Have you ever wondered what your odds were of winning a handicapped race?
We all know that the longer the race is, the more it favors the stronger player, but by how much???
Carter sent me the below Excel spreadsheet (that somebody obviously had way too much time on their hands to put together). If you plug in the two players’ handicaps in percentages (You’ll like this one, Bob!) then you can mathematically see how severely the weaker player’s chances of winning drop.
First, you’ll need to calculate the handicap percentages:
If Player A is racing to 3 and Player B is racing to 9, 3 is 25% of 12 (the total of the two handicaps) which becomes Player A’s handicap. Player B’s percentage will automatically formulate.
Enjoy!
What are your odds of winning?
Okay, I’m confused twice.
For one, 3 into 12 is four. Perhaps you meant 12 into 3, which would be .25 (25%).
Second: once we plug that in, what do we look at for the race? 3? 9? 12?
Okay, I fixed the text. Hope it makes more sense now.
First, click on the image to download the spreadsheet.
Once you plug in the percentage at the top, the first column in red/blue has races 1-13. The last red/blue column that reads “Odds that player A will win race” shows just that.
Hope this helps. Enjoy!
Right. Perhaps the toughest match for me (skill 7) in APA 8 ball is against skill 4, a 5-2 race. (That’s 2/7 = 28.57% for the underdog, according the spreadsheet.) The “Games to Win” in the APA race chart are rounded off to small integers (to limit match time), so some skill pairings favor the better player, while some skill pairings favor the better player less. I never did the math on this, but I think I am right about SL4 having a better chance against SL7, compared to SL6, SL5 or SL3 or SL2 against SL7.
Samm didn’t quite describe how to use the spreadsheet correctly.
Here’s my attempt:
You only have to enter one number: cell B2 – Player A’s odds of winning each game over Player B. The rest of the tables will fill out.
So if Player A is estimated to be stronger than Player B and should win 60% of the time, enter 60% in cell B2.
Player As odds of winning a race to 1 is 60%
Player As odds of winning a race to 2 is 64.8%
Player As odds of winning a race to 13 is 84.6232%
Notice if the players are very close competitively, say 51% to 49%, Player As odds of winning a race to 13 only goes up to 54.0231%.
But if Player A is much stronger than Player B, say 75% to 25%, Player As odds of winning a race to 13 is 99.6630%. So longer races pretty much guarantees a much stronger player will win but doesn’t make much difference when the players are comparable in strength.
This is just statistics. It doesn’t take into account things like hot and cold streaks, poor performance under pressure, etc. I think its still useful though, kind of like knowing your chances of winning at various games in a casino; you hope to beat those odds but still want to choose the games with the best statistical odds of winning.
I don’t get this, at all.
Help!?
Samm, Now you know why my 14.1 handicaps aren’t a linear function. I won’t bore you (or other readers) with the gory math details of spline geometry, monte carlo analyses & logarithmic functions…
In regards to Carter’s last comment, yes, it does indeed take into account hot and cold streaks, poor performance under pressure, etc.
That is all accounted for when you enter the winning percentage for player A.
Unless he meant strictly how Samm did it (Figuring the handicap based on the race)–but that’s not what the rest of his post was about.