On Minimizing Variance When Ahead

Hey everyone, Konduit here. Today we're hitting an important topic in the realm of execution and risk analysis - minimizing variance when you're ahead. As I've mentioned before, I play card games quite a bit (Hearthstone, and a lot of Magic: The Gathering). Today's topic originates from these kinds of games...

When you're ahead in Hearthstone or MtG, the way you play the game changes. Because you've got a board advantage or card advantage, you have the very distinct luxury of being able to play around a great deal of things your opponent could potentially do. You can take your time, play conservatively, and close the game while avoiding/dealing with many of the potential 'outs' that your opponent could draw to get back into the game. Gradually, the number of ways and opportunities for your opponent to come back dwindles, and you find yourself totally in control of the game flow. By not rushing to close things out too quickly (and having something potentially go wrong), you've increased your odds of winning of the game without giving up too much headway. Recently, it dawned on me that this same play pattern and strategic approach has a great deal of relevance to League of Legends.

Professional MtG player Reid Duke (on the left), taken from Grand Prix Philadelphia in 2014.

Because execution in a teamfight, skirmish, or 1v1 is never something that's absolutely certain (you can be quite confident about it - but ultimately it's an unknown quantity!), you want to minimize the importance of your own execution and avoid the burden of having to play perfectly to win a fight. Now when you're ahead, you've got a great deal of Margin for Error. Your burden of execution is much lower (because of your gold, item, and general combat statistics advantage), so you can take lines of play and create engagements that you wouldn't be able to take if both teams were at parity (tower dives, aggressive pushes) - and still be the favorite in that fight. However, what you have to be careful of (and this is the focus of today's article) is taking engagements that are 50/50, or sometimes even close to 50/50, when you're ahead.

Let's step back for a bit and discuss the mentality and playstyle you should (in general) have when you've got an advantage. The standard textbook, tried-and-true strategy is to make solid rotations, take objectives, and gradually expand your gold lead by taking control of the enemy jungle and map in general. The goal here is to put a 'stranglehold' on the enemy team, not allowing them to make big plays, punish mistakes, and claw their way back into the game. This same line of play applies in lane as well: if you've got a gold lead from a kill, you should try to press that advantage as much as you can, but with the caveat of not giving your opponent a shot at gaining back parity.

As Renekton, it's easy to overextend while bullying your lane opponent. Temper aggression with caution to avoid giving back your lead.

The caveat here is crucial - when ahead, you must balance the desire to press your advantage and get more ahead with the consideration of giving your opponent critical opportunities to get back into the game. This can be very difficult to do, and it's not always possible to avoid those opportunities arising, but in most cases you can do a great deal to minimize variance when you're ahead.

In a nutshell, this principle says "Don't take engagements, fights, or lines of play that have a 50/50, or sometimes even as low as a 60/40 chance to succeed." Let's say you've just won a teamfight, have lost a couple members, but aced the enemy team. Your remaining 3 members go to dragon, but the travel distance gives the other team's members time to respawn and make their way over as well. You could take the 3v4 and still win the fight - your team is ahead, you're fed, and you've got the confidence to likely outplay the other team. However, because of the straightforward numbers disadvantage, the ensuing dragon fight is still a 50/50 endeavor.

If you take the dragon fight and lose, you're giving the other team not only the dragon, but the gold from your deaths (including any shutdown gold), map position, the ability to push out the lanes, etc. This is a major step for the enemy team in bringing the game back to parity, diminishing your gold lead, and gaining some degree of control over the game. On the other hand, by letting your opponents have their (presumably) first dragon, you give them an objective for free...but the other team is still nowhere near as strong as you are, even with the dragon buff. The power differential closes a little bit between the teams, but your opponents are still undeniably behind.

Pick engagements where your mechanical burden of execution is low. Your odds of taking the game skyrocket if most fights meet that criteria!

These kinds of conservative, minor concessions are major components of the principle of minimizing variance when you're ahead. Taking the 3v4 dragon fight in that scenario is a high-variance play. You could win and get even more ahead; however, you have a great deal more to lose in terms of gold differential if you end up on the bad end of the fight. It's in your best interest to concede the objective, avoid the fight, and keep your considerable lead, rather than risking it for a bigger lead - which isn't even necessary to win the game! Bide your time a bit and select an engagement in which you have eliminated most of the unknowns with regards to map position and execution. These kinds of scenarios come up all time, and not just with regards to dragon fights...keep an eye out for them and maneuver the game into a position in which you can easily employ and demonstrate your advantage, rather than fighting the opposing team on unsure footing while you have a gold lead.

That's all for today, I hope you enjoyed the article. If you'd like to discuss anything League, have comments/questions/feedback on this article, or just want to say hi, feel free to tweet me @k0nduit and I'll get back to you.