Isn't the cricket toss just an illusion of control?

Question

The cricket toss gives each team a 50% chance of being able to choose whether they bat or bowl first. I think this is an illusion of control, and there's no advantage to winning it. I'll try and explain why.

Let's say we change the toss so that it's a simple "Heads = home team bats first, Tails = away team bats first". Let's say the home team wants to bat first. Then they have a 50% chance of getting what they want. This is equivalent to them winning the toss and electing to bat.

These two situations result in the same probability that a given team will start with what they want - so why do we use the (slightly) more convoluted method of giving the toss winner the option to choose? If we did a simple "H = home team bats, T = away team bats", then the overall outcome would be the same, and it would remove all this debate around what kind of advantage winning the toss gives (because there is no "winning" the toss, you either get what you want or you don't).

Is there something wrong with my analysis?

Answer 1

Pretty much, yes - although this is illusion of control isn't really unique to cricket; there are plenty of other sports where there is no real choice for the team losing the toss, or one of the two possibilities given is clearly stronger than the other so is always chosen.

One minor scenario your idea of "heads home team bats" doesn't cover is the situation where the captains would make opposite choices when winning the toss - e.g. the home team would choose to bat if winning the toss, while the away team would choose to field (or vice versa), but that could be worked around by seeing if the captains agree beforehand and not bothering with the toss at all in that case.

Answer 2

Overall, I agree with your analysis (Practically, It is only Illusionary) and the corner case by Philip Kendall (Both teams may be unhappy) but the Purpose of Coin Toss is a little more than that here, in terms of Psychology, Audience Attraction and Communication.

(1) All televised Sports are entertainment for audiences, where "winning" is Important, Psychologically. It may be winning the toss, winning the Decision review or winning the Purple Cap.

Supporting Material:

https://www.crictracker.com/stats-is-virat-kohli-the-unluckiest-captain-ever-in-terms-of-winning-the-toss/

https://www.dnaindia.com/cricket/report-netizens-spark-meme-feast-after-virat-kohli-toss-loss-yet-again-in-wtc-final-2896207

(2) When audiences join to watch on TV, it gives 5 more minutes of match build up, advertisements and commentary before the game actually starts.

Supporting Material:
https://www.espncricinfo.com/story/to-toss-or-not-to-toss-icc-may-scrap-tradition-1146844

Numerous others, including Ricky Ponting, Michael Holding, Ian Botham, Shane Warne and Steve Waugh, have also endorsed the idea. "The concerned authorities must look at what Ricky Ponting suggested - no more tosses," Holding wrote for Wisden India in 2015. "The minor setback there in my opinion, is that tosses are big for television. It makes for good tension, everyone is focused on that coin when it's in the air and the winning captain's decision and so on."

(3) In Audience Communication, it sounds better to say with Excitement "Team X has WON the coin toss and has OPTED to bat" rather than "Team X has been randomly selected to bat" which lacks Excitement.

Supporting Material:
TBI