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# Simulating Nazem Kadri's 2015-16 season

What can simulating Kadri's goalscoring drought to start the year tell us about the probability of such an event occurring.

It’s undeniable that Nazem Kadri is a talented hockey player. His elusiveness with the puck and his offensive awareness are standout traits even at the NHL level. If you just watched the games, and didn’t look at the numbers, you would perhaps even consider Kadri to be the Leafs best player so far in this young season. His point totals, however, tell a different story.

As we all know by now, Kadri is mired in a rather remarkable point-scoring slump to start the season. We also suspect that this is likely a mirage since an absurdly low percentage of his shots are turning into goals. I typically consider it to be a rather lazy analysis to simply look at a players’ shooting percentage and call for regression one way or another. However, when a bonafide NHL player is shooting 2.3% on the year, there’s likely something to it.

What I want to explore is the likelihood of a player like Kadri experiencing a drought of this severity. Including this year, Kadri is an 11.1% shooter for his career – above the average rate for an NHL forward. Based on a binomial distribution from his scoring rate to date, the probability of him scoring two goals from 87 shots is about 0.21%. Obviously, that’s quite low. Not exactly shocking news there.

This season, Kadri is on pace for 324 shots on net – a remarkable total for any NHL player. We can divide a 324-shot sample into 238 distinct groups of 87 consecutive shots.

I was curious about how likely it is to have any 87 shot sequence with at most two goals appear in those distinct collections, so I wrote an R script to model it. My initial goal was to calculate exact probabilities, though since these sequences aren’t independent of one another, it is a somewhat tedious effort.

The script simulates 10,000 ‘seasons’ worth of shots, each consisting of 324 independent shots, with the probability that the shot results in a goal of 11.1%. Based on the output of the script, we expect roughly 5% of Kadri’s seasons would include at least one sequence where he scores at most one goal from 72 shots. To put that into perspective, if Kadri played 20 years in the NHL (with the same shot rate and shooting percentage), we could expect a two-for-87 shooting streak to happen in one season during his career. Exploring this further, the proportion of 87 shot sequences that have at most one goal scored in them is roughly 0.5% (which is on the same order of magnitude as being struck by lightning in a lifetime).

The numbers we’re seeing here are, if anything, a reassurance. A reassurance that the top center on the Maple Leafs, and hopefully a big part of their future, is just as promising a player as he has been at any point in his career. And while the chances of experiencing this sort of goal scoring drought are obviously small, having this occur at some point during a season or career isn’t at all unheard of.

Kadri is simply part of an unlucky 5% of seasons (where the player in question has his production metrics) where this sort of drought can happen, all due to the randomness of this sport. He’s even more unfortunate than the average member of this club, since his cold spell is coming at the start of the season, where it’s easy to identify and easy for a narrative to take over.

I've included a link to my script, so you can replicate my results (if you have R): Link