T20 International -- Over by Over Correlations

Following my previous analysis of correlation analysis of over by over runs and wickets I provide further details on the correlation structure of the runs and wickets I estimated the cross-correlograms.
A cross-correlogram estimates the correlation between one variable and other variable considered at different shifts. When we calculate the correlation between Run from over 1-20 and Wickets from 1-20, it is correlation between the two variables (runs and wickets) at zero lag. We can also do the same calculation for Runs from overs 1-19 and wickets from 2-20 overs. This will be correlation for +1 lag. Similarly one can do it for all positive and negative lags. Physical meaning of the correlogram is following.

If we find a peak in correlogram at a different lag than zero, it means that one variable preditcs another at some point in future. For instance, in panel A of figure below, the red trace peaks at -1, it means that if there is high scoring in an over there is 20% chance of fall of a wicket in the following over. In the figure above I show cross-correlograms between Runs and Wickets per over (Panel A) for both first (blue) and second (red) innings. The light-blue and pink lines show the shuffled correlations i.e. provide a way to calculate the significance of the correlations. Similarly in panel (B) crosscorrelogram is shown for Avg. runs and Av. wickets per over.

It is interesting that the in second inning a high scoring over is likely to lead to a fall of wicket in the following over. This dependence is more evident in averages. On average high runs in an over would lead to fall of wicket in next over in 40% chances and 60-70% in the very same over.
I wonder if this the case in general of a feature of only the shortest form of the game. My guess is that in Test Cricket there should be no correlation between runs and wickets but in 50 over matches it should exist, particularly in slog overs.


Further, there is something more interesting in the auto-correlogram function of the Wickets. Auto-correlogram is same as the cross-correlogram, except that now instead of two different variable, we cosider only one variable. The secondary peaks in the auto-correlation function indicate oscillation i.e. repeating phenomenon.
The auto-correlogram of Wickets per over shows some periodicity of 3 overs but only in the second inning. This means that in second inning of the T20 international matches wickets are likely to fall at 3 over interval. Needs to be checked in raw data...


right arm over
Arvie