Pappus' plane - cricket stats

I've left things too late for a comprehensive post, but since I'm disappearing again for a few days (Toulouse and Carcassonne this time), I thought I'd do a little post on those effective average curves without coming to any sweeping conclusions.

Some of the fits seem to have fallen into a local minimum that doesn't describe the effective average curve very well. Most obvious of these is Mark Richardson, who apparently always bats like he averages 57 but really only averages 45 (eyeballing his empirical hazard function, I think his effective average starts high and decreases). Such clearly wrong curves seem to be pretty rare, so hopefully they don't poison the overall trends too much.

Best and worst on nought (qualifications: average of 35, and some minimum number of innings, probably 50):

name          µ(0)  µ(1)  µ(10) µ(30) avg
MH Richardson 57,4  57,4  57,4  57,4  44,8
AN Cook       53,3  49,5  46,5  44,3  43,5
AL Hassett    52,1  52,1  52,1  48,0  46,6
CL Walcott    47,1  47,2  50,1  62,8  56,7
CH Lloyd      42,6  46,7  47,7  48,3  46,7
H Sutcliffe   41,0  73,8  75,0  75,6  60,7
Saeed Ahmed   39,1  41,3  41,3  41,3  40,4
CC McDonald   36,8  41,1  41,1  41,1  39,3
PE Richardson 35,8  36,8  36,8  36,8  37,5
GM Ritchie    35,8  16,9  33,4  34,9  35,2
---
DL Amiss      7,8   29,4  39,6  46,2  46,3
NS Sidhu      7,7   37,0  46,8  52,6  42,1
MW Gatting    7,6   26,2  37,1  44,4  35,6
VL Manjrekar  7,4   42,5  42,5  42,5  39,1
DM Jones      7,1   35,7  46,1  52,2  46,6
FMM Worrell   6,9   37,6  51,5  60,2  49,5
JA Rudolph    6,9   23,0  33,9  41,4  36,2
FE Woolley    6,5   41,1  44,3  46,0  36,1
CG Borde      6,5   36,7  41,1  43,5  35,6
MS Atapattu   6,1   32,5  36,4  38,4  39,0

But as I said in my previous post, much of the variation in how players do on nought can be put down to chance. Not all of it, though, so some of those names in the table above should belong around where you see them.

Here's a plot of effective average at nought against regular average:



Now the effective average on 1 against regular average (there's much less scatter because there's basically no smoothing done at nought, but there is at 1):



Effective average at 10:



Effective average at 30:



The effective average at 10 is very good at predicting the overall average — the scatter is noticeably less than at 1 or 30 (I haven't tried numbers in between to see where the minimum actually is). Part of this might be an artefact of the model, but I think that part of this is a real effect, especially the larger scatter at 30. Good players should have their eye in by 30 and do much better than their overall average. Bad players don't improve so much from how they did earlier in their innings. Why don't they improve? Why do they get as much eye in as possible (which is not very much) early in their innings? Questions for psychologists perhaps.