Calculating effective average lap time.
Given:
S = number of laps in a tire shift or stint (whole number)
L = average non-pitstop lap time, in standard time units (usually seconds)
P = overall pitstop cost in same units
R = number of laps in the race
Number of pitstops in the race is
N = ceiling(R/S - 1), which gives zero if S >= R
(The -1 occurs because you do not take a pitstop if your tires are worn-out at the end of a race).
Distributing the time for those pitstops over all laps gives
N*P/R
as the average cost per lap of pitstops.
That is, average lap time will be
A = L + N*P/R
As R becomes very large that tends towards
A = L + P/S
which is an intuitive figure, and a good mental approximation. That is, the time penalty for a pitstop is distributed over the laps in the shift.
It is very important, however, to remember that the number of pitstops taken must be a whole number--you either take a whole pitstop or you don't; you cannot take a fractional pitstop. (In games with fuel consumption this changes, as pitstop length can actually change).
I created charts corresponding to the SSR11 races and the GV300 which show the average penalty per lap of various stint lengths, assuming a range of pitstop times from 20 to 40 seconds (by 5).
Code:
R=30,P=20 to 40, N=# of pitstops
S N N*20 N*P/R N*25 N*P/R N*30 N*P/R N*35 N*P/R N*40 N*P/R
1 29 580 19.3 725 24.2 870 29.0 1015 33.8 1160 38.7
2 14 280 9.33 350 11.7 420 14.0 490 16.3 560 18.7
3 9 180 6.00 225 7.50 270 9.00 315 10.5 360 12.0
4 7 140 4.67 175 5.83 210 7.00 245 8.17 280 9.33
5 5 100 3.33 125 4.17 150 5.00 175 5.83 200 6.67
6 4 80 2.67 100 3.33 120 4.00 140 4.67 160 5.33
7 4 80 2.67 100 3.33 120 4.00 140 4.67 160 5.33
8 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
9 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
10 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
11 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
12 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
13 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
14 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
15 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
16 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
17 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
18 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
19 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
20 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
21 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
22 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
23 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
24 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
25 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
26 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
27 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
28 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
29 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
30 0 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00
Code:
R=60,P=20 to 40, N=# of pitstops
S N N*20 N*P/R N*25 N*P/R N*30 N*P/R N*35 N*P/R N*40 N*P/R
1 59 1180 39.3 1475 49.2 1770 59.0 2065 68.8 2360 78.7
2 29 580 19.3 725 24.2 870 29.0 1015 33.8 1160 38.7
3 19 380 12.7 475 15.8 570 19.0 665 22.2 760 25.3
4 14 280 9.33 350 11.7 420 14.0 490 16.3 560 18.7
5 11 220 7.33 275 9.17 330 11.0 385 12.8 440 14.7
6 9 180 6.00 225 7.50 270 9.00 315 10.5 360 12.0
7 8 160 5.33 200 6.67 240 8.00 280 9.33 320 10.7
8 7 140 4.67 175 5.83 210 7.00 245 8.17 280 9.33
9 6 120 4.00 150 5.00 180 6.00 210 7.00 240 8.00
10 5 100 3.33 125 4.17 150 5.00 175 5.83 200 6.67
11 5 100 3.33 125 4.17 150 5.00 175 5.83 200 6.67
12 4 80 2.67 100 3.33 120 4.00 140 4.67 160 5.33
13 4 80 2.67 100 3.33 120 4.00 140 4.67 160 5.33
14 4 80 2.67 100 3.33 120 4.00 140 4.67 160 5.33
15 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
16 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
17 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
18 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
19 3 60 2.00 75 2.50 90 3.00 105 3.50 120 4.00
20 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
21 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
22 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
23 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
24 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
25 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
26 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
27 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
28 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
29 2 40 1.33 50 1.67 60 2.00 70 2.33 80 2.67
30 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
...
59 1 20 0.67 25 0.83 30 1.00 35 1.17 40 1.33
60 0 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00
The important thing is the change in penalty as you go down a particular "N*P/R" column.
To clarify a bit, consider just the P=25 columns, since I think 25 seconds is a good approximation of the time taken by pitstops in [size=+1]
GT1[/size].
Code:
R=30,P=25 to 40
S N N*25 N*25/R
1 29 725 24.2
2 14 350 11.7
3 9 225 7.50
4 7 175 5.83
5 5 125 4.17
6 4 100 3.33
7 4 100 3.33
8 3 75 2.50
9 3 75 2.50
10 2 50 1.67
11 2 50 1.67
12 2 50 1.67
13 2 50 1.67
14 2 50 1.67
15 1 25 0.83
16 1 25 0.83
17 1 25 0.83
18 1 25 0.83
19 1 25 0.83
20 1 25 0.83
21 1 25 0.83
22 1 25 0.83
23 1 25 0.83
24 1 25 0.83
25 1 25 0.83
26 1 25 0.83
27 1 25 0.83
28 1 25 0.83
29 1 25 0.83
30 0 0 0.00
Code:
R=60,P=20 to 40
S N N*25 N*25/R
1 59 1475 49.2
2 29 725 24.2
3 19 475 15.8
4 14 350 11.7
5 11 275 9.17
6 9 225 7.50
7 8 200 6.67
8 7 175 5.83
9 6 150 5.00
10 5 125 4.17
11 5 125 4.17
12 4 100 3.33
13 4 100 3.33
14 4 100 3.33
15 3 75 2.50
16 3 75 2.50
17 3 75 2.50
18 3 75 2.50
19 3 75 2.50
20 2 50 1.67
21 2 50 1.67
22 2 50 1.67
23 2 50 1.67
24 2 50 1.67
25 2 50 1.67
26 2 50 1.67
27 2 50 1.67
28 2 50 1.67
29 2 50 1.67
30 1 25 0.83
...
59 1 25 0.83
60 0 0 0.00
Notice how once you get to the "realistic" range of stint lengths (6 laps or more), the change in per-lap penalty for taking one less pitstop is less than 1 second. If you can gain more than 1 second per lap with softer tires, but need only 1 more pitstop, you will have a better average lap time.