The most popular argument against this idea seems to be that people are not unintentionally banning a team mates champion the majority of the time. (i.e. people are intentionally banning their team mates champion picks at least 51% of the time)
Let's look at the statistical probability of this actually being the case, since it's being thrown around here by alot of people without really anything to back it up.
Riot's latest estimate is that there are at least 100 million monthly players logging in and playing games in the league of legends community.
http://www.riotgames.com/our-games
Note that is 100 million+ estimated, which means it's likely more.
This would be a fair assumption given that Riot has released several metric reports of steady player base increases since 2011:
http://www.riotgames.com/tags/player-numbers
But, for the sake of this analysis, we are simply going to use the most conservative estimate of 100 million.
Now let's look at how many games are played on average every month. The last released metric for this was in 2012, and is stated as 1 billion+ game play hour per month:
http://www.riotgames.com/articles/20121015/138/league-legends-growth-spells-bad-news-teemo
(click the info graphic on the page to see the actual metric numbers)
Which given a 4 year increase is probably substantially larger currently. But again, we are going to use the most conservative estimate available of at least 1 billion monthly game play hours.
So some quick math:
1 billion hours per month / 100 million players per month = 10 hours per player per month (on average).
Many players have substantially more than this per month, and many have substantially less. This is just the rough average of all monthly players.
Then we look at average game length:
http://www.leaguemath.com/match-duration-analysis/
This is a pretty good 3rd party analysis (based on match sampling), though not official his sources are from Riot metrics. And the results are not unreasonable in that the conclusion is found to be 35 descending to 30 minutes average at bronze to Challenger respectively.
It's pretty safe to assume for the purposes of this analysis that the average game length is somewhere around 35 minutes.
So:
35 minutes to 1 game or 1/35 is the actual time being spent by average players on league per game
And we want to figure out what the actual game play time (in game matches) is per hour for purpose of our calculations:
1/35 / 1/60 (actual average length per hour / 1 game per 1 hour) = 60 / 35 = 1.71429 (rounded up to the 5th decimal place) average games per hour.
And finally:
10 hours per player per month * 1.71429 average games per hour = 17.1429
Since you can't have a fraction of a game as a final result we will simply concatenate the fractional portion of our result.
So we have an average of 17 games per 1 player per 1 month
Now lets look at a recent 2016 study conducted (by Microsoft) which analyzes the average human attention span (hit it has decreased since last major findings):
http://time.com/3858309/attention-spans-goldfish/
This study found, based off Microsoft human interaction with their routine analytics gathering (Web browsing, Windows OS interaction, Windows App store viewing, ect...), that the average human attention span is approximately 8 seconds. Previously was said to reside around 12ish seconds.
Now consider this:
Before Bans and Picks even begin people have a 40 second window in which to indicate the champion they want to play. As far as I can tell, there is at least a 10 second delay from when this phase begins and when the selection is actually available (due to champ select animations). So that's 10 - 8 (attention span) = 2 or 25% longer than the average human attention span.
This is BEFORE THEY EVEN GET AN ATTEMPT TO INDICATE. Furthermore, they are then going to have to either scroll through, or type in search the champion they want to indicate (or not if they want to skip it). Let's be generous and say this takes another 4 seconds for the average person to accomplish.
So now we are at 14 - 8 = 6 or 57.1429% longer than the average human attention span. Then, they have a remaining maximum of 26 seconds to look at their team mate's indications. Lets give people the benefit of the doubt, and say that 75% of all league players do this every game (as statistically improbable as that might be). Then we are left with 25% of people who haven't even looked entering ban phase, because they've literally sat through 5 times the average human attention span of waiting and simply put their brain on auto-pilot.
Now we are down to the probability of whether or not these same 25% of people who didn't even look during the window of the indication period, are now going to take advantage of another 40 second window to look in which they have a chance to ban. How likely do you think that these same people are going to give that another go with another period of 5 times the average human attention span?
Let's do some more math shall we?
The reason I chose 25% as an example is this:
5 (times the average attention span) * 2 (indicate and ban) = 10 times average attention span
And let's generously assume that each time we pass the average attention span length that we have a small 10% chance of losing that person's focus, we would still get: 0.1 * 10 = 1 or 100% chance that at some point the average person has stopped paying attention.
