Pappus' plane - cricket stats

That's right people, a new post! Now that I'm back at uni, I have less time for cricket analysis, so I'll be aiming to get about one post per week, maybe two if I find something simple and interesting on Statsguru.

Some long time ago at Well Pitched, there was a discussion on great batsmen and how they supposedly "lift" their teammates when batting with them. I was sceptical about this being a real effect. Analysing it properly will take at least a couple of posts, and this is the first one.

Getting data on partnerships from summary scorecards always carries with it the problem of retired hurts. It's not just a question of definition (if an opener retires hurt before the fall of the first wicket, do you have two first-wicket partnerships or a three-way partnership?). The problem is that retired hurts are not always recorded on scorecards if the batsman in question returned to the crease. (Certainly in my lazy database, this is never recorded.) So it sometimes happens that you look at the FOW's to work out which partnerships happened and how many runs each was worth, subtract and you find that a batsman contributed negative runs during some passages of play.

So before I started gathering partnership data, I did my best to get rid of innings where there was a retired hurt. Innings were deleted if:

- a batsman finished retired hurt;

- the number three was the first wicket to fall, etc.;

- reconstructing the FOW's from the minutes batted by each batsman (where possible) disagreed with the actual FOW's;

- any partnerships required negative runs from one batsman to make sense.

Point three is an interesting one, because careful traces through of the minutes batted can identify both the presence of retired hurts and also of errors in the minutes as given. One curious error is in this Test, in which Manoj Prabhakar apparently batted for 304 minutes, while the rest of the batsmen combined for only 274.

Anyway, the above procedure isn't perfect — it won't pick up all retired hurts, especially if the minutes aren't recorded, and there are probably some innings where the anomalous minutes are just scorer/Cricinfo/CricketArchive errors and not actually showing retired hurts. But it seems to do a reasonable job, and about 430 innings were removed.

Now to the analysis proper. For each batsman and each innings, I took the runs in his partnerships and subtracted off his own score, so that we're left with the runs scored by his partners and extras while he was at the crease. Then you count how many times he saw his partners get out, and you have the average of his partners (plus extras) when he was at the crease.

To get an expected average, I added up the averages of all his partners, and divided by the total number of partnerships.

Then divided the actual partner-average by the expected partner-average, and you get a measure of how well people bat with him, relative to their careers.

When you do this, you find that players with short careers have much more variation than players with longer careers. Graph (qual. 20 innings, batsman's average at least 30):



(The average ratio across all these batsmen is about 1,1.)

Now, what I think I should do at this point is to work out how reliable the statistic is (i.e., how much of it is skill, and how much just luck), and then regress each player to the mean appropriately. (I'm learning from the baseballers, who do this sort of thing a lot.) But working out how reliable this stat is will require some thought (you're welcome to do the thinking for me). One problem is that part of what it measures might be called flat-track-bully-ness. If a batsman does disproportionately well on flat tracks, then it might be the case that he is part of many big partnerships which bloat his partner average.

But I will ignore this for now, and instead find z-scores. I ordered the batsmen in order of innings batted, found the moving standard deviation of the next 30 ratios, and then fitted a curve to it. It goes a bit like 1,3/sqrt(no. inns), for those interested. Then for each batsman, you use this as the standard deviation, and find how many standard deviations from the overall mean his ratio is.

(In terms of the reliability, the question is: Does being a standard deviation above the mean after 20 innings mean that you'll probably be a standard deviation above the mean after 200 innings?)

In the table below are the batsman's average, innings batted (having excised team innings probably involving retired hurts), runs by partners (incl. extras), total number of partnerships, expected partner average, actual partner average, ratio, z-score. Note that the partnership average is not just the partner runs divided by the number of partnerships — it's the partner runs divided by the number of times the batsman saw partners dismissed.

                                            partner-avg
name            avg   inns  p-runs  pships  exp   act   ratio z
RT Ponting      58,6  183   9622    308     43,7  63,7  1,46  3,94
RL Dias         36,7  33    1260    54      28,9  54,8  1,89  3,67
DS Lehmann      45,0  42    1733    62      43,8  78,8  1,80  3,66
DJ Bravo        33,0  44    1601    70      33,7  59,3  1,76  3,52
RWT Key         31,0  25    895     36      39,1  74,6  1,91  3,24
RT Robinson     36,4  45    1971    72      37,0  61,6  1,67  3,06
HH Dippenaar    30,1  60    2237    88      43,0  67,8  1,58  2,96
ME Trescothick  43,8  136   5890    234     38,8  54,5  1,41  2,88
Shoaib Mohammad 44,3  65    3673    123     37,1  56,5  1,52  2,73
G Pullar        43,9  44    1898    67      43,7  70,3  1,61  2,70
CL Cairns       33,5  97    2815    158     30,0  42,7  1,42  2,55
FA Iredale      36,7  22    930     42      25,1  44,3  1,76  2,48
V Sehwag        53,8  82    2794    128     39,7  57,0  1,44  2,44
Javed Miandad   52,6  172   8715    335     35,8  47,6  1,33  2,42
MLC Foster      30,5  23    624     26      45,2  78,0  1,72  2,39
GC Smith        49,5  107   4905    191     40,0  55,1  1,38  2,31
Habibul Bashar  30,9  96    2775    189     21,3  29,5  1,38  2,22
M Prabhakar     32,7  57    2064    89      35,8  51,6  1,44  2,06
CG Greenidge    44,7  175   7559    301     41,8  54,0  1,29  2,00
AH Jones        44,3  71    3560    144     31,9  44,5  1,39  1,97

Make of that what you will....

The bottom-end, those who apparently make their partners bat badly:

                                            partner-avg
name            avg   inns  p-runs  pships  exp   act   ratio z
Saeed Anwar     45,5  84    3287    194     34,3  29,3  0,86  -1,92
DJ Cullinan     44,2  111   3965    217     38,3  33,9  0,89  -1,95
WR Hammond      58,5  129   6160    284     40,1  36,0  0,90  -1,98
RA McLean       30,3  66    1049    105     31,0  25,0  0,81  -2,02
FE Woolley      36,1  92    2404    162     37,0  31,2  0,84  -2,10
SM Pollock      32,3  151   3704    249     30,3  27,2  0,90  -2,16
JT Tyldesley    30,8  54    1655    129     29,0  21,8  0,75  -2,16
AG Chipperfield 32,5  20    431     52      24,4  12,3  0,50  -2,19
MA Noble        30,3  70    2277    162     29,7  23,0  0,77  -2,30
WJ Cronje       36,4  105   3764    219     36,7  30,6  0,83  -2,32

Well if Hansie Cronje coming last on this statistic isn't the most appropriate thing I've ever put on this blog, then I don't know what is! Good to see his worshipper Shaun Pollock also down there.

Two names mentioned in the Well Pitched discussion were Steve Waugh and Inzamam-ul-Haq. They are at z = -1,22 and z = -0,40 respectively.

When I next attack this problem, I will also check to see if there are any patterns with batting position, and also look at batting with the tail.