), matching, reweighting, propensity scores and regression adjustment
Regression discontinuity design
Instrumental variables
Now maybe you’re still confused and thinking to yourself, “Scott this doesn’t make sense. What does Braveheart have to do with this causal inference workshop you’re doing other than the fact that you love Braveheart and you’re teaching the workshop?” I thought you might say that. So bear with me while I try to explain how all of this fits together.1
The Apocryphal Battle of Stirling Bridge in Braveheart
In Braveheart, the Battle of Stirling Bridge is an extended sequence in which William Wallace rallied an outnumbered Scots with a rousing speech about Scotland. It displays the tension within Scotland (inequality) as well as across Scotland (multiple clans). It also has William Wallace in war paint. You may remember it because it was where the British calvary race directly across an open field, with a bridge nowhere in sight despite the name of the battle, only to be completely slaughtered when Wallace and his men surprise them with tree length spikes that impale the riders and their horses almost instantly. It also has the old man getting his hand cut off right before killing his attacker, tons of brutal close quarters combat, and doing what Mel Gibson tells me no one had ever done before which was defeat an English army in open battle. In case you needed a reason to watch them kill all those English soldiers with those spikes in a surprise attack, I’m attaching a 2 and a half minute short YouTube link here.
What Really Happened at the Battle of Stirling Bridge
On September 11, 1297, the forces of Andrew Moray and William Wallace faced the combined English forces of John de Warenne, 6th Earl of Surrey, and Hugh de Cressingham near Stirling, on the River Forth. Perhaps one thing that happened that Braveheart left out is that the reason it is called the Battle of Stirling Bridge is because it literally happened on the Stirling Bridge, which gave Wallace and his soldiers an advantage because as the English began to cross the bridge, a bottleneck happened and Wallace and Moray’s forces just devastated the English. The English couldn’t deploy their armies, they were routed, they were forced into the river, and then I think the Scots drowned them and chopped them up.
But some might say that’s karma coming to get you because when you invoke the medieval practice of “Prima Nocta”, an institution that was both widely practiced and legally sanctioned and apparently completely fictional also, well — you may just have to find yourself being simultaneously stabbed with a giant stake while you ride your horse across an open field only to fall from a bridge and drown.
What Mel Gibson Got Right
Moving along, I asked Cosmos to tell me what Mel Gibson in Braveheart. Here’s what he said.
William Wallace as a fierce and charismatic leader.
The Scots were significantly outnumbered but used strategic ingenuity to win.
And that was all he said.
What Mel Gibson Got Wrong
So then I said tell me what he got wrong.
The setting: The real battle centered around a strategic choke point at Stirling Bridge, not an open field.
The tactics: The Scots used the bridge to their advantage, a clever ploy absent in the movie’s depiction.
Historical accuracy: No blue face paints, and the armor and weaponry were not quite as Hollywood depicted.
Well shoot. That kind of stinks. I would’ve liked to seen that Director’s Cut of William Wallace and his boys killing soldiers at a bottleneck on a bridge like the 300 Spartans fighting the vastly larger Persian army led by King Xerxes depicted so wonderfully in Zach Snyder’s historically accurate adaptation of Frank Miller’s comic book 300. [Cosmos: Scott, 300 is also historically inaccurate].
Scoring the Battle’s Accuracy
Nevertheless, I am undeterred, so I asked Cosmos to rate Braveheart on two scores of accuracy: (1) historical accuracy and (2) awesome accuracy. Then I asked him to present a compelling argument for why we should believe the Braveheart version of events despite the low historical score that I knew was coming. Here’s what he said.
Historical Accuracy: 3/10. Braveheart captures the spirit of rebellion and Wallace’s leadership, but the details are largely dramatized or fictionalized.
Awesome Accuracy: 9/10. Despite its historical liberties, Braveheart delivers an unforgettable cinematic experience, full of drama and excitement.
Cosmos: “When you think about it, since none of us were actually there, maybe Wallace did wear blue face paint just to mess with the historians.”