Even if we only assumed that we had a 5% chance of losing that person's focus each iteration we would still be at a 50% chance that person got lost on the way to banning a champion. But what if we decreased it even further? 0.025 * 10 = 25% chance. If you only had a 2.5% chance to lose someone's attention during each pass of the average human attention span and did 10 passes, you'd still end up with 25% chance that someone stopped paying attention.
6 players with a 25% chance of being a player who didn't even look. Meaning that the average lobby (assuming minimum 25% auto-pilot rate) has at least 1.5 players in it that didn't even look (meaning sometimes 1 and sometimes 2). We'll take the lesser of the two and say 1 though, now we roll the dice on whether this person is in one of the ban slots:
3/6 = 1/2 or 50% chance of a given player being in a ban slot. And since we said on average you have a very good rate of getting 1 person in each lobby that would stop paying attention in a given lobby, we are now at a 50% chance of someone who would lose focus during indications and bans being in a ban slot 50% of the time on average per lobby.
That may seem entirely too much to you because you might say, well then why aren't we seeing this happen every other game? Well you also have to take into consideration that at any given time the majority of bans (and remember there are 6 of them) are being drawn from a pool of top meta champs the majority of the time.
Let's use the tier list from NerfPlz for instance: http://www.nerfplz.com/2016/12/2016-best-champions-tier-list-solo.html
Just as an example, and say that the vast majority of the bans made in champ select are high win rate champs listed in the god tier and tier 1 lists only.
That's usually around 20 to 25 champs for god tier, and another whopping 60 to 75 champs for tier 1. I've looked at this site for a long time and it's pretty reputable and has a very good track record of picking out the top meta champs that are literally picked or banned in almost all of my games.
Going with the lesser estimate: 80 champs. This leaves a 1/80 chance that a person wants to play a particular champ from this roster. Let's reduce that significantly though, let's say only 30 of these champs are very popular, 1/30 chance or 3.33% chance a given player wants to play one of these. 6 * 3.33% = 19.8% chance. This doesn't take into consideration that most of the time people won't ban champs that are indicated if they are paying attention (at least I'd say so based on my past experience and own personal behavior).
But just for further evidence: 0.198 * 0.5 (chance of one of these players being in lobby with you) = 9.9% chance
Point is the more factors the more drastically reduced the chance of both a summoner that is not paying attention being in a ban slot occurring every other game is greatly reduced when you factor in that they have a very small random chance of also unintentionally banning one of the popular upper 30 champs in meta that a team mate wants to play.
Yet going with even half of the above say 5%, you now have a 5% chance of someone in champ select not paying attention and banning someone else's indicated champ. And, if even 50% of the times that happens someone is either extremely irritated an/or trolling from start of the game causing them to play poorly, or other people interacting with that person (who is already very tilted), you still end up with 2.5% chance of your games being much more difficult to win. And all simply because there is no easily implemented warning safe guard against some poor inattentive fella banning his mate's champ.
Is 2.5% to 5% extra chance of having a worse gaming experience worth not doing something easy to prevent said chance to you?
So this argument wants me to believe that the majority of people are simply intentionally banning their team mates champion and then lieing about it if asked. Yet, the numbers are showing a pretty good possibility of this happening on an all too frequent basis. And since I can't really quantify lies that people tell (well I could probably but im too tired now to average out the probabilities given average numbers of lies people tell per day), then I'm just not inclined to take your word for it over things I can actually quantify and see have a good chance of actually occurring.
and 
. I picked my emergency pick 
as a result (don't hate me). It really didn't effect me until one of them came top and just downright took the kill from the gank and proceeded to "tax" me for 2 waves of minions. I got a little tilted, but nothing bad. Then, as the game drew on longer, the Yasuo (one of the duo partners) was caught out. I briefly considered leaving him out to dry (considering the circumstances, he probably deserved it). However, I decided to take the high road and help him out. Did he deserve to die? Probably. But sometimes being the nice guy gets you a whole lot further than holding a grudge.
