Thursday, June 17, 2010

What gets measured gets improved

There's a well known concept in cricket of 'playing for your average'.

It's generally considered a pretty despicable thing to do.

The reputation of my childhood hero, Geoffrey Boycott, is marred by a suspicion that he cared more about his average than about the success of the teams he played for.

T'Great Man

And yet I'd be surprised if it wasn't a fair bit more widespread than people think.

At the end of the season, how many games your team has won is one statistic, which is shared between all the members of the team.

Your own performance, your position in the averages table which every cricket club calculates, is another statistic, but it gives you local bragging rights.

Lording it over your friends is an excellent feeling. Lording it over people you don't know isn't nearly as good, even on the rare occasions when it's possible. Bragging to third parties is pretty much impossible unless you're playing for the national side.

But if you are playing for the national side, everyone is looking very carefully at your average. If it's not good, you get the blame for defeats. If it is good, then you get credit for playing well in a team full of losers.

These are classic circumstances for hypocrisy. I predict that everyone is playing for their average as much as they can get away with, whilst loudly telling everyone who will listen that playing for your average is a selfish thing to do, and getting very offended indeed if anyone accuses them of doing it.

Of course, anyone who is caught playing for their average to the obvious disadvantage of their team gets severely told off. Anyone caught repeatedly doing it is thought to be a traitor, and even if, at the end of the season, they can point to the best batting average in the side, they won't be given much credit for it.

Of course, I never play for my average. How dare you even think it? But the hypocritic urge is so strong that I feel quite brave writing this post, because I know that a lot of my cricketing friends will read it and assume that it means that I do, and worse, that my attitude gives them licence to do so.

If a team were to adopt the attitude that playing for your average was acceptable, that team would do badly.

So writing a blog post like this when you're captain of a cricket team is a really stupid thing to do.

To clarify, I'm talking about batting averages. I haven't thought about bowling yet. I think it's much less of a problem there, although I did detect a certain amount of jealousy when I topped our bowling averages a few years back, by virtue of not being very good, and therefore only being asked to bowl against the other team's tail-enders.

Anyway, one of the fundamental ideas of running things is:

What gets measured gets improved.

It's a double edged maxim:

If you want something to get better, measure it.

Be careful what you measure. That is what's going to get improved, not the thing you really want.

Once upon a time, I think batting average was a sensible thing to measure. You calculate it by the number of runs scored, divided by the number of times you're out.

In the ancestral days of timeless games, this was pretty much exactly what you wanted. How many runs will a batsman, on average, give his wicket away for? You have ten wickets to spend, how many runs will you get back for them?

In this form of the game, it's a good thing to 'play for your average'. Your average-incentive and the team's success-incentive are usually perfectly aligned. In fact I can't think of a situation where a batsman should do one thing for the team, but a different thing for the record books.

However no-one plays timeless games any more. They go on forever.

The last timeless test was in 1939, when England abandoned a test match they were probably going to win against South Africa, which had been going on for twelve days.

They abandoned it because they were about to miss their boat home.

Once you start putting a time limit on games, it's less appropriate to calculate batting averages. With a short time limit, it's vastly less appropriate.

The most extreme form of timed cricket is 20 overs a side. Both sides get 120 balls, and the winner is the team who can score the most runs.

Suppose we have two batsmen.

Algy scores 30 runs from 80 balls and is not out
Ben scores 30 runs from 10 balls and is out.

Who is the better batsman?

In a timeless game, your money is on Algy. He's not out. He will probably score more runs. If the game is over because everyone else is out, then in the next game you want to put him up the order, so that he can score more. Whatever his average is, it has just gone up.

In a 20 over game, Algy is a disaster. He has just single handedly lost you the match. Your other ten batsmen have 40 balls to share between them. Even if they do really well, your final score is only going to be about 70. You'd have to be very lucky to win.

Ben, on the other hand, is pretty rubbish in a timeless game. He has thrown his wicket away. If everyone on your team plays like Ben, you're going to end up with 315 runs and get murdered. Ben had better be a bowler if he wants to stay in the team. His average is now closer to 30 than it was before.

In a 20 over game, Ben is awesome. He may well be your top scorer. He's contributed a handsome thirty to your total, and he's left 110 balls for your other 10 batsmen, who if they play really well will probably leave you with a total of 140, which is pretty comfy.

This shows that we've got a perverse incentive.

In a 20/20 game, a man who plays for his team aspires to play like Ben.

A man who plays for his average aspires to play as much like Algy as possible, whilst still staying friends with his captain and his team.

In case you think I'm overstating the case, what should happen on the last ball of the first innings in a limited overs game?

Firstly, the batsman should try to score as many runs as possible. He should either loft the ball for a six (which might be caught for no run), or try to swing madly at it to get a more certain four. He should completely ignore where his wicket is. It no longer matters.

Then, whether he hits or misses, he should immediately start running, and not stop running until the opposition have run him or his batting partner out.

From a team point of view, there's no other sensible thing to do.

How many times, if you watch limited overs cricket, do you see the last ball played defensively for no run?

That is someone playing for their average. There is no other reason for it.

Even worse, they're often playing for their partner's average. You wouldn't be at all popular if you called a suicidal run on the last ball that was suicidal for the man at the other end. You've just spoiled his batting average. You don't do that to friends.

