If anyone is still confused on how to work out the math for multiple sets, here's an example.
Let's say Donny Mills and Siming Chen are gonna play another match,
but this time it's race to 50 per set, and first to win 3 sets.
Let's say you wanna figure out Donny's chances (you can pick either player) of winning the entire match.
Here's the steps you'd take:
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1. Go to
https://fairmatch.fargorate.com/ and click "
find a player" and find Donny's rating.
Then look up Siming's. Remember them or write them down.
2. Refresh the page, or click "home", to get back to that same page. This time click "
find match odds."
Put Donny's rating in the top left, and siming's in the top right. Or vice versa.
As of 3/20/19 that's
751 for Donny,
785 for Siming.
Now put in "50" for the race length, under both players, and click "
Calculate".
So Fargo predicts that Siming's chances are
88%, Donny's are
12%.
That's for a single set.
3. So now we can use a "binomial calculator" to figure out the rest. That sounds complex but it's not,
because there's a website that makes this easy.
Go to this page:
https://stattrek.com/online-calculator/binomial.aspx
Think of each set as a coin flip, except it's not a fair coin. It's weighted funny.
The coin comes up heads 88% of the time, and tails only 12% of the time.
We're talking about a race to 3 sets, which is the same thing as saying a best 3 out of 5.
So we're basically asking "what are the odds this coin will come up tails 3 out of 5 times?"
...for the sake of clarity, let's pretend they're gonna play out all 5 sets, no matter who wins each one.
4. So in the first blank, "
probability of success on a single trial", we put in .12
(same thing as 12%... donny's probability of success, in a single set).
The "
number of trials" blank should have 5, because we're talking about a best-of-5 series.
The "
number of successes" blank should have 3, because we're calculating the odds of Donny winning 3 (or more) of these sets.
5. Click "
Calculate".
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So the rest of the blanks show you results.
The result we're interested in is the very last blank. This shows Donny's odds of winning at least 3 sets.
It's shown as a decimal instead of a percent, so it shows
0.0143188992.
That's the same as saying
1.43%.
The first blank is like the odds of doing a weird prop bet where you stipulate that Donny wins EXACTLY
3 sets... no more, no less. So that's your odds of hitting the "exacta" bet. Around 1.33%.
The 2nd and 3rd blank are Siming's odds of winning, but 2 slightly different cases -
The first is betting she wins MORE than 3 sets (so if she gets exactly 3, the bet would be a push). That's 98.56%.
The second is betting she wins at LEAST 3 sets. Her odds are a little higher here,
because she can win 3, 4, or 5 sets (whereas in the previous set, just winning 3 sets was a push).
The 4th blank is just the inverse of the previous one. So if she's 99.9% to get 3 or more sets... she's 0.1% to lose 3 or more sets.