Let me start off with an apology: this will be the most boring column I have ever written. It's about probability and random variation.
If those sentences did not scare you away and you are still reading, you must be a bit like me: interested in every aspect of our 3-cushion game. And this is actually quite fascinating: it's about scoring high, scoring low and how to explain why every 3-cushion player has a Dr. Jekyll and Mr. Hyde personality.
I was roughly a 1.000 average player for many years, and this is a score sheet I have never produced in my life: 1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1. That's 25 points in 25 innings, and it hasn't happened to anyone, ever. This is why we speak about an AVERAGE: the combination of all my innings, the good, the bad and the ugly, made me about a 1.000 player. My score sheets looked more like this: 2-0-0-0-4-0-1-0-0-1-0-0-7-1-0-0-3-3-0-0-1-0-0-0-2. That's also 25 points in 25 innings.
Did I play fantastic 3-cushion in six of those innings, normal quality in four innings, and horribly bad in the remaining fifteen? No, there are all sorts of reasons why I had fifteen misses, and there are also reasons why I made a 4 and a 7. Quality of play is hardly a factor here: I may have played poorly when I made the two runs of three and I may have played a few superb shots in the empty innings. The same player is at the table all through the match, and it makes sense that we produce shots of comparable quality throughout, whether we score or miss.
What is true for me, is also true for a 0.500 player, or a 2.000 average player. No matter what your playing strength is, in the majority of your innings you will score much higher or much lower than your average. This is called "random variation", and billiard players can understand that concept quicker and better than most people, because they see the principle in action every day.
It's really intuitive and easy to understand that a run of four does not make you world class, and three consecutive zeroes don't make you a pathetic loser. We know that "random variation" produces results that can be miles away from a player's ability. As long as it's about "innings", we get it. We understand.
And then innings turn into matches, and all of a sudden, we tend to forget about random variation. We start to say silly things like: "How can he make 40 in 18 on Thursday, and not even get to 1 average on Friday? This is unbelievable."
No, it isn't. It is quite normal.
He won on Thursday, made 40 in 18. He lost on Friday, made 18 in 24. That gives him a 1.380 average for the tournament. Guess what, he's a 1.400 player. This is what 1.400 players do.
"But have you seen that second match? He missed three childishly easy shots!"
Again, that is what a 1.400 player does. If he never did that, he'd be a 1.800 player. Nothing out of the ordinary has happened. The only thing crazy about this, is the way we respond to it. We'll praise him if he plays 0.750 first, then 2.200. He "can raise his game", he's mentally strong. We'll burn him to the ground if he starts with 2.200, then produces 0.750. "He can't handle the pressure."
A match is basically the same thing as an inning. Here's a comparison for you: If you let a machine drop a coin and you count heads and tails; ten drops mean nothing of course. Could be 8-2, or 1-9. What about a hundred? Not enough. A thousand? No. Scientists say they need about 5000 drops of a coin to be fairly certain the heads and the tails will both be very close to 2500, or 50 %. Random variation has now dissolved into the sea of large numbers.
In billiard terms: 100 or even 250 innings are not enough to make a fair judgment about a player's ability. Or, for that matter, about his "form". What is often referred to as good form, a hot streak, is mostly just random variation, the coin falling on heads four times in a row.
Let's add to what we've seen so far. Three-cushion has a habit of dishing out good and bad fortune to players, and making their results look better or worse than their play actually was. We're not even talking about flukes here: just a roll of the ball. Under the rail: unmakeable shot. Six centimeters off the rail: unmissable ticky. Good shot, full contact on third ball: no position. Poor shot, only just clipped the third ball: open position. It's stuff like that, and the impact is huge.
Going back to the 1.400 player, with his two matches on consecutive days. Random variation would give him (for instance) a 1.200 and a 1.800 match. A funny roll of the ball here and there (to his advantage) in the first match and some poor luck in the second could turn those matches into 1.400, both times. And of course, if we reverse the good and the bad luck, he may have scored 0.750 and 2.200. Same player, same knowledge, same concentration, same ability. In many cases even: comparable quality of play.
Is it all just luck and random variation then? Do 3-cushion players never play poorly, never outstanding? Of course not. They sometimes had the wrong thing for breakfast, or quarreled with their girlfriend, and their concentration is poor. Or they woke up with a smile, feel energetic and focused, play with confidence and courage. They do have good and bad days.
But we can't ever tell by looking at the score board. We'll have to look at the table.