A look at the randomness of best-of-ones

While the randomness of best-of-ones has been a popular topic among the community for a couple of years now, especially once the growth of social media allowed players to chime in on the topic as well, this weekend’s MLG Columbus qualifier has made the topic more timely than it has been for a while. In this article I set out to look at just how random best-of-ones are, and what can be done to improve a format that is getting criticized by just about everyone following these events.

How random are best-of-ones?

Mathematically speaking, the odds of a team beating another team can be directly applied to determine how often, per hundred times, team A should beat team B in a best-of-one. For example, if a team is good enough to have a 60 percent chance to win, it should win twenty more times, if they were to play a hundred games, than the weaker team – whose odds are 1-60 percent = 40 percent.

As the players and fans often suggest this randomness is fixed by introducing best-of-three series, meaning a team needs to win two maps to be win, we should take a look at the math then. In a best-of-three, that team with a 60 percent chance to win, will come out on top 64.8 percent of the time. In other words, prolonging the game by up to two maps only improves the better team’s chances by less than 5 percent.

If we were to add potentially two more games and extend the series to a best-of-five, we should see a large improvement – correct? Well, not quite. Using the same 60/40 odds, the better team will now win 68.3 percent of the time – more than 60 percent, but still not that large of a difference. In fact, the difference in the probabilities between one and five maps is smaller than the original difference between the two teams!

To draw a few more comparisons, at 50 percent vs. 50 percent, the odds are naturally always that. At 70 percent vs. 30 percent they are 78.4 percent vs. 21.6 percent in a best-of-three, and 83.7 percent vs. 16.3 percent in a best-of-five. Further, at 80 percent vs. 20 percent the odds jump to 89.6 percent vs. 10.4 percent in a best-of-three, and 94.2 percent vs. 5.8 percent in a best-of-five.

Clearly the upsets become rarer, but not nearly by as much as you would think. Perhaps the difference is somewhere else?

What causes the apparent randomness of best-of-ones?

Before we get to the real issue, we should point out one thing that clearly makes best-of-ones harder to play for some teams: there is significantly more pressure when you know you cannot afford to lose. In a best-of-three, you have a safety cushion until you are facing elimination. In a best-of-one that does not exist. As a result, the players who are prone to playing worse under pressure – or choking – will suffer more from the one map format than the ones whose play does not change.

So, unlike the added maps, what will instantly change the odds significantly in almost any given match is the map changing. In fact, when you are comparing two teams that are roughly equal, the difference often is in the map. In a seven-map pool where both teams remove two, it is possible – if not probable – that each team has a map they would be favored on, and there is one map that remains more even between the two. Well then, is not the real problem of best-of-ones Valve’s random map draw?

The cobblestone generator all but gifted Ninjas in Pyjamas ESL One Cologne 2014. It is impossible to say how many group stage matches and playoff series would have gone differently if the random draw hit one of the other 33.3 percent chances. Impossible to say how many stories could have changed or careers altered. But it seems obvious, and impossible to argue against, that the random map draw has changed the course of matches and series in the past at the majors.

Valve’s random map draw came as a response to the community at large complaining about certain maps never being played, with notably inferno being incredibly popular at the time. It certainly forced teams to practice more maps, and in that sense accomplished what it set out to. But are you ready to hurt the game’s competitive integrity by introducing a new random factor, merely so that you would see different maps being played more often?

Teams should come ready to play all seven maps. If not seven, then at least six – because they are allowed to veto one. They are professional gamers, mostly full-time at that, and they are getting paid hundreds of thousands of dollars to be good at all the maps tournament organizers throw at them. Or so the casual observer, who is bored of seeing the five maps that are “completely outplayed” and where “nothing new ever happens,” would have you believe.

In reality a seven-map pool is already pushing it, and there is little doubt the level of play would be higher if all teams only needed to practice five. Why are we letting Valve’s random draw control results then? How is it not painfully obvious to everyone – and more talked about – that the best-of-one format is not nearly as big of a problem as the random map draw?

More randomness that could be eliminated

In addition to the above, there are a couple of other features in current tournaments that add randomness to the results, and could – likely even should – be eliminated. First of all, we need to let go of this system where groups are drawn based on seeding pools. It allows no one to be held responsible for seedings, and technically is fair – chance always is. But why would we not prefer having tournaments speak to select experts to seed teams as accurately as possible, given certain criteria?

Consider this: MLG Columbus could have a group consisting of Fnatic, EnVyUs, G2 and Cloud9, and a second one with Splyce, Vexed, NiP and FaZe. Last time around there were no major upsets in the group stage, but you can still have two contenders and two teams capable of upsets against anyone, and a group with zero teams favored to make the top four, and two that are not even close to being top ten in the world. Why do we accept this kind of randomness?

If we were to poll a number of experts and have them seed the teams, even in groups of 1-8 and 9-16, you would never have groups that are as unbalanced as those outlined above. That already tells you that the system needs to change. You can never make perfect groups – and there will always be criticism. It can even be easier to have fans blame a lottery machine than actual human beings. But the people can also hide anonymously, and that does not have to be an issue.

Conclusions

There is no doubt best-of-threes and best-of-fives are less random than a best-of-one. In addition, a round robin group stage with a minimum of five matches – as is the one at next week’s IEM Katowice – is likely less random than a two-and-out GSL group stage. In an ideal world we would have best-of-three groups, preferably larger ones that allowed teams to play more than a minimum of two games. That, by the way, can be accomplished by events hosting two streams, and playing two games at once. But even in the case of best-of-ones, we can improve other aspects to tackle the main issue.

We should have proper seedings leading up to the tournament, thus giving us more even groups. If the groups are even, it is less likely that you will get situations where a strong team gets knocked out in one group, while a weaker team advances in another. In addition, it would actually reward teams based on their past performance, as opposed to allowing lottery machines potentially define players’ careers. Sounds ridiculous, but there have been cases a team barely made playoffs, only to win it all later on.

Finally – and this is the big one – we absolutely need to get rid of the random map draw. In best-of-one games, this means allowing both teams to veto three maps in a seven map pool, and playing the final remaining map. In best-of-threes you can pick maps after one round of vetos – to increase variance in the actual maps that end up being played – but there has to be a second round, as opposed to the random draw determining the deciding map out of three remaining ones.

There is no perfect system, and budget constraints (time, space at the venue, streams, actual money…) will always be a factor. But this article has – hopefully – shown that playing one map alone is not significantly more random, mathematically, than a series of three maps. Random map draw makes a much larger difference and luckily is incredibly easy to solve – all it takes is a very minor decision on Valve’s part, and the issue is gone.

I do not mind the added pressure. In fact, I enjoy it. I am okay with teams losing, despite having had better results, because they could not play up to their usual level because there is so much on the line. That is partly what makes sports fun to watch, and the pressure is even worse at the major itself.”

But we must also remember this – and I am quoting Fnatic’s old player, Harley “dsn” Orwall here – Counter-Strike is a fair game. The better team usually wins. Cloud9 might be worse than Dignitas, and Splyce than Counter Logic Gaming. But those teams were better in their matches this weekend.

Cover photo by Patrick Strack/ESL, eslgaming.com

Former professional Counter-Strike player whose team was ranked the world's best in 2007, and who led Evil Geniuses for two years. Since retiring, he has been an active member of the media.

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