1 point lines in American sports

[GOJONNY]

I've been quite a successful gambler across a number of sports, mainly tennis and rugby union, but it amazes me how the American handicappers always seem to get the lines within 0.5-1.5 points of the actual results. In rugby union you'll be lucky to see many games fall close to the line, and if they do, it's just luck. Most of the time it's quite easy to get an edge.

I imagine no insiders here would give anything away, but I'm just curious how they would do it - just a simple backlog of mathematical data that they use to determine it? How long does it take to spit out a probability of a line occurring?

This was my first year of betting on NBA and I struggled in the middle part of the season and started to get some money back over the past month or so. It turns out the principles I learned about value in other sports don't apply to NBA - anyone who can hit 54%+ over 5 years + is a genius.

[Arnold]

but it amazes me how the American handicappