Model

What keeping versions costs in hit rate

Version retention is billed to the whole population as points of hit rate.

Δ h = \frac{ln V}{ln N}

$V$: Versions; versions per key
$N$: Items; items in the corpus

Recurring principle: Costs are conserved

How it behaves

One input on the horizontal axis, the others held fixed.

N = 10⁶N = 10⁹

Data table

Hit-rate points lost to retained versions (Zipf α ≈ 1)
Versions per key V	series	Hit rate lost (points)
1	N = 10⁶	0
1.04	N = 10⁶	0.271
1.08	N = 10⁶	0.542
1.12	N = 10⁶	0.813
1.16	N = 10⁶	1.08
1.21	N = 10⁶	1.36
1.25	N = 10⁶	1.63
1.3	N = 10⁶	1.9
1.35	N = 10⁶	2.17
1.4	N = 10⁶	2.44
1.45	N = 10⁶	2.71
1.51	N = 10⁶	2.98
1.57	N = 10⁶	3.25
1.63	N = 10⁶	3.52
1.69	N = 10⁶	3.79
1.75	N = 10⁶	4.07
1.82	N = 10⁶	4.34
1.89	N = 10⁶	4.61
1.96	N = 10⁶	4.88
2.04	N = 10⁶	5.15
2.11	N = 10⁶	5.42
2.2	N = 10⁶	5.69
2.28	N = 10⁶	5.96
2.37	N = 10⁶	6.23
2.46	N = 10⁶	6.51
2.55	N = 10⁶	6.78
2.65	N = 10⁶	7.05
2.75	N = 10⁶	7.32
2.85	N = 10⁶	7.59
2.96	N = 10⁶	7.86
3.08	N = 10⁶	8.13
3.19	N = 10⁶	8.4
3.31	N = 10⁶	8.67
3.44	N = 10⁶	8.94
3.57	N = 10⁶	9.22
3.71	N = 10⁶	9.49
3.85	N = 10⁶	9.76
4	N = 10⁶	10
4.15	N = 10⁶	10.3
4.31	N = 10⁶	10.6
4.47	N = 10⁶	10.8
4.64	N = 10⁶	11.1
4.82	N = 10⁶	11.4
5	N = 10⁶	11.7
5.19	N = 10⁶	11.9
5.39	N = 10⁶	12.2
5.6	N = 10⁶	12.5
5.81	N = 10⁶	12.7
6.03	N = 10⁶	13
6.26	N = 10⁶	13.3
6.5	N = 10⁶	13.6
6.75	N = 10⁶	13.8
7.01	N = 10⁶	14.1
7.28	N = 10⁶	14.4
7.55	N = 10⁶	14.6
7.84	N = 10⁶	14.9
8.14	N = 10⁶	15.2
8.45	N = 10⁶	15.4
8.77	N = 10⁶	15.7
9.11	N = 10⁶	16
9.46	N = 10⁶	16.3
9.82	N = 10⁶	16.5
10.2	N = 10⁶	16.8
10.6	N = 10⁶	17.1
11	N = 10⁶	17.3
11.4	N = 10⁶	17.6
11.8	N = 10⁶	17.9
12.3	N = 10⁶	18.2
12.8	N = 10⁶	18.4
13.2	N = 10⁶	18.7
13.8	N = 10⁶	19
14.3	N = 10⁶	19.2
14.8	N = 10⁶	19.5
15.4	N = 10⁶	19.8
16	N = 10⁶	20.1
16.6	N = 10⁶	20.3
17.2	N = 10⁶	20.6
17.9	N = 10⁶	20.9
18.6	N = 10⁶	21.1
19.3	N = 10⁶	21.4
20	N = 10⁶	21.7
1	N = 10⁹	0
1.04	N = 10⁹	0.181
1.08	N = 10⁹	0.361
1.12	N = 10⁹	0.542
1.16	N = 10⁹	0.723
1.21	N = 10⁹	0.903
1.25	N = 10⁹	1.08
1.3	N = 10⁹	1.26
1.35	N = 10⁹	1.45
1.4	N = 10⁹	1.63
1.45	N = 10⁹	1.81
1.51	N = 10⁹	1.99
1.57	N = 10⁹	2.17
1.63	N = 10⁹	2.35
1.69	N = 10⁹	2.53
1.75	N = 10⁹	2.71
1.82	N = 10⁹	2.89
1.89	N = 10⁹	3.07
1.96	N = 10⁹	3.25
2.04	N = 10⁹	3.43
2.11	N = 10⁹	3.61
2.2	N = 10⁹	3.79
2.28	N = 10⁹	3.98
2.37	N = 10⁹	4.16
2.46	N = 10⁹	4.34
2.55	N = 10⁹	4.52
2.65	N = 10⁹	4.7
2.75	N = 10⁹	4.88
2.85	N = 10⁹	5.06
2.96	N = 10⁹	5.24
3.08	N = 10⁹	5.42
3.19	N = 10⁹	5.6
3.31	N = 10⁹	5.78
3.44	N = 10⁹	5.96
3.57	N = 10⁹	6.14
3.71	N = 10⁹	6.32
3.85	N = 10⁹	6.51
4	N = 10⁹	6.69
4.15	N = 10⁹	6.87
4.31	N = 10⁹	7.05
4.47	N = 10⁹	7.23
4.64	N = 10⁹	7.41
4.82	N = 10⁹	7.59
5	N = 10⁹	7.77
5.19	N = 10⁹	7.95
5.39	N = 10⁹	8.13
5.6	N = 10⁹	8.31
5.81	N = 10⁹	8.49
6.03	N = 10⁹	8.67
6.26	N = 10⁹	8.85
6.5	N = 10⁹	9.03
6.75	N = 10⁹	9.22
7.01	N = 10⁹	9.4
7.28	N = 10⁹	9.58
7.55	N = 10⁹	9.76
7.84	N = 10⁹	9.94
8.14	N = 10⁹	10.1
8.45	N = 10⁹	10.3
8.77	N = 10⁹	10.5
9.11	N = 10⁹	10.7
9.46	N = 10⁹	10.8
9.82	N = 10⁹	11
10.2	N = 10⁹	11.2
10.6	N = 10⁹	11.4
11	N = 10⁹	11.6
11.4	N = 10⁹	11.7
11.8	N = 10⁹	11.9
12.3	N = 10⁹	12.1
12.8	N = 10⁹	12.3
13.2	N = 10⁹	12.5
13.8	N = 10⁹	12.6
14.3	N = 10⁹	12.8
14.8	N = 10⁹	13
15.4	N = 10⁹	13.2
16	N = 10⁹	13.4
16.6	N = 10⁹	13.6
17.2	N = 10⁹	13.7
17.9	N = 10⁹	13.9
18.6	N = 10⁹	14.1
19.3	N = 10⁹	14.3
20	N = 10⁹	14.5

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

V = 3, N = 10⁹ → ≈ 5 points

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Caching
What happens when we deliberately keep a second copy of data that no protocol forces to be correct?
$Δ h = ln V / ln N$
Read it in place →