To the world, gymnast Dipa Karmakar's decision to go with the life-threatening Produnova vault during the preliminaries and then the final of the women's vault event was an act of indomitable courage. It won her fans round the world, and not just in India.

However, that's not all there was to it. The choice of the Produnova was in fact a daring act of strategy Karmakar employed with a view to vaulting into the medal bracket. It was deployed after careful calculation of the strengths of her competitors and the best way in which she could hope to outscore them.

After all, no one was going to try what she was about to. As eventual champion Simone Biles put it when asked whether she'd attempt the Produnova: "I'm not trying to die."

As things turned out, it almost worked.

### The mathematics of the Produnova

Consider the final result. Karmakar's tally was 15.066. Or, 0.9 points short of gold medal winner Simone Biles's 15.966; 0.187 points short of silver medallist Maria Peseka's 15.253; and a mere 0.15 points short of bronze medal winner Giulia Steingruber's 15.216.

Karmakar knew only too well that her competitors, having trained with the best infrastructure, support and technique, would most likely outscore her on execution. So, her road to a medal had to be through a jump with a high degree of difficulty.

The way the scoring works, the degree of difficulty of a jump is added to the execution score, and penalties deducted, if any, to arrive at the final score. A participant has to perform two different jumps – Karmakar couldn't have repeated the Produnova – and the average of the two scores is the one used for the medal rankings.

So, knowing that she might lag behind on execution, Karmakar chose the jump with the highest degree of difficulty: 7. How much of an edge did this bring her? Well, because her first jump was much easier, with a degree of difficulty of 6, her average from this aspect of the scoring was 6.5 – compared to Biles's and Paseka's 6.35, and Steingruber's 6. In other words, if Karmakar could match them on execution, she would have an advantage of 0.15 points and 0.5 points, respectively.

And that would have at least won her a bronze.

Obviously, the Produnova is much tougher to execute. In the event, Karmakar ended up with execution scores of 8.866 on the easier jump – the Tsukahara 720, a half-turn off the springboard on to the vault table, and then a push backwards stretched with a 2/1 turn – and of 8.266 on the tougher Produnova. And these turned out not to be good enough to bridge the gap with the leaders.

But Karmakar's thinking was clear. And she'll be back.

Yelena Produnova was a Russian gymnast who retired in 2000 after the Sydney Olympics, where she finished with silver and a bronze medal. She was 19 when she first tried the Produnova and by time she retired, it became one of the most difficult vaults in the world.

The Produnova requires a gymnast to run up to the vault and first execute a handspring, which tosses her up into the air. Then, she has to perform two somersaults while up there, and land on her feet. Because the chances of landing on one's neck or head are high with this jump, it's widely considered a life-threatening one.