Tuesday, June 20, 2017

The Basic Historical Strategies for CFR

This is the first in a planned 4-part series looking at the Historical Strategies I built for Championship Formula Racing and what I was thinking.  [ Historical Driver rules, video demo ]

Broadly, I tend to group strategies for CFR along a continuum defined by when in a race wear is spent.  On one end is the Front strategy where wear is mostly spent early in a race.  On the other end is the Back strategy where wear is spent late in a race.

A classic Front strategy would see a driver bid high for pole, start off fast, and spend more wear early.  When you see extreme examples of this, you will often see the driver run through half or more of their total wear through the first third of a race and end up with only a wear or 2 before the last third of the race.  A classic Back strategy would see the driver spend no wear at all for the first third of the race.  Spending most of their wear over the last half of the race.

So lets kick off the series by looking at each phase of three strategies that illustrate this continuum: Front A, Back Standard, and Even.

First a quick acknowledgement that these are not exactly the strategies that were published under these names.  Three minor editorial choices I've made since publication: 1) HDs can push start using only 1 green skill (the start speed test table changed a bit right before publication...); 2) I decided that the red skill chip could be used more places in relation to HD die rolls; 3) there were a few tactics that had 6 symbols on them and my BYO tool only allows for 5...  Links to these version in my BYO tool are at the end of this article.

Phase 1

The main way to measure a phase's intent is to look at the first starred and non-stared symbols in each tactic.  This gives you a sense of how much faster the car will likely try to go.  Think about it this way -- a car that wants to spend 1 wear in the upcoming corner will try to go 20 mph faster than a car that does not want to spend any wear, all other factors being equal.

If you then multiply each of those possible results by the odds of them being first choice, I get a net result of how much faster this car wants to go.  It might not be able to go that fast, but that's on the driver not the strategy.  I'm going to call this "net" in tables below.

Note that anything with 3 circles of any kind, should be considered starred because that is how the tracks are designed.  Also note, that if a tactic does not lead with a starred option, I'll count the first un-starred option for that tactics starred value since its more likely to be used.

Not Starred:
Front A: net +29 mph (52.9% +20, 47.2% +40)
Even: net +5 mph (72.3% +0, 27.8% +20)
Back S: net +0 (100% +0)

Front A: net +42 mph (52.9% +40, 27.8% +60, 19.4% +20)
Even: net +28 mph (58.4% +20, 41.7% +40)
Back S: net +5 mph (72.3% +0, 27.8% +20)

In the first phase we can also look to see how likely the car is to push it's start speed:
Front A: 92%
Even: 33%
Back S: 28%

Phase 2:

Front A stays faster here.  Note that Even is much faster in this phase if it has more wear than c.  Otherwise, Back S is actually faster under starred conditions.

Not Starred:
Front A net +38
Even (if w >= c) net +20
Even net +6
Back S net 0

Front A net +44
Even (if w >= c) +31
Back S net +20
Even net +14

Phase 3:

Even is now the faster strategy in this middle part of the race:

Not Starred:
Even net +34
Front A net +15
Back S net +11

Even net +34
Front A net +23
Back S net +26

Phase 4:

Lots of conditions here.  But in the end each strategy ends up being as fast as their remaining wear let them.  Without stars, if wear <= c their nets are between 17 and 20.  When wear >= c their nets rise to 20 to 32.  When wear >= 2c their nets are all +40.

But since Front A and Even have been faster earlier in the race, Back S is likely to be faster here with more wear to burn.

Strategy Trends

Over the course of a race, HDs will spend most of their time in phases 2-4.  So let's quick see each strategy's progression over time:

(Not Starred) phase 2 >> phase 3 >> phase 4
Front A net +38 >> +15 >> +17
Even net +6 >> +34 >> +20
Back S net +0 >> +11 >> +20

Some caveats... Front A cars often do not spend much time in phase 4 because Front A HDs often run out of wear early and skip out of phase 4 into phase 5 after a corner or 2.

Even HDs will likely be faster in phase 2 than net +6 because they will frequently have more wear than c and use net +20 options.

Back S' real speed will vary on how much it can save wear in the early race.  Save enough and it will skip into phase 4 early and spend at its higher rates of +32 or +40 for a while.

Hopefully that all made some sense and sounded like real CFR strategies at work.  Next up I'll discuss the variations on the Front A strategy.  Until then, feel free to tinker in the BYO tools with your own strategies.

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