I did it accidentally in the last game we played (sorry Joe). Everyone realises that it's the right thing to do.  I feel guilty. Joe feels annoyed. I had to buy him a beer and say sorry.

My conclusion is that calculating batting averages in a team which plays mainly limited-overs cricket is stupid, counterproductive, and must stop.

But how do we stop it?

We can't just not calculate them. Batting averages are part of the game. People calculate them in their heads. I'm playing for several different teams occasionally, and keeping a careful record of my scores so I can work out my overall average at the end of the season even though it's completely meaningless, I know it's completely meaningless, and even if it made any statistical sense to add up scores for different teams like that it would be the wrong thing to calculate anyway.

But very few people have the statistical sense to realise that. So, as with all numbers calculated ever, they are taken to be the Word of the Lord by those who don't understand them, and they are so important as a result that it's totally unrealistic to expect people to forget about them.

Go look at the Wikipedia article about Boycott. To me it paints a picture of a very gifted man, tortured by a selfishness and a fear of failure and bad luck that was completely understandable given what happened to him as a child, and to his father when he was on the verge of adulthood.

He could have been a real cartoon hero without too much trouble. Random events twisted him into a tragic hero. He is in fact, even more my hero after reading that than he was when I was a boy.

But my point is that this article is absolutely littered with references to his batting average! He's been heavily criticised for trying to improve it at all costs, and at the same time lauded for having one of the best averages ever.

This is a bit like the man who burned down the temple at Ephesus so that his name would be remembered forever. I forget his name.

So should you. Never speak it. Never write it down. Tipp-ex it out of books.

We need a better measure of a batsman's usefulness to replace batting average with.

Scoring rate won't do.

Someone who scores 4 off 1 ball and then gets run out on the next has been next to useless unless he's gone in in the last over. Someone with the same scoring rate of 4 runs per ball who's got 80 off 20 balls in a 20/20 game is an impossible god who will be man of the match.

The first thing to do is not to worry about whether a batsman's out or not. If you're the eleventh wicket, you're still out for averaging purposes. This disadvantages the lower order batsmen, but it gives everyone better incentives. The lower order probably don't worry about their batting averages so much anyway. That's not what they're for.

I wonder if we should quote something like total runs scored and total balls faced, both divided by the number of matches played.

So you might get something like

'Algy has scored an average of 15 runs off an average of 25 balls per game'
'Ben has scored an average of 15 runs off an average of 10 balls per game'

I'm sure that's not perfect. It doesn't account for the situation where you're running out of wickets, and a batsman who can just not get out becomes really valuable even though he's scoring slowly, because you're going to pick up extra byes and wides and no balls just by virtue of him being there.

Maybe we should count byes, wides and no-balls as runs to the batsman, even though they're nothing to do with him, just in order to get the incentives aligned properly.

Another problem is that if you've got two numbers, like 15/25 or 15/10, it's not obvious what order you want to put your table of best batsmen in.

15 off 15 is better than 15 off 16, and worse than 16 off 15, clearly.

16 of 16 is slightly better than 15 off 15.

But what about 16 off 17? That probably depends on the match situation.

But actually that doesn't matter.

We can work with a partial ordering. It's just that there'll be ties in the rankings.

I don't think that's a problem. If it is, then we can use something irrelevant as a tie breaker, like average catches. That probably correlates nicely with batting prowess anyway, and although you don't really need any extra incentive to take catches, it might be an extra incentive to practice catching.


  1. I'm happy to be run out for the good of the team any time. I'm only sad that I still haven't managed to wash the mud out of my kit.

  2. Good stuff!

    To reinforce what you're saying, take the situation I faced in my last match with respect to my batting average. The numbers are mercifully small, and shouldn't tax anyone's arithmetic faculty.

    After two miserable ducks to start the season, I had a good knock of 26. Average of 8.7 (or near enough). In the last game, I was put in on the last ball of the innings - a perfect example of the type of situation you describe. No time to get my eye in. I walked to the wicket thinking "right, have this". Then about 2 yards from the crease a weaselly little thought popped into my head "Hold on, if you swing and get out, your average will be down to 6.5" (I didn't actually do the maths on the spot, you understand, I'm simply filling in detail to aid comprehension now) "That's a 25% reduction in average" (as I mention, I didn't know this exact number at the time, but it was clearly going to be a hefty reduction). I banished this weaselly traitor by the time I took guard. When the ball came I gave it the onions, swung and missed.

    But what if I hadn't known about my average? Perhaps I would have come down the wicket to him? Scored a 6? Then we would have won the match by 118 runs instead of 112.

    It is, perhaps, to be expected that a mathematically inclined chap like you proposes to fix the pernicious effect of statistics by designing more complex statistics. Personally, I'd rather we abandoned them at amateur level. Remember the good innings / catches / overs and brag about those. Conveniently forget the times we're out foolishly playing across the line to a pie chucker who has unusually got one to land near the stumps. Life would be better if those didn't come back to haunt us.

    If we must use stats, let's use really complicated ones. Not so much because they're more accurate, but to make it impossible for a player to work out what effect his actions would have on his stats and get on with playing the game.