Dota and the science of winning

Dota 2 is a complex game. Myriad factors go into winning a match: hero selection, last hits, item choices, and positioning in team fights are but a few of the variables that can affect the outcome. Thats not even going into the random factors such as runes, crits, and bashes (all hail the RNG gods), and despite thousands of hours and words theory-crafting to find that perfect line up or hero build, no one has found a perfect strategy that beats every other or a build that works every time. There are so many variables at work that creating hard rules about any game play situation seems all but impossible .

But two computer scientists look set to change all that, with the power of maths. In a study titled Extractable Human Knowledge Rules in Complex Time-evolving Environments  Pu Yang and Dr. David L. Roberts have been able to reduce Dota down to its constituent parts and using mathematical manipulation to create sets of rules to show decisive factors in the outcome of a game depending on the types of heroes on the team, the growth rate of state over time, the difference in these stats between the two teams and the point in the game at which these differences occur.

 

Mathemagic

The first step was to figure out which stats should be measured to create a rule set that is universal to every game of Dota. For this study they took five attributes that are important to a team's success regardless of specific hero choices and could be applied to both teams in any given match: gold, strength, agility, intelligence, strength, and damage. After gathering the replays of almost 3,000 games both amateur and professional from GosuGamers, normalising for a consistent game length, they measured stat changes throughout the length of the game, and transformed it to split the game into four quarters of roughly 12 minutes each. By correlating stat differences at each of these points in time with win and loss information Roberts and Yang then created a decision tree which resulted in a series of rules being created.

These rules can be used to analyse the likelihood of victory based on the difference in certain stats and the time at which these differences occur. For example if team A has achieved a damage advantage of more than 59.7 over team B by the second quarter, then team A has a 96% chance of victory. However if team A has this same advantage in the second quarter but team B has an agility advantage greater than 18.1 and a strength advantage of over 27.7 in the third quarter of the game, then team B has a 97% chance of winning. By comparing the two rules, it seems that although damage is an important attribute in the second quarter, any deficits can be overcome by having a strength and agility advantage in the third quarter.

 

 

So what does it all mean?

There are several interesting results hiding amongst all the formulas and science-speak of the study. The above table is shows the percentage of rules that pertain to each column, and how accurate each rule is. As you can see, every rule generated mentions at some point both damage and the second quarter of the game. Which means that damage is by far the most important attribute, which makes sense because if a hero has a huge amount of damage they’ll kill you before you can do much about it. We’ve all been one-hit by a Bounty Hunter with all of the damage at some point, and the sense of powerlessness is palpable. It also means that the game is largely won or lost during the 12-24 minute mark. This is proof of the importance of a team's ability to roam and get kills, at this point the game is roughly the end of the laning phase. It also shows the importance of the role of ganking heroes. As you may have noticed while being stomped by Spirit Breaker in the last few weeks, this 12-24 minute mark is when gankers like him really start to hit their stride. Their ability to dominate this phase of the game and snowball into late game makes them incredibly powerful and I think we’ll start to see them more in the competitive scene in the coming months (more on their importance in the next article, where I’ll look at Robert and Yang’s second Dota study).

Interestingly, there are no rules that mention either gold or the fourth quarter of the match. This isn’t to say that a last minute comeback isn’t possible, but rather it is rare enough that there are no rules that can be stated with any confidence. Nor does it mean that gold isn’t important for winning a game. Of course high rolling with six slots full and a buyback to spare gives you an advantage, but the gold itself isn’t what’s important. It’s the items that you spend it on that matter more.

 

 

That is but a taste of the full results, as they ended up with a total of twenty rules. Unfortunately for now they have only released these two from that study, but these two rules provide a great deal of insight into the important factors between victory and defeat. Bear in mind that this analysis was conducted between 21/06/2010 and 14/02/2012 on the original Warcraft III mod, so the rules generated in this study are probably not as relevant in modern day Dota 2. However it does provide some great food for thought, as well as the means to replicate the results with more up to date data. Make sure to keep an eye out for my next article where I’ll discuss Roberts’ and Yang’s other Dota study: Knowledge Discovery for Characterising Team Success or Failure in (A)RTS Games, which is more interesting than it sounds. These two studies came to my attention thanks to an article on Gamasutra, which also has links to the original studies that you can download and check out for yourself. To keep up to date with everything I write make sure to check me out on twitter , and until next time, happy gaming!