Not sure if this is the correct forum for this 'theory', but why do bowlers' runs conceeded also have to include fielders' mistakes (such as dropped catches, misfields and overthrows)? Why can't something like they have in baseball be instituted? (whenever I bowled I used to loath others causing runs to be added to my tally and by reactions of the internationals I think they are of similar opinion)

An off-topic question: you mentioned players' Batting Position Index. Are there any weighted versions of this stat? It is clear that a player who has played 100 tests at 1 and 100 tests at 11 (batting position index of 6) will not have a similar result as a player who has played 200 times at 6. Do you know of a version that weights this such that the first player would have a position index much closer to 11?

I was just wondering what the adjusted stats for Sangakkara the batsman would look like using this method after going through this week's Ask Steven column. He seems to have scored over 2000 runs at a 90+ average. From my calculations, the average drops to around 71 from 96 (including the latest test vs Eng)

In many distributions the average as a measure of central tendency not only provides the 'average value' i.e. the the area under the curve divided by the no of instances, but is also a good predictor of the most likely value.

Batting averages though mean nothing of the sort. Batsman's scores invariably have an inverted bell (of U shaped) distribution - the greatest # of outs is single digit, followed by a large number before the batsman crosses twenty. Then you get a few instances around the actual 'batting average' and again the # of instances goes up towards the higher scores. This holds for every batsman, and Lara's and Dravid's distributions are not that dissimilar as you would expect. So the least probability is actually around the batting average. So if Ponting has an 'average' of 59, he is actually least likely to score b/w 50 - 60. So not really sure what the average indicates for a given innings. At best it can be used the way we use it - comparing greats across time...

the average should suggest to the spectator how many runs a particular player is likely to make before he leaves the field.. After all, having made 25 not out twice is less likely to help his team win than a battling fifty, followed by a 0 not out. both players would have an average of fifty but everyone would know that once player A got into the twenties, he would be on shaky, unfamiliar ground.
I think therefore that Runs Per Innings is fairer to spectators, rather than the deceitful Average that is currently employed.

An average is also the sum of observations multiplied by the proability of that observation occuring ie the sum of all (x*P(x)). So while the probability of scoring on or around the average is probably very low, the average does take into the consideration that you might, as the fielding team, spend a few days watching a Lara compile a 400 run innings. To determine the plausibility of the statistic, you should ask your self, if you were fielding captain and Lara walked in, would you be expecting the mode (the value with the hghest probability) or the average.

Precisely my point, Malcolm. In terms of expectation from an innings when a batsman walks in, you should be expecting a modal value, which in all batsmen's case whether a Lara or a Harmison is less than 20.

Batting averages are higher or lower depending on 3 factors - a) The shape of the distribution - while the U shape holds in general, for the better batsmen, the % of cases in the 10s, 20s and 30s tends to be higher, b) The really high scores, and I find this is a huge influencer - the really great batsmen tend to run up very high scores which drives their avergae and c) the proportion of not-out innings.

Of the three, only a) the shape of the distribution really influences the modal value. My point being that if you compare someone with an average of 40 with someone with a 55, your start expectations may be significantly different; but between 55 and 57, your start expectations should be no different.

The runs per innings is also deceptive. If you are a number 5 or 6 batsman coming in after four really good batsmen, you could realistically be called on to get small scores or have a large amount of your innings cut off by decalrations. You would then end up with a low average runs per innings. It would not be a true reflection of your talent which is what the average is supposed to be. Obviously there are more sophisticated statistical techniques that could be used to analyse the performance of a player but the average, strike rate and conversion rate that you get are an excellent indication of the quality of the player, remembering, of course that the accuracy of any statistic increases as the number of obvservation increases.

Hmm, good point Malcolm.
I wonder if anyone out there would care to perform a statistical analysis of the top 25 players' MODE, to determine their most likely score on walking out to the middle? It may raise a few eyebrows, not to mention the ire of millions!!

I don't think EBA can be more than normal batting average, as shown for Sir Sobers and other follwoing batsman:
Garry Sobers 93 57.78 44.06 58.16
George Headley 22 60.83 45.61 61.33
Brian Lara 131 52.89 49.76 52.97
Kevin Pietersen 30 52.69 50.44 52.84
Kumar Sangakkara 68 55.74 46.16 56.26

Kindly ractify.

There is nothing in the calculation methodology to conclude that the EBA cannot be greater than the normal Average. In fact it can be seen that I have referred to these 5 batsmen in my article.

Ananth