Cricket World Ratings 11th October 2018

Two series of test cricket have got underway in the last week. Back at home, following their defeat in England, India smashed the West Indies.  Australia, meanwhile, dug themselves out of a hole to secure a draw in their match in the United Arab Emirates, which is still serving as a temporary home venue for Pakistan. The effect on my rankings is as follows:
 
South Africa  179
India         168 +9
Australia     159 -7
England       152
New Zealand   144
Sri Lanka     125 
Pakistan       47 +7 
West Indies     6 -9    
Bangladesh    -99 
Zimbabwe     -260
Ireland      -295
Afghanistan  -325

But one feature of my rankings is that they take no account of home advantage.  Teams with a winning streak at home always move up, even if this is only to be expected.  To draw in the U.A.E is arguably more of an achievement for Australia than Pakistan, but Australia have been penalised as the previously higher ranking team.

In the earliest posts on this blog, I explored how my ranking system works, with the ratings gap between the two teams used to predict a result, and then teams credited or penalised according to how much the actual results differ from the prediction.  But the default prediction takes no account of home advantage.  Can we change that?

Well, the first thing to do is to calculate the expected result for home sides.  We've been working on an assumption it's 0.5 (scoring 1 for a win and 0.5 for a draw).  In fact, it's much higher than that - over all test matches played, the home side averages 0.775 points per game, a much bigger skew than I expected. So how can we take advantage of this in the ratings system?  Amazingly, if there was no home advantage, a team would need to have a ratings gap of 178.5 points in its favour to expect such an outcome.

So if we temporarily shift the ratings of each team by such a margin to calculate the expected output we should correct for home advantage.  And we get a rather different set of scores:

India         235
Australia     224
South Africa  203
Sri Lanka     165
Pakistan      160
England       141
New Zealand   113
West Indies    -6     
Bangladesh   -142
Zimbabwe     -323
Ireland      -366
Afghanistan  -403


Most notably, India suffered in my usual ratings for losing at home to England, who gained notably; but in this revised system, England get fewer plaudits, and India suffer less punishment.  And Australia actually gained a little - rather than losing - from drawing in Pakistan.

One question we can ask is, which is the better predictor, the old method or the new one? One can calculate this by summing the difference of actual results from predicted ones (the same method we used to calculate the optimal k-factor). Rather disappointingly, it makes almost no difference - the sum of the errors actually goes up a little, from 1510 to 1512.

Might there be some other weighting for home advantage that will actually minimise the error?  This seems to be worth trying to calculate.Stay tuned...