Deriving Team Total Value from Spread + Game Total (Ganchrow?)

[calm]

Let's say that Team A is facing Team B in the NBA. The game total is set at 200, and Team A is favored by 10 points. Thus I believe it's safe to say that the expected (?) outcome is a final score of 105-95 in favor of Team A.

Let's say we find a line of O/U 97 for Team B's total points. Does the following "work"?

We "set" Team A's points to 105, and then add the 97 representing the team total line we want to look at. This gives us a total of 202. Thus our bet on under 97 for Team B is essentially equivalent to a bet on under 202 for the total game. Plugging that into the half point calculator gives a fair value line of -118.8.

How accurate will this method be? Team A and B's team totals will be somewhat correlated due to factors such as pace, but will that have any effect on this calculation?

Edit: Obviously this won't work for something like football where points aren't evenly distributed, but what about basketball?

[SBR Lou]

Calm, I am no Ganch so I'm unsure how to take a stab at this mathematically, but I will say that in situations like this I generally won't take both bets. I know you mentioned game totals as an example, but the other day I liked a dog ML a little bit but felt their first half team total was a safer bet.

[HedgeHog]

Calm, the total of 200 is probably the more accurate line, especially if it appears in several places. I would simply bet Under 97 for Team B as you have an advantage there. To quantify that advantage is beyond me (other than to say it's 2 points better than 95--the expected total for Team B).

[Justin7]

If you're paying 10 cent-juice (e.g. laying -110), i'd bet any team total that looks 1.5+ points off. In your example where it is 2 points off, I'd consider it a play that will hit 54%.

[pico]

Let's say that Team A is facing Team B in the NBA. The game total is set at 200, and Team A is favored by 10 points. Thus I believe it's safe to say that the expected (?) outcome is a final score of 105-95 in favor of Team A.

Let's say we find a line of O/U 97 for Team B's total points. Does the following "work"?

We "set" Team A's points to 105, and then add the 97 representing the team total line we want to look at. This gives us a total of 202. Thus our bet on under 97 for Team B is essentially equivalent to a bet on under 202 for the total game. Plugging that into the half point calculator gives a fair value line of -118.8.

How accurate will this method be? Team A and B's team totals will be somewhat correlated due to factors such as pace, but will that have any effect on this calculation?

Edit: Obviously this won't work for something like football where points aren't evenly distributed, but what about basketball?

i have a feeling you're looking at mav utah game

9:05 pm (NBA)
703 Dallas Mavericks +220 97
704 Utah Jazz -6½ 200½ -260 103½

the book expect the final to score to be around 103.5 to 97 with some degree of error

i don't really understand your question, but i'll be waiting for ganch's reply.

come to think of it, mav played a long game aginst the lakers, so they might not be defending that hard today. utah over 103.5 seems like a good play here.

[LT Profits]

No Pico,

The OP is talking about a case where Team A is -10 over Team B, the total on the game is 200 (which SHOULD translate to Team A 105, Team B 95), and the team total for Team B is 97 (two point variance from derived total).

[Ganchrow]

Let's say that Team A is facing Team B in the NBA. The game total is set at 200, and Team A is favored by 10 points. Thus I believe it's safe to say that the expected (?) outcome is a final score of 105-95 in favor of Team A.

It's a commonly held misconception that under market efficiency game lines (be they spreads or totals) correspond to expected outcomes. Rather games lines really correspond to median outcomes. (This is the difference between setting a game line to minimize mean square error and setting a game line to minimize mean absolute error.) Generally speaking, the expected deviation of a game total will be higher than the median deviation. This is because in most sports the distribution of game totals is positively skewed due to the fact that while there is a lower bound to possible total scores (0 or 1 depending upon whether or not ties are permitted) there is (at least in theory) no upper bound.

In the NBA totals market for example, over the 20,559 games for which Covers has a listed total, the average deviation between score and game total is about 0.3923 points while the median deviation is 0 points.

Let's say we find a line of O/U 97 for Team B's total points. Does the following "work"?

We "set" Team A's points to 105, and then add the 97 representing the team total line we want to look at. This gives us a total of 202. Thus our bet on under 97 for Team B is essentially equivalent to a bet on under 202 for the total game. Plugging that into the half point calculator gives a fair value line of -118.8.

How accurate will this method be? Team A and B's team totals will be somewhat correlated due to factors such as pace, but will that have any effect on this calculation?

To be perfectly honest I haven't spent much time on team totals but I think the real problem here is that you can't overlook the correlation effect (to which you alluded) without "breaking" these calculations. In the NBA there is substantial positive correlation between game opponents' results versus their imputed team totals -- a correlation coefficient in the neighborhood of about 40%.

Technically speaking, however, the issue isn't just one of correlation but rather of the lack of independence because team scores (even if deviations were uncorrelated they still might not be independent).

So even though the probability of Team B scoring > 96 points may indeed be 50%, the probability of Team B scoring > 96 points conditioned on Team A scoring (say) 106 points could very well be different than 50%. As such it's entirely likely that using the HPC as you've described will produce biased estimates.

[calm]

Ganch,

Thanks for the response.

It's a commonly held misconception that under market efficiency game lines (be they spreads or totals) correspond to expected outcomes. Rather games lines really correspond to median outcomes. (This is the difference between setting a game line to minimize mean square error and setting a game line to minimize mean absolute error.) Generally speaking, the expected deviation of a game total will be higher than the median deviation. This is because in most sports the distribution of game totals is positively skewed due to the fact that while there is a lower bound to possible total scores (0 or 1 depending upon whether or not ties are permitted) there is (at least in theory) no upper bound.

In the NBA totals market for example, over the 20,559 games for which Covers has a listed total, the average deviation between score and game total is about 0.3923 points while the median deviation is 0 points.

Yeah, I wasn't sure whether to write expected or median, and I obviously picked the wrong one.

To be perfectly honest I haven't spent much time on team totals but I think the real problem here is that you can't overlook the correlation effect (to which you alluded) without "breaking" these calculations. In the NBA there is substantial positive correlation between game opponents' results versus their imputed team totals -- a correlation coefficient in the neighborhood of about 40%.

Technically speaking, however, the issue isn't just one of correlation but rather of the lack of independence because team scores (even if deviations were uncorrelated they still might not be independent).

So even though the probability of Team B scoring > 96 points may indeed be 50%, the probability of Team B scoring > 96 points conditioned on Team A scoring (say) 106 points could very well be different than 50%. As such it's entirely likely that using the HPC as you've described will produce biased estimates.

Thanks for your thoughts. What does HPC stand for? Didn't realized there was a name for this type of analysis. I was afraid it wouldn't be accurate enough, so I guess I'll have to wait til I finally learn how to program to get my hands on some data.

[Ganchrow]

What does HPC stand for?

HPC is the ultra-technical term for Half-Point calculator.

That's in rot-13.