Comments on: How Close is Close

By: 5harad

5harad — Fri, 08 Jun 2012 11:58:00 +0000

Yes, this approach could be used to make predictions earlier in the game as well. But the earlier you attempt to apply it, the better it would be to incorporate additional sources of information. For example, the current method suggests both teams have an equal likelihood of winning at the beginning of the game (before either team has scored), because it doesn’t incorporate factors such as team strength or home court advantage.

The heuristic outlined in this post is simply a fun rule-of-thumb for making predictions while you watch the game. If the goal is to achieve the best possible possible predictive accuracy, I’m sure one could do much better.

By: B_pengelly

B_pengelly — Thu, 07 Jun 2012 00:42:00 +0000

This article and research is all based on the last 12 minutes of a game. Is there any reason that this equation wouldn’t work just as well for the rest of the game? For example, would it be accurate after calculating 30 minutes left along with the current point margin?

By: Daniel Reeves

Daniel Reeves — Wed, 06 Jun 2012 00:32:00 +0000

Lots of options! Simplest might be WolframAlpha. Note also the widget I linked to in the comments above.

By: B_pengelly

B_pengelly — Wed, 06 Jun 2012 00:26:00 +0000

Ok, glad I wasn’t losing my mind. Now I have this new problem because neither versions of Excel prior to 2010 or Goog Docs can calculate ERFC functions when x is a negative number. Do you have any suggestions of calculators I can use to easily use this formula?

Thanks for taking the time to respond to my messages.

By: Daniel Reeves

Daniel Reeves — Wed, 06 Jun 2012 00:11:00 +0000

Oh! I bet my formula is for number of minutes, not seconds.
Yeah, here’s WolframAlpha confirming that’s true:

http://www.wolframalpha.com/input/?i=plot+1%2F2+Erfc%5B-%285%2F%28Sqrt%5B2%5D+%281.26336+%2B+1.61989+Sqrt%5Bt%5D+%2B+0.0642438+t+-+0.0010607+t%5E2%29%29%29%5D+from+1+to+12

I’ll edit my comment above. Thanks for catching that!
(Good thing Sharad didn’t let me include that in the post or it would’ve cost me $20 for the typo bounty!)

By: B_pengelly

B_pengelly — Tue, 05 Jun 2012 22:00:00 +0000

Maybe this could help dial in the issue. If I use the assumptions of a 5 point lead and 300 seconds left and only use the part of the equation after 1/2 ERFC, I get 7.54%. If that matches your results then the issue is clearly with my ERFC function. Is that what your equation gives you?

By: B_pengelly

B_pengelly — Tue, 05 Jun 2012 20:46:00 +0000

Yeah, Excel has the ERFC function. I also tried it in Google docs and got the same result. All my results end up being close to 50% no matter what time and score assumptions I use. Uggggg

By: Daniel Reeves

Daniel Reeves — Tue, 05 Jun 2012 20:01:00 +0000

Does Excel know the erfc function? If not you could find an approximation of it: http://en.wikipedia.org/wiki/Error_function

By: B_pengelly

B_pengelly — Tue, 05 Jun 2012 19:51:00 +0000

Thanks for providing this formula Daniel but for the life of me I can’t get it to work properly in Excel. Do you have any suggestions on how I can make it work? I will put in assumptions like 450 seconds remaining and up 5 pts and it will return a value close to 49%. I really want to figure this out.

By: Matthias Kullowatz

Matthias Kullowatz — Tue, 05 Jun 2012 19:36:00 +0000

Exactly. For instance, which team is actually the better team and which team is playing at home may have something to say about this. I put together a model for the Blazers for the 2009-2010 season that suggested when the Blazers were playing at home, they were able come back with a higher probability than when they were on the road. This was just one team in one season, but a more thorough, league-wide analysis may reveal the same conditional expectations.