Probability question

[Andrew Hughes]

My understanding of statistics/probability is rather inadequate so I wanted to check something with the assembled minds of TRF. It is cricket-related so I have posted it here, though it could apply to any sport.

If Batsman A averages 50 and Batsman B averages 40, am I right to conclude that the probability of Batsman A outscoring Batsman B on any given day (or rather, any given innings) is 55.55%?

(Leaving aside questions of fitness, form, conditions etc. and assuming that the average in both cases is a fair reflection of the individual’s ability).

Obviously I have simply totalled the averages and divided Batsman A’s average into the total. Am I going about things the right way or have I missed something?

[Pompete]

Yes Andrew you’re correct. Batsman A should out-score Batsman B 55% of the time or to place it the context of cricket 55 times in every 100 innings played all other things being equal.

I won’t bore you with my thoughts but it maybe interesting to question exactly how significant probabilities are when applied to sports, or, perhaps more importantly whether we are able to properly understand them in the world of sports, so to speak..

[Andrew Hughes]

Thanks Pompete, much appreciated.

I find the subject of probabilities fascinating, so feel free to share your ideas. I wonder whether the usefulness of the approach might depend on the figures you are using – for example batting average is both a reasonable guide to the ability of the competitors and an actual result that the competitors will produce. But then obviously, you need to somehow factor in form, fitness, conditions and so on.

I am at the moment interested in focusing on top scorer markets in cricket and was looking for a way to convert averages into probabilty and hence odds, not as an automatic way of coming up with a selection, but as a basic framework. From that point on, I prefer to use judgement rather than attempt to create elaborate systems that accurately take account of all the relevant factors. (This is partly out of preference and partly due to my lack of mathematical ability).

[BennyB]

To answer the question Andrew you would need to know the distribution of their scores around their averages – i.e. how consistent they are.

To take an extreme example, if Batsman A averages 50 because he scores 50 in every single innings, and Batsman B averages 40 because he scores 40 in every single innings, the probability of A outscoring B is 100%.

To take another extreme example, if Batsman A averages 50 because he scores 100 in half of his innings and a duck in the other half, and Batsman B averages 40 because he scores 40 in every single innings, the probability of A outscoring B is 50%.

Impossible to answer the question without knowing exactly how consistent each player is. Even if you did know, then it would be fairly complicated mathematically to compute the probabilities.

[BennyB]

edited as double post

[Andrew Hughes]

Thanks for that – fascinating. I hadn’t thought of it in such depth.

The consistency of a batsman would be fairly easy to establish – more than one website provides a list of every score they have made. You say that it would be fairly complicated to compute probabilities from this information – in theory, how might you go about it?

[BennyB]

I would construct a distribution curve for each (a bell curve would be an example), though a batsman’s would probably look nothing like that – scores are unlikely to be concentrated around the mean. More likely concentrated around 0-10 and spread thinly across the remainder.

(Unless it’s Ian Bell we’re talking about, and then it probably would be concentrated around the 40 mark!)

You would then need to use ‘integration’ to find the area which overlapped under the two curves when you drew them on the same graph.

I think….

Long time since I did any heavy maths.

[Pompete]

While not wishing to complicate things further I’m of the view any meaningful analysis would need to take into account the bowling averages of the bowlers faced – ideally current, within a specfic timeframe rather than career.

Also as part of the equation I would attempt to factor in both a batmans and the bowlers strike-rates, not quite sure how but something along the lines of one being the inverse of the other.

Are there any sites where this information is available if so I’ll give it a go.

[Andrew Hughes]

It is indeed getting complicated, but having come this far, I’m not going to give up without a fight. I’ll have a look at distribution curves (presumably Excel can handle that sort of thing).

I think the information you mentioned is available on Cricinfo via their Statsguru facility, Pompete, although it is a little slow at certain times, probably due to traffic.

[Pompete]

Andrew, I can’t seem to find to information I was after: bowler, batsman, outcome, for each successive ball in an innings. This may be a good thing as there is only so much time I can get away with not working and messing about on things like this and the gee-gees.

Nevertheless is this information available anywhere else?

Btw, how you getting on with your stats?

[Andrew Hughes]

My distribution curves came to nothing, unfortunately. I am stuck with a much cruder model. Of late I have gone back to compiling my own tissues for horse races but I hope to have another look at this when time allows.

I think the information you are after is contained in the text commentary section for each individual match. It is a time consuming process extracting it though. Cricinfo is just about the only place where you can get this. I have looked, even tried to find out if there are cricket data bases available for purchase, none I tried seemed to fit the bill.

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