Thread by @Mykuhl

#cricket #stats #geeky thread alert - don't bother reading this thread if you're not interested in either cricket or statistics.

A few people have asked me why I never talk about a batter's average in particular countries. There's a really simple reason for that.

There just isn't enough international cricket played - particularly not international test cricket - to make most of those "averages in a country" statistics meaningful in any way.

There's so much randomness in results that looking at a sample size of (say) 12 innings is nuts.

What do I mean "randomness?" Well let's think about it this way. Each ball there's a chance that a batter will get runs, not get runs or get out. For the best batters, that risk of getting out will generally be lower, and it will fluctuate throughout an innings.

We know that players are more likely to be dismissed in the first 20 balls that they face than they are in the balls from 101 to 120 (if they last that long). They're also more likely to be dismissed if they're facing a top bowler than a part timer. And so on.

However, the probabilities actually don't tend to change that much - surprisingly. The best players tend to average about 10 more after they "get their eye in" than when they first start, but generally they manage the risk of getting out by adopting more judicious shot selection.

Because of that self regulation, the distribution of risk throughout an innings, when measured by runs scored, is actually remarkably consistent. They tend to have a similar probability of going from 20-30 as they do of going from 110-120.

An good example of this is Sachin Tendulkar. He played so many innings that he's one of the few players to give us a really good sample size.

In 16% of his innings where he got to 30, he got out before 40.
From 60 to 70, 15%
From 110 to 120, 13%

But even with him, we start getting very small sample sizes once we get over about 130. However, the fact remains that the risks of getting out do remain relatively stable, after an initial period of being more likely to be dismissed.

There's some really interesting work that has been done in this area, and I've personally really enjoyed looking through some of the stuff that @StatsSteves has done in this field, as well as some of @cricketingview 's excellent database work.

@StatsSteves @cricketingview But for the purpose of what I'm going to look at next, I'm going to assume that the risk of getting out before getting the next run is completely consistent, regardless of the score. I know that it isn't, but let's just pretend. We'll address how this impacts my result at the end

I'm also going to assume that a batter's ability is fixed. That's a bit unrealistic. Player's ability isn't a fixed thing. In statistical terms I'm very much a Bayesian - I don't believe that there's a single number that can be used to model a batter's skill throughout a careeer.

However, again, for the purpose of this exercise, I'm going to assume that that is the case. Again I'll address the implications of that on the result at the end.

I'd say that by now I've lost all but the geekiest readers. If you're still going, well done!

If we assume that a player has equal chance of getting out in any progression from one run to the next in their career, we can say therefore that that player's career can be modelled.

Modelling is where we use a mathematical method to create an algorithm that can tell us about the properties of the way that their scored might be distributed.

Using this model, we'd expect that Sachin Tendulkar would have averaged about 54.5. Not far from his average of 53.8.

So it isn't perfect, but it's pretty good.

Once we model something, we have many ways that we can use that data. One of them is by using that model to generate random numbers to look at what the expected results might look like.

I did just that, and generated 500 different batters, each of whom had the ability of a batter who averaged 40.

I gave each of them 200 innings, and then looked at their average after those 200 innings. Here's a graph showing it:

We see that there's actually a lot of variation in their actual average, after a few innings, but they start to settle down as time goes on. But, interestingly, there's still a lot of variation after even as many as 50 innings.

Now 50 innings is a lot of test innings. That's at least 25 tests. For most players in the world, that's roughly 3 full years. And even after that, a player who is good enough to average 40 could be averaging as little as 23.2 or as much as 59.5.

Roughly 10% are averaging over 48, and roughly 10% averaging under 33. We would describe one of those as a potential great, and there would be calls for the other to be dropped. But both groups have exactly the same ability. One group have just been lucky, and the other unlucky.

Now you'll remember that I made some assumptions at the start. All of those assumption made the spread more predictable, and reduced the variation.

In real life, we would expect an even greater difference in the data from players of exactly the same ability.

I really can't look at that distribution, and look at what I know about how cricket works, and bring myself to write off a player as being "unable to handle bounce" because they average 21 in 7 innings in South Africa (for example).

And if you're going to come on my post and try to tell me that someone is no good because they average 26 in 9 matches in Sri Lanka, then I'm very likely to not pay your argument much heed at all.

Cricket is a beautiful game, with high amounts of skill and luck.

To be successful you need to be both good enough and lucky enough. I love analysis of cricket players and matches. I really enjoy looking for stories in the numbers, and seeing if they relate to what I observe on the field. But numbers can be very deceptive if you aren't careful.

And if you aren't careful, and you do come at me with "well they failed in Pakistan, so they can't be any good" expect that you'll get this graphic heading your way.