Tickled Pink Part II (The Geek Version)

There was something else to relate to you about my visit to the cricket, but it's more of a geeky post, so I thought it deserved a seperate entry. Those of you who shiver at the thought of mathematics have my permission to skip past this.

Sat behind us were 4 older gentleman. Typical 'toffs' who obviously enjoyed cricket, but found the concept of Twenty20 a step too far. I'll recount a statistical conversation two of them had, named Toff 1 and Toff 2 for the sake of arguing. You have to imagine the upper class accents.

N.B. The sections of text in brackets are just me giving my thoughts as we go along. The sections in bold are the real mathematic theories behind what he was trying to say.

Toff 1: I met this statistical professor last night in the bar and he told me some fascinating mathematical facts.

(Yeah right! I've claimed to be a professor of mathematics in the pub before now, in the hope it'll get me a free drink)

Toff 2: Oh really? such as?

Toff 1: Well, take any two sports teams. Lets say Liverpool and Chelsea. How many times would you think they have to play each other before you could accurately say one is better than the other?

Toff 2: Oh, I don't know, three or four I suppose?

Toff 1. Twenty-three. Isn't that fascinating?

(I rolled my eyes at this point. I think I audibly groaned too. Toff 3 butted in, thankfully with a sensible response.)

Toff 3: But what if the first two or three games are all eight-nil to one side. After three big defeats you know one team is better.

Toff 1: Ah, but each individual game is a random element. They could all just be lucky wins.

(I groaned again. He carried on..)

Toff1: ...and if there is no clearly better team after twenty-three games, they'd need to play over two hundred more before you could claim one team was better than the other.

Ok, I don't know who got the wrong end of the stick, either Toff 1 himself, or the 'Professor' in the first place, but what he should have been talking about is a truely random 50/50 bet. Tossing a coin for instance. If you wanted to see if one side of the coin was bias, after about 20 tosses, if one side was at least eight or nine ahead, there would be an arguement for it being a bias coin. Anyone who remembers Normal Distribution from school should understand what I mean. There is absolutely no way you can apply this to two soccer teams. Toff 3 was spot on by saying the scale of the victories can determine a better side quite quickly. Would Manchester United really need to play Accrington Stanley twenty-three times before you knew which team was better?

(Toff 1, now proud of his new knowledge, had even more 'wisdom' to share with Toff 2)

Toff 1: ...and if those two teams play each other a few times, and one team gets four games ahead, what chance do you think that the other team can overtake them?

Toff 2: Oh, well it'll be harder for sure.

Toff 1: Statisically it would be almost impossible.

(I almost spat out my beer as I choked. He repeated it as though to hammer the point home.)

Toff 1: When a team gets ahead, it's almost statisically impossible to catch them.

(I couldn't see their faces but I assumed Toff 2 was frowning right now)

Ok, I think I know what he was on about, but either he, or the Professor had the wrong end of the stick again. Lets go back to the coin toss. If 'heads' gets three ahead in the race against 'tails' then 'tails' would need to get four in a row to overtake, which is a 1 in 16 chance. Certainly hard, but also certainly not impossible. I think that was the point he was trying to make, the further ahead one side of a random bet gets, the harder it is to catch up, but it's never impossible. Anyone who has ever watched a roulette wheel will testify they've seen 8 or 9 red numbers in a row several times a night. Lets take the University boat race as a sporting example. After the first ever 9 races, Cambridge were 5 victories ahead (7 wins to 2). After the next 17 races had finished, Oxford were 6 ahead (16 wins to 10). Should Oxford have given up after 9 races because 'it was statisically impossible for them to overtake'?

(and then the sensible one of the group finally speaks.....)

....Toff 4: Who's round is it?