Is there something like "getting in"

Or:

Is a batsman more likely to get out at the start of his innings than later on?

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