Or:
In order to answer this question, I will look at the statistical evidence.
Let's first start the analysis using just one batsman: Sachin Tendulkar
Tendulkar has a batting average in tests of 57.64. This should mean that he has a 1/57.64 chance of getting out before scoring every extra run. This would mean that he has a 1.73% chance of not scoring a run. This also translates into him having an 83.94% chance of reaching double figures.
How does this compare to reality:
Of his 194 innings, 12 ended in a duck (6.19%) I don't consider that to be very important, since it is very hard to score 1,2 or 3 before getting out.
In 2 innings, he was not out before reaching 10 runs. That leaves 192 innings to be considered. He was out in single figures 51 times (26.56%). This is far more than one would expect
| score | nr of times started at |
not-out in next dec. |
inns considered |
out in next dec. |
% out |
|---|---|---|---|---|---|
| 0 | 194 | 2 | 192 | 51 | 26.56 |
| 10 | 141 | 3 | 138 | 23 | 16.67 |
| 20 | 115 | 1 | 114 | 12 | 10.53 |
| 30 | 102 | 2 | 100 | 15 | 15.00 |
| 40 | 85 | 1 | 84 | 11 | 13.10 |
| 50 | 73 | 1 | 72 | 10 | 13.89 |
| 60 | 62 | 1 | 61 | 7 | 11.48 |
| 70 | 54 | 0 | 54 | 8 | 14.81 |
| 80 | 46 | 0 | 46 | 6 | 13.04 |
| 90 | 40 | 0 | 40 | 6 | 15.00 |
| 100 | 34 | 1 | 33 | 1 | 3.03 |
| 110 | 32 | 1 | 31 | 5 | 16.13 |
| 120 | 26 | 2 | 24 | 3 | 12.50 |
| 130 | 21 | 0 | 21 | 2 | 9.52 |
| 140 | 19 | 1 | 18 | 3 | 16.67 |
| 150 | 15 | 1 | 14 | 1 | 7.14 |
| 160 | 13 | 0 | 13 | 2 | 15.38 |
| 170 | 11 | 0 | 11 | 5 | 45.45 |
| 180 | 6 | 0 | 6 | 0 | 0.00 |
| 190 | 6 | 1 | 5 | 1 | 20.00 |
| 200 | 4 | 1 | 3 | 0 | 0.00 |
| 210 | 3 | 0 | 3 | 1 | 33.33 |
| 220 | 2 | (2) | 0 | 0 | ---- |
So it does seem as if a batsman is more likely to get out before 10 than later in his innings.
Where is the cut-off point?
Apparently, there is a pretty constant chance of getting out, once past a certain number of runs. This chance is lower than the average might suggest, because the average is calculated using also those early "outs".
In Tendulkar's case, this is:
| score | nr of times started at |
runs scored so far |
runs still to score |
outs to come |
avg to come |
not out on |
inns cons. |
out on |
chance out |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 194 | 0 | 9973 | 173 | 57.65 | 1 | 193 | 12 | 6.22 |
| 1 | 181 | 181 | 9792 | 161 | 60.82 | 0 | 181 | 5 | 2.76 |
| 2 | 176 | +176=357 | 9616 | 156 | 61.64 | 0 | 176 | 4 | 2.27 |
| 3 | 172 | +172=529 | 9444 | 152 | 62.13 | 0 | 172 | 1 | 0.58 |
| 4 | 171 | +171=700 | 9273 | 151 | 61.41 | 0 | 171 | 5 | 2.92 |
| 5 | 166 | +166=866 | 9107 | 146 | 62.38 | 0 | 166 | 3 | 1.81 |
| 6 | 163 | +163=1029 | 8944 | 143 | 62.55 | 0 | 163 | 4 | 2.45 |
| 7 | 159 | +159=1188 | 8785 | 139 | 63.20 | 0 | 159 | 5 | 3.14 |
| 8 | 154 | +154=1342 | 8631 | 134 | 64.41 | 0 | 154 | 8 | 5.19 |
| 9 | 146 | +146=1488 | 8485 | 126 | 67.34 | 1 | 145 | 4 | 2.76 |
| 10 | 141 | +141=1629 | 8344 | 122 | 68.39 | 0 | 141 | 5 | 3.55 |
| 11 | 136 | +136=1765 | 8208 | 117 | 70.15 | 1 | 135 | 2 | 1.48 |
| 12 | 133 | +133=1898 | 8075 | 115 | 70.21 | 0 | 133 | 1 | 0.75 |
| 13 | 132 | +132=2030 | 7943 | 114 | 69.68 | 0 | 132 | 1 | 0.76 |
| 14 | 131 | +131=2161 | 7812 | 113 | 69.13 | 0 | 131 | 0 | 0.00 |
| 15 | 131 | +131=2292 | 7681 | 113 | 67.97 | 1 | 130 | 7 | 5.38 |
| 16 | 123 | +123=2415 | 7558 | 106 | 71.30 | ||||