Persberichten - Sponsorship - Assistant's Notes

Sponsorship - Assistant's Notes

First of all, thank you for mentioning me in your write up. However, I must stress that I only played a very small part in this after you had done all the hard work.

The credit is all yours, my friend.

I have done very similar work to establish formulae in other games in the past, so when I started reading your research notes I immediately recognised a sound mathematical approach, which gave me a lot of confidence that your interim results were accurate.

It was high quality work.

After reading your research notes I used your work to calculate what my current sponsor offer would have been if my rating were zero. This gave me 2 points, my current sponsor offer and the predicted zero rating offer.

I already had the view that the effect of rating on the sponsor offer was probably linear and if there were any possible exponential element it was likely to be small.

Since you only need 2 points to find a straight line I was immediately able to calculate the effect of rating on the weekly offer. Which was that the rating element of the offer was a simple multiplier of (1 + Rating/500).

This strongly suggested that the rating aspect was indeed linear. Although you would need 3 points to prove a straight line, the fact that it used simple rational constants (the 500) was strong evidence of a man made formula. I then made contact to confirm that we had the same result. We did.

My suggested formula was:

Weekly payment = 640/3 * C * (1 + R/500) * (1 + P)

Where P = 80% * (P1 + P2/2 + P3/4 + P4/8 ...)/100

(This eliminates the mathematical notation for the summation of a series, so is a little easier for most people to understand.)

My plain English explanation.

1. The basic weekly sponsorship offer with zero rating, 50 charisma and no PR manager is 640/3 * 50 = 32,000/3.

2. In order of importance this can be increased by driver rating (c. x13), PR managers (c. x2.5) and charisma (x2).

3. Increasing charisma from 50 to 100 will double the weekly sponsorship.

4. The first PR manager increases the basic offer by a maximum of 80%, then 40%, 20%, 10% and so on. The effect of each is PR rating/100. As jcgoble explains the theoretical maximum multiplier is 2.6. In practise it would be difficult to achieve much better than four 100 rated PR managers, which would give you a multiplier of x 2.5. (1 + 0.8 + 0.4 + 0.2 + 0.1)

5. The rating multiplier of (1+R/500) is limited by a maximum driver rating of around 6,000, so it's a little over 13.

Thanks again to jcgoble for all the hard work and especially for his generosity in publishing his work for everyone else's benefit.