mathmatical explanation

[raincntry]

I need some help settling a friendly dispute at my job. Quite often I need to compute prison sentences and that requires me to work with inmates good time. Recently my state changed the rules and has decided to award people all their good time each month. We are unsure in my office how this award will happen, which leads to my problem.

If someone is serving a 5 year sentence, and they earn 10 days of good time a month, I argued that a award upfront of the total of 600 days (10x12x5) is more than would be earned if inmates were required to serve each month then receive their award (meaning that on January 31 of year one, the total sentence is reduced by 10 days, on February 28 year one an additional 10 days, etc...). My boss argues there is no difference in the two. I say the second system would reach a point where the inmate would serve time that the lump sum would have already deducted.

Who is right?

 

[tkhunny]

They are exactly equivalent over exactly 60 months. Any period shorter than 60 months, the "upfront" method gives credit for months that are never served. Since "good behavior" gets one out before the five years are expired, the "upfront" methodology must be viewed as advantageous to the incarcerated. (Assuming getting out is to the convict's advantage.)
<PRE>
Days Remaining To Serve
---------------------------
Months Award Credit No "Good
Served Up Front Monthly Behavior"
0 1,225 1,825 1,825
1 1,195 1,785 1,795
2 1,164 1,744 1,764
3 1,134 1,704 1,734
4 1,103 1,663 1,703
5 1,073 1,623 1,673
6 1,043 1,583 1,643
7 1,012 1,542 1,612
8 982 1,502 1,582
9 951 1,461 1,551
10 921 1,421 1,521
11 890 1,380 1,490
12 860 1,340 1,460
13 830 1,300 1,430
14 799 1,259 1,399
15 769 1,219 1,369
16 738 1,178 1,338
17 708 1,138 1,308
18 678 1,098 1,278
19 647 1,057 1,247
20 617 1,017 1,217
21 586 976 1,186
22 556 936 1,156
23 525 895 1,125
24 495 855 1,095
25 465 815 1,065
26 434 774 1,034
27 404 734 1,004
28 373 693 973
29 343 653 943
30 313 612 912
31 282 572 882
32 252 532 852
33 221 491 821
34 191 451 791
35 160 410 760
36 130 370 730
37 100 330 700
38 69 289 669
39 39 249 639
40 8 208 608
41 OUT 168 578
42 OUT 127 547
43 OUT 87 517
44 OUT 47 487
45 OUT 6 456
46 OUT OUT 426
47 OUT OUT 395
48 OUT OUT 365
49 OUT OUT 335
50 OUT OUT 304
51 OUT OUT 274
52 OUT OUT 243
53 OUT OUT 213
54 OUT OUT 182
55 OUT OUT 152
56 OUT OUT 122
57 OUT OUT 91
58 OUT OUT 61
59 OUT OUT 30
60 OUT OUT OUT
</PRE>

 

[raincntry]

So 5 years is the break even point for the sentence calculation, with shorter sentences than 5 years benefitting from an up front award. Does that mean an up front award is disadvantageous for sentences longer than 5 years?

 

[tkhunny]

'5' is not a magic number. That was just the sentence we were working on.

If we had started with a 4-year sentence, I would have said the same things about 48 months. Exactly equivalent at 48 mos, but the credit gets them out early, so the sentence never gets to 48 months.

If we had started with a 10-year sentence, I would have said the same things about 120 months. Exactly equivalent at 120 mos, but the credit gets them out early, so the sentence never gets to 120 months.

"Up Front" gives credit for time that NEVER WILL be served. That will ALWAYS be a greater credit than a system that gives credit for time served ONLY. The length of the original sentence is of no consequence.

 

[raincntry]

that is exactally what I thought. thanks!