Friday, 12 October 2018

Home Advantage

In the previous post, I explored how one might compensate for home advantage in the rating system.  I measured actual home advantage (which was surprisingly large) and adjusted the ratings; but the new ratings turned out to be worse predictors than the old!  How come?  The answer turns out to be a coding bug! Measured properly, home advantage is much less than I asserted: the home team's expected yield from a game is 0.573 points, not 0.775; and that corresponds to a ratings advantage of just 42.5 points, not the massive 178.5 points I was applying yesterday.  And when I use the correct factor, the predictivity of the ratings improves, with a cumulative error over all past test matches down to 1470 from 1510.  So what do the adjusted ratings look like? Here's the answer:

South Africa  174    
India         174    
Australia     165    
England       144    
Sri Lanka     133   
New Zealand   133    
Pakistan       68    
West Indies     5    
Bangladesh   -100    
Zimbabwe     -264    
Ireland      -301    
Afghanistan  -331

With this adjustment factor, Pakistan's recent draw with Australia gained Pakistan (and lost Australia) just 4 points: the prediction of a better results for the visitors (with their higher rating) partially offset by their home advantage. South Africa have been top since September; prior to that, India were top from August 2016.  This almost exactly reflects the "real" ratings, wherea similar change occured, albeit one match earlier.

So how do the two ranking systems differ in the longer term?  As we've discussed, the gap (in points) between any two teams has meaning, but the absolute scores less so. So one statistic we've looked at in the past is to ask, for every team that has ever held first place, what was the moment when it held that position by the greatest margin over the team in second place? Using the old rankings, our results were like this (showing also the period for which the team held the number 1 ranking):

Dec 1999    Nov 2009    Australia     Dec 2007    222
Mar 1885    Jan 1898    England       Aug 1890    198
Sep 1983    Dec 1991    West Indies   Jul 1986    172
Aug 2016    Aug 2018    India         Aug 2017    123
Nov 2012    Nov 2015    South Africa  Mar 2013     94
Jan 1983    Feb 1983    Pakistan      Jan 1983     22

Under the new system, the results are as follows:

Dec 1999    Dec 2008    Australia     Jan 2008    223
Dec 1884    Feb 1898    England       Aug 1890    195
Jun 1980    Jan 1992    West Indies   Nov 1984    170
Nov 2012    Nov 2015    South Africa  Mar 2013    109
Aug 2016    Sep 2018    India         Aug 2017    104

The timing of the peaks are nearly identical, although the periods each side's dominance lasted differ.  Most notably, the West Indies are rated as having been the world's best team for over a decade in the 1980s and early 1990s, and Pakistan's brief period marginally on top of the old rankings (the only ever time they were rated number one) has disappeared.  It's notable that India's recent peak is marked down, however; this reflects the fact it was based primarily on outstanding results at home.

Another question we can ask is if the new rankings more stably define teams in the number one spot.  This isn't necessarily a mark of improvement - we have no absolute standard to say who really was the best team in the world at a given point in time, and how often this has changed. In fact, there's almost no difference overall in terms of length of tenure at the top: the old system has had 93 different periods of leadership, and the new system 92.

Lastly, let's look at the what's happened since the turn of the millenium.  Firstly, under the old system:

Dec 1999    Nov 2009    Australia     Dec 2007    222
Nov 2009    Jan 2010    India         Dec 2009     31
Jan 2010    Jan 2010    Australia     Jan 2010      1
Jan 2010    Feb 2010    India         Feb 2010      3
Feb 2010    Feb 2010    Australia     Feb 2010     16
Feb 2010    Mar 2010    India         Feb 2010      1
Mar 2010    Aug 2010    Australia     Jul 2010     40
Aug 2010    Jul 2011    India         Oct 2010     59
Jul 2011    Feb 2012    England       Dec 2011     99
Feb 2012    Nov 2012    Australia     Mar 2012     33
Nov 2012    Nov 2015    South Africa  Mar 2013     94
Nov 2015    Aug 2016    Australia     Feb 2016     51
Aug 2016    Aug 2018    India         Aug 2017    123
Aug 2018    -           South Africa  Sep 2018     13


And under the new one:

Dec 1999    Dec 2008    Australia     Jan 2008    223
Dec 2008    Jan 2009    South Africa  Dec 2008      2
Jan 2009    Dec 2009    Australia     Mar 2009     68
Dec 2009    Dec 2009    India         Dec 2009     10
Dec 2009    Oct 2010    Australia     Jul 2010     56
Oct 2010    May 2011    India         Oct 2010     48 
May 2011    Jun 2011    England       May 2011      5
Jun 2011    Jul 2011    India         Jun 2011     19
Jul 2011    Feb 2012    England       Dec 2011     94
Feb 2012    Nov 2012    Australia     Jun 2012     27
Nov 2012    Nov 2015    South Africa  Mar 2013    109
Nov 2015    Nov 2015    Australia     Nov 2015      1
Nov 2015    Nov 2015    South Africa  Nov 2015      6
Nov 2015    Aug 2016    Australia     Feb 2016     45
Aug 2016    Sep 2018    India         Aug 2017    104 
Sep 2018    -           South Africa  Sep 2017      5


And if we ignore brief reigns of less than 2 months, the succession is Australia; India; Australia, India; England, Australia, South Africa, Australia, India, South Africa under both systems.  So although the transition periods from one dominant team to another have been handled differently, the stories are remarkably similar overall.

Finally, what's happened in the official ratings during this period? Data is available from June 2003 onwards:

Jun 2003    Jul 2009    Australia
Aug 2009    Nov 2009    South Africa
Nov 2009    Aug 2011    India
Aug 2011    Aug 2012    England
Aug 2012    May 2014    South Africa
May 2014    Jul 2014    Australia
Jul 2014    Jan 2016    South Africa 
Jan 2016    Feb 2016    India
Feb 2016    Aug 2016    Australia
Aug 2016    Aug 2016    India
Aug 2016    Oct 2016    Pakistan
Oct 2016    -           India


Overall, the offical ratings are more stable than mine, but also slower to react to recent results - India are still rated number one.  Ignoring very short periods, both my systems have Australia on top throughout most of 2010, in between two periods of India dominance, but this was a single period of Indian ascendency according to the ICC; also note that the ICC briefly had Pakistan in the top spot, which under my old system they have last held in 1983 and under my new system, never.  But overall there's a broad concordance.

But I like my new system, with it's improved predictive power, and compensation for the skew that comes with playing home or away.  I think I'm going to stick with it from now on.



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