I’m happy to announce that today I’ve released the second volume of the series “Great Formulas Explained”. The aim of the series is to gently explain the greatest formulas the fields of physics, mathematics and economics have brought forth. It is suitable for high-school students, freshmen and anyone else with a keen interest in science. I had a lot of fun writing the series and edited both volumes thoroughly, including double-checking all sources and calculations.
Here are the contents of More Great Formulas Explained:
Part I: Physics
Law Of The Lever Sliding and Overturning Maximum Car Speed Range Continued Escape Velocity Cooling and Wind-Chill Adiabatic Processes Draining a Tank Open-Channel Flow Wind-Driven Waves Sailing Heat Radiation Main Sequence Stars Electrical Resistance Strings and Sound
Part II: Mathematics
Cylinders Arbitrary Triangles Summation Standard Deviation and Error Zipf Distribution
Part III: Appendix
Unit Conversion Unit Prefixes References Copyright and Disclaimer Request to the Reader
I will post exerpts in the days to come. If you are interested, click the cover to get to the Amazon product page. Since I’m enrolled in the KDP Select program, the book is exclusively available through Amazon for a constant price of $ 2.99, I will not be offering it through any other retailers in the near future.
Remember what Benjamin Franklin once said: “Knowledge pays the best interest”. An investment in education (be that time or money) can never be wrong. Knowledge is a powerful tool to make you free and independent. I hope I can contribute to bringing knowledge to people all over the world. In the spirit of this, I have permanently discounted this book, as well as volume I, in India.
The Elo rating system is a commonly applied tool to judge the performance of players in sports. Most associate it with chess, but it is in use in other sports as well, for example American Major League Baseball and Basketball. A nice thing about the rating system is that you can easily estimate the win probabilities given the difference in Elo rating of the opponents.
So if the difference is zero (opponents of equal strength), the win probability is obviously 0.5 = 50 %. If one player has a 200 Elo points advantage, his win probability is about 76 %. In case you prefer a table over a graph, you can find the corresponding values here. And for those interested in formulas, I found that the Boltzmann function models the values extremely well (r stands for Elo rating, p for the win probability):
p = 1 – 1 / ( 1 + exp ( 0.00583 * r – 0.0505) )
For example, plugging in r = 200 leads to p = 0.75 = 75 %, close enough. For a very rough linear approximation this formula will do:
p = 0.5 + 0.001 * r
By the way, what sports event is happening right now in India? Right, the World Chess Championship. At the moment Anand and Carlsen are locked in a bitter battle to death (ok, a little too dramatic, but still very interesting) and I just finished watching their brilliant third match, which was yet another draw. Here’s the current top ten for chess:
As you can see, Carlsen is currently the leading chess player with an Elo rating of 2870 and Anand is on rank eight with a rating of 2775. The difference is 2870 – 2775 = 95 points, which translates into a win probability of about 63 % for Carlsen and 37 % for Anand. If you have to bet, bet on Carlsen, but it’s going to be a close one. Both have shown a great performance so far, though it seemed that in the third match Anand did miss some opportunities. I’m looking forward to tomorrow’s match.