How to counter Kayn
Let us take a look on how to beat Kayn. We will look at champions who are strong against Kayn and who are weak against Kayn. Use win rate, gold difference and creep score difference at minute 10 to find the best 
Jungle champion who counters Kayn. You can already win in champion select with the right counters for Kayn. If you want to know how to counter Kayn then you need to take into account the best picks vs Kayn and the worst picks vs Kayn. This Kayn counter data is based on matches played by Pros on patch 13.24 and previous ones. It is important to see whether Pros counter picked Kayn or whether they played as Kayn.
Champions used by Pros to counter pick Kayn
Looking at the matches from Pros (see table Pros counter picked Kayn) we can see that they picked 
Lee Sin most often to counter pick Kayn. The matchup Lee Sin vs Kayn occured 43 times. Kayn has 26 wins and 17 losses in this matchup. Learn how to counter pick Lee Sin to get another perspective on the data.
Lane outcome for Kayn
When looking at Kayn counters you will notice that win rates alone are not conclusional. Therefore we provide an overview (see table Lane Outcome) where you can see the lane outcome of Pros who played Kayn. The lane outcome of Kayn consists of three outcomes: Win, Loss or Draw. Let's take a look of Kayn lane and match outcome for specific matchups. Considering the lane outcome and the match outcome of a specific matchup, might enable you to find the right counter for Kayn.
Conclusion
Analyze the available data and learn how to beat Kayn. To master Kayn take also a look on Kayn builds and runes for Kayn. Good luck, Summoner!