Probability Theory and Vivegam
Vivegam is an another flick from the well-known director Siva — Ajith combo which was released a month ago. People who saw the movie were awestruck by the stunt scenes and they just can’t keep quiet without talking about it in their social media circles. It was not because of the way it was portrayed but because of the probability of it happening in real life. All the arguments around the topic had one thing missing in common, a number. Everyone who claimed that these stunts were highly unlikely to ever happen in real life, never said how unlikely it was. This blog is an attempt to quantify that probability.
There are several instances of stunts in the movie for which probability can be computed. There is a scene where Ajith shoots exactly at the same place on the bulletproof window of a moving car six-times consecutively. Then there is that scene where he protects his wife from thugs being a sniper sitting in a faraway place. He even manages to sign his initials AK on the walls using the bullets from the sniper and finally there is this introduction damn .. oops dam scene which is very much spoken about. In the interest of time and interest of faint-hearted people who might end up finding this blog lets pick only one scene and measure its likelihood of occurring.
So there was a scene where AK, the protagonist was stranded on the top of the dam and gets surrounded by heavily armed gunmen and 5 choppers. When everyone in the audience was on the edge of the seat wondering what he would do next, he jumps off from the dam and during his journey towards the bottom of the dam he manages to fire few times in which two bullets pierce the heads on the gunmen standing above and one pierce the helicopter, causing it to burst off. The gunmen also were trying their luck to kill AK shooting from above but luckily, as you know bullets are an intelligent creation of God and they know whom to hit and whom not to. Finally, AK escapes with a minor damage to his right shoe.
I saw the scene more than once so that I could actually note down few numbers that will help me calculate the probability score. Let’s now rephrase the same scene using some math and physics. The time difference in the shots between AK jumping off the edge and splashing into the water was 34 seconds.
So if he was actually airborne for 34 seconds he should have covered a distance of 5.6 km falling down but unfortunately, the worlds tallest dam is only 305 meters high. A person falling down from a distance of 305m will be in air only for a period of around 8 seconds.
Okay, let’s consider that the free fall time only 8 seconds and it was the different perspectives to the scene and few slow-motion shots which made it 34 seconds long. This perfectly makes sense. But let’s not forget the fact that within that time span of 8 seconds AK has managed to pull the guns from his pants and managed to kill two other gunmen and blast off a chopper.
This is something many heroes do. There are Vishals who can fly cars and Vijays who can fly cycles. With all this given it would not be fair to calculate the probability from the hero’s perspective as all heroes are superhuman by default. But there were armed people who were spraying bullets all over when AK was air bound. Considering they were sane people who were recruited as a task force personnel let’s calculate how insane it is for them to miss a target.
There are around 50 people in this Image that I picked up from Google. But When he falls down there were only around 24 of them(yes, I did count) firing bullets at him. Think others were trying to translate and understand what AK uttered before jumping.
Let’s say 3 seconds were lost in these gunmen reach the edge and actually start firing. That leaves us with remaining 5 seconds.
Total Fall time = 8 Seconds.
Time lost in reaching edge = 3 Seconds.
From the looks of it, the gunmen were carrying something like a Machine gun. After a bit of googling found that modern semi-automatic rifle can fire at the rate of 25 rounds per 2.5 seconds. Thanks to Quora. Let’s consider these people were using modern international weapons as the makers were claiming that this movie matches international standards. So with 5 seconds left each armed men can fire 50 rounds each.
A little more bit of googling got me here. This website has stats that talks about the probability of hitting a target from different distances based on historic military data. From the website for a person with a PK series machine gun chances of hitting a moving man-sized target with 6–9 round burst in the distance of 300m roughly will be around 50%.
Here the stats is on 6–9 round burst but in our case, each armed men can fire 50 rounds of bullets. So as it stands for a person with 50 rounds at his disposal is at least twice likely to hit a target as 6–9 rounds gun. So let’s summarise all the facts together:
Probability of hitting target from distance of 300m – 0.5
Probability of missing target from distance of 300m = 0.5 (1–0.5)
Probability of missing in our case = 0.25 ( twice the probability of missing with 6–9 round- 0.5*0.5)
The probability of all the 24 gunmen missing the target = 0.25^24( raised to the power24) which is 3.552713679E-15. Which gives us the odds of 2814749766948.5005 or 0.28 * 10¹³
In other words, there are chances of this happening is once in two trillion, eight hundred fourteen billion, seven hundred forty-nine million, seven hundred sixty-six thousand, nine hundred forty-eight times.
Was just curious to know what was the least probable event that was ever recorded. Seems like there were a couple from Belmont US who won two different lottery jackpots in a single day with odds of 24 trillion to one. It is surprising to see there are actually few people in this world who are luckier than Director Siva’s protagonist. But still, this is a very unlikely event to happen and remember we are talking about only one such event in the movie.
A hero might be superhuman but that does not make the people firing at him or the people watching the movie dumb ducks. Even this blog is not perfect but at least I tried to fact check from one or two sources before writing which hardly took me some time. I feel any content that is presented to the large public in a theatre should have some sort of logic behind it. Forget logic, but I strongly feel there has to be at least some level of sanity when stunt sequences get choreographed.
looks like Ajith and Siva are going to come together for a project again. The story is rumoured to be set in space. At least in the next flick, it would be great if director Siva could allocate some space for simple math and probability.