Why It Matters: Braveheart and Causal Inference
But putting all that aside, let’s be serious for a minute. What possibly could the apocryphal film Braveheart have to do with causal inference? I asked Cosmos to help me with this part too.
Potential Outcomes: Throughout the movie, we hear stories that the Scots have heard tall tales about who William Wallace is, including that he is 7 feet tall. Perhaps, just perhaps, Mel Gibson’s story is the counterfactual history, which is consistent with Gibson’s own messaging in the movie that there are many stories about William Wallace. This is my favorite.
Selection Bias: Remember selection bias can be represented as this:
\(E[Y0|D=1] \neq E[Y0|D=0]\)IOW, it's when expected potential outcomes differ on average but for the same untreated potential outcome. What's the untreated potential outcome here? Maybe it's a world without Scottish independence and the ensuing inequality that would exist in absence of that? Cosmos said something else that didn’t make sense (no offense Cosmos), so I’m going with that one.
Treatment Effects: The Scots’ strategic use of the bridge can be seen as the “treatment” that led to their victory. Me to Cosmos, “Or maybe those giant spikes were the treatment too, right Cosmos?” Cosmos to me, “Sure that can be the treatment too, Scott.”
Independence: In estimating average treatment effects, randomization means that some treatment is assigned independent of potential outcomes, which causes:
\(E[Y0|D=1]=E[Y0|D=0]\)When choices are made “independent of potential outcomes”, it means that choices are made without regard to particular returns on those choices. In Imbens (2004) review of unconfoundedness, he notes that sometimes forms of this can hold because while economic actors may make decisions for one reason (i.e., to maximize utility), that can be a different objective than what the research wishes to know (i.e., effect of schooling on marriage outcomes). So let’s just contrast Wallace’s choices and his motivations with that of the clan leaders. The clan leaders make choices based on material gains (i.e., Y1-Y0>0). Wallace makes his decisions independent of those because he is driven by the memory of his wife who was murdered in cold blood all because he would not comply with Prima Nocta!
Unconfoundedness: The Scots’ victory wasn’t due to random luck but strategic planning, similar to how unconfoundedness requires that treatment assignment is independent of potential outcomes given observed covariates. (Cosmos, I think this one is barely working but since I came up with the last two, I’m going to leave this one - sc).
Matching and Reweighting: The Scots had to “match” their strategy to the battlefield to ensure they could “reweight” their smaller numbers to overcome the English. (Hate to throw Cosmos under the bus but he came up with that one not me —sc)
Instrumental Variables: An instrument is a variable that determines the treatment but is both independent of unobserved confounders and cannot directly cause the outcome. This one is tough, but that’s because finding good instruments is always tough. But Cosmos and I talked about it, and here’s what he came up with. “Cosmos: One possibility is the betrayal by the Scottish nobles. Their political maneuvering and betrayal can be seen as an external factor that influenced Wallace’s strategies and alliances (treatment) but did not directly determine the outcome of the battles (the military victory).” Gotta think about that a little. Not sure I buy the exclusion restriction but I’m going to mull it over.
Regression Discontinuity: The narrow bridge created a “discontinuity” that the Scots exploited, similar to how an RDD design exploits a threshold to identify causal effects. (Ooh. Wish I knew any military strategy or military history to even have a clue if this is right, Cosmos —sc).
The Cunningham Clan
Finally, one more thing. The Cunningham clan supported Robert the Bruce in the fight for Scottish independence, and so my story is intertwined with the broader story of Scotland’s own struggle for freedom, which means in a way, Braveheart is also telling my story.
In conclusion, I think we can all agree that you should come to this workshop. Here’s where you sign up! See you there soon!
HT to ChatGPT-4o (“Cosmos”) without whom the entire following section could not have been written.
I was so sad when I learned that the name ‘braveheart’ probably refers to To Robert the Bruce, not William Wallace.
Movie is still awesome though. Awesomely accurate.