People like to talk about which Control map format they like more, Best of 3 or Best of 5. And most of those arguments go the direction of “Bo3s are over before they began” or “Bo5s give a team the chance to reverse sweep their opponent which can add excitement to the series”. What I will do in this article is not argue on such a subjective basis, but I will use numbers to outline why Bo5s actually award random advantages and disadvantages to the competing teams.

I will mainly show this by talking about two hypothetical scenarios, one that is very extreme and one that’s closer to something that can occur in reality. *I actually thought about writing this piece more than half a year ago, but I thought it was way too obvious for anyone not to notice, so I am pretty surprised no one wrote up something like this thus far.*

**EDIT**: The author made a mistake at calculating the correct chances to win the whole map. Instead of just adding and dividing the cumulative percentages you need to calculate the sum of Bernoulli distributions.

This mistake does not alter the point of this article it actually even enhances it’s strength, because most percentages are actually more extreme than in those pictures. *The correct percentages (if they are different from the original) are stated in the caption below the corresponding picture.*

## Scenario 1: The Extreme

In both scenarios we will take a look at the match of our hypothetical teams “Team A” and “Team B”. The Control map we look at has three sub-maps which are called “Map 1”, “Map 2” and “Map 3”. For this first scenario we assume that Team A has a 90% chance to win Map 1, Map 2 is a 50-50 map and Team B has a 90% chance to win Map 3.

As one can easily conclude, both have the same chance to win a Bo3, 50%. Here it also doesn’t matter if the map would end after 2 sub-maps or all three are played and it is not important in which order the sub-maps are played, the overall Chance to win the map stays the same.

The Chance to win the map can be calculated by **dividing a teams’ cumulative percentage by the sum of both cumulative percentages**. So, in this case to get the chance of Team A to win the map you do the following: (150/(150 + 150)) = 50% (**EDIT**: This calculation is incorrect, if you want to see how to calculate the chance to win the fight correctly, read the “Edit” above. In this case the result is still 50%).

Now lets get to the part that’s random. To get the teams’ chances to win a Bo5 it again does not matter if all 5 sub-maps are actually played, but we still need to take all 5 potential sub-maps into account. The difference to Bo3s is that there are three different possibilities for what the 5 maps are in a Bo5. Either you don’t play Map 1 twice, you don’t play Map 2 twice or you don’t play Map 3 twice.

When taking a look at the chances to win the map we will see that Team B suddenly has a higher chance to win the whole thing, because Team A’s favourite sub-map is only played once. *Again, it does not matter whether all 5 sub-maps would actually be played if this match was to occur, the overall chance to win this map (for this specific scenario: “Map 1 is not played twice”) is always the same, no matter if the actual result is 3-0 or 2-3.* If you are still uncertain on how to calculate the chance to win the map, you do it like this for the “Bo5 (1)” for Team B: (290/(210+290)) = 58% (**EDIT**: The actual percentage is 68.2%).

I also want to stress again that it does not matter in which order the sub-maps are played, it merely matters *which* sub-maps are played.

In Possibility 2 both favourite maps are in the pool twice, so the whole Control map is a 50-50 again, but in Possibility 3 Team A is favoured. **When looking at all those three possibilities one can see that only one possibility is “fair”** and it basically depends on the randomizer to select which team is favoured the next time around.

One could argue that if you play enough Bo5s against a specific team things everything will even out over time. And while this is correct, I don’t think you should use this logic to explain why you went from a totally fair Bo3 to a randomized Bo5 to begin with. Plus, teams actually don’t play enough official Control maps against each other for this evening out to occur.

All in all this whole Bo5 thing already seems kind of unreasonable. But I can promise you that things will get even more horrendous in our second scenario.

## Scenario 2: Closer to Reality, Closer to Hell

For this scenario I picked sub-map win chances that actually could represent reality. The result is that the chances to win a Bo5 don’t vary from something insane like 32% to 68% like in scenario 1, but you will quickly understand why this scenario is even more displeasing than the first one. The assumption is that Team A has a 60% chance to win two of the sub-maps and Team B has a 70% chance to win the third one.

For a Best of 3 the chances to win the whole map are still at about 50%, but what happens for Bo5s seems weird to say the least:

To sum up what you can deduce from the pictures above: **The team that is heavily favoured on one sub-map will in general be favoured by the randomizer instead of the team that is the favourite to win the two other sub-maps**. What this means is that you are better off trying to be extremely good on one sub-map instead of just trying to be good on two. While all of this would result in (almost) a 50-50 match-up in Best of 3s, the more specialised team gets 2 out of 3 Bo5 scenarios where they are considered the favourite.

You might want to say that 54% does not seem like too much of a problem, but if you consider that a Bo3 would be (almost) a 50-50 you will have to admit that Bo5s are hurting the competitive integrity of the game (even, if its *only* by 4%).

## A Real-World Example

A great example where you can see the randomizer having an effect on the map-result is the Lower-Bracket match between Cloud9 and Movistar Riders at TakeOver2. In this match they played Lijiang Tower, which already was a map in their group-stage match, as the first map and after the first 3 sub-maps we had the following situation:

So far in the tournament MR won two times on Garden against C9 (2-0), C9 was leading with 3-1 on Control Center and their head-to-head standing on Night Market was 1-1 at this point. After those first 3 sub-maps Cloud 9 was also ahead, leading 2-1.

In that specific situation it was up for the randomizer to decide whether we will see Garden or Control Center or both as the last two sub-maps. If Garden is not in their it gives the edge to C9, since MR is favoured their. If Control Center is missing MR has a chance to come back, if both are in the pool it should be “fair”. What ended up happening was that the next two sub-maps were Garden and Night Market, thus favouring MR and MR actually won both of those and the map. Now, it is unreasonable to say that C9 would have definitely won the map if Control Center was one of the last two sub-maps, but I think we can agree that it at least would have been way more likely for them to win.

All in all there should not and must not be a randomizer that decides which team is favoured to win a map. At least when a scenario exists, Best of 3s, where the match is totally “fair” in terms of it depending on how well you practiced as opposed to you having more luck.

This is false. The correct formulae are difficult to express in this comment.

Think about the case when team 1 will always win stages 1 and 2 and always lose the third. Your model suggests that team 1 will only win 2/3 of matches.

Are you seriously ignoring probabilities completely in the last step? Just having a chance of >50% does not guarantee a win.

What do you think the chances for the different Bo5 possibilites are? 1/3 each?

Then this:

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Makes no sense at all.

Yeah, Team B is favoured by 4% on 2/3 of Bo5s, but guess what, Team A is favoured by 8% in the other 1/3.

So what is your problem? 50.112% instead of 50.4%. Wow. 0.288% difference. That's about1 in 347 matches.

And that's what you call "heavily favoured"?

Even better, in your first example the winrate stays exactly at 50%.

How is that unfair?

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