Tyre Strategy: First Guess at a Strategy Model

Following on from a comment to How do you calcluate and optimal tyre stategy by Malcolm33, I had a go a putting together a Python script to identify the relative penalties accruing from different strategies compared to completing the race using an ideal, non-degrading tyre.

# Strategy Calculator
# Inspired by comment by Malcolm33 to 
# http://f1datajunkie.blogspot.com/2011/06/how-do-you-calculate-optimal-pit-stop.html?showComment=1309963019997#c2438489699153529837

tyredegradation={}
#Use a really crude tyre model for now: tyre degrades at additive rate 'phase 1 degradation' per lap
# until start of phase 2, then at incremental phase 2 degradation per lap
#The bias term rate base lap time of each tyre relative to best performing tyre
#tyremodel: bias, phase1 degradation, start of phase2, phase2 degradation
tyredegradation['H']=(1,0.05,99,0.05)
tyredegradation['S']=(0,0.1,15,0.5)
pitloss=12
pitstop=4
laps=52

pitTime=pitloss+pitstop

#If I'm right in remembering sum of i from 1 to N is 0.5*N(N+1)...
def stintTime(lapstodo,tyremodel):
 bias,ph1d,ph2s,ph2d=tyremodel
 if lapstodo < ph2s:
  t=bias*lapstodo+0.5*lapstodo*(lapstodo+1)*ph1d
 else:
  xlap1=ph2s-1
  xlap2=lapstodo-ph2s+1
  t=bias*lapstodo+ph1d*0.5*xlap1*(xlap1+1)+ph2d*0.5*xlap2*(xlap2+1)
 return t

#The strategy calculations sum the total "lost time" compared to completing race on best tyre
# with no pitstops, bias or degradation
#Strategies are calculated for each tyre combination and each possible stop combination
 
#One stop
strategies=[('H','S'),('S','H')]

for strategy in strategies:
 min=999
 t=0
 print "Strategy",strategy
 tph1,tph2=strategy
 for lap in range(1,laps-1):
  tp1=stintTime(lap,tyredegradation[tph1])
  tp2=stintTime(laps-lap,tyredegradation[tph2])
  t=tp1+pitTime+tp2
  #print 'One stop: stop on lap',lap,'timeloss:',t,'from phase 1',tp1,', phase 2',tp2
  if t < min:
   opt=(lap,t)
   min=t
 print 'Optimal 1-stop on',strategy,opt


#Two stop
strategies=[['H','S','S'],['H','S','H'],['H','H','S'],['S','S','H'],['S','H','S'],['S','H','H']]

for strategy in strategies:
 min=999
 t=0
 print "Strategy",strategy
 tph1,tph2,tph3=strategy
 for endstint1 in range(1,laps-1):
  for endstint2 in range(endstint1+1,laps):
   tp1=stintTime(endstint1,tyredegradation[tph1])
   tp2=stintTime(endstint2-endstint1,tyredegradation[tph2])
   tp3=stintTime(laps-endstint2,tyredegradation[tph3])
   
   t=tp1+pitTime+tp2+pitTime+tp3
   #print 'One stop: stop on lap',lap,'timeloss:',t,'from phase 1',tp1,', phase 2',tp2
   if t < min:
    opt=(endstint1,endstint2,t)
    min=t
 print 'Optimal 2-stop on',strategy,opt

#Three stop
strategies=[['H','S','S','S'],['H','S','S','H'],['H','S','H','S'],['H','S','H','H'],['H','H','H','S'],['H','H','S','H'],['H','H','S','S'],['S','H','H','H'],['S','H','H','S'],['S','H','S','H'],['S','H','S','S'],['S','S','S','H'],['S','S','H','S'],['S','S','H','H']]

for strategy in strategies:
 min=999
 t=0
 print "Strategy",strategy
 tph1,tph2,tph3,tph4=strategy
 for endstint1 in range(1,laps-2):
  for endstint2 in range(endstint1+1,laps-1):
   for endstint3 in range(endstint2+1,laps):
   
    tp1=stintTime(endstint1,tyredegradation[tph1])
    tp2=stintTime(endstint2-endstint1,tyredegradation[tph2])
    tp3=stintTime(endstint3-endstint2,tyredegradation[tph3])
    tp4=stintTime(laps-endstint3,tyredegradation[tph4])
    
    t=tp1+pitTime+tp2+pitTime+tp3+pitTime+tp4
    #print 'One stop: stop on lap',lap,'timeloss:',t,'from phase 1',tp1,', phase 2',tp2
    if t < min:
     opt=(endstint1,endstint2,endstint3,t)
     min=t
 print 'Optimal 3-stop on',strategy,opt

---

Here's what I get for a 52 lap race using the crude, guesstimated tyre model parameters shown above:

Optimal 1-stop on ('H', 'S') (33, 95.05)
Optimal 1-stop on ('S', 'H') (19, 95.05)
Optimal 2-stop on ['H', 'S', 'S'] (18, 35, 85.55)
Optimal 2-stop on ['H', 'S', 'H'] (18, 35, 96.69999999999999)
Optimal 2-stop on ['H', 'H', 'S'] (18, 35, 96.69999999999999)
Optimal 2-stop on ['S', 'S', 'H'] (17, 34, 85.55)
Optimal 2-stop on ['S', 'H', 'S'] (17, 35, 85.55)
Optimal 2-stop on ['S', 'H', 'H'] (17, 35, 96.69999999999999)
Optimal 3-stop on ['H', 'S', 'S', 'S'] (4, 20, 36, 88.5)
Optimal 3-stop on ['H', 'S', 'S', 'H'] (9, 25, 42, 97.5)
Optimal 3-stop on ['H', 'S', 'H', 'S'] (9, 25, 35, 97.5)
Optimal 3-stop on ['H', 'S', 'H', 'H'] (12, 29, 41, 107.6)
Optimal 3-stop on ['H', 'H', 'H', 'S'] (12, 24, 35, 107.6)
Optimal 3-stop on ['H', 'H', 'S', 'H'] (12, 24, 41, 107.6)
Optimal 3-stop on ['H', 'H', 'S', 'S'] (9, 18, 35, 97.5)
Optimal 3-stop on ['S', 'H', 'H', 'H'] (17, 29, 41, 107.6)
Optimal 3-stop on ['S', 'H', 'H', 'S'] (16, 25, 35, 97.5)
Optimal 3-stop on ['S', 'H', 'S', 'H'] (16, 25, 42, 97.5)
Optimal 3-stop on ['S', 'H', 'S', 'S'] (16, 20, 36, 88.5)
Optimal 3-stop on ['S', 'S', 'S', 'H'] (16, 32, 48, 88.5)
Optimal 3-stop on ['S', 'S', 'H', 'S'] (16, 32, 36, 88.5)
Optimal 3-stop on ['S', 'S', 'H', 'H'] (16, 32, 42, 97.5)

---

If you think I've messed this model up, please post a critical analysis of it in the comments:-)

A major issue is the simplicity of the tyre model. Even within the tyre model I've used, there may be "issues" with the parameters (incremental degradation rates, bias and phase boundary. Ideally, I'd be able to use practice timing data to tune these values (or even in race timing data), so suggestions for how to go about this would be appreciated. (You can get a link to the timing data as a spreadsheet from the Data page.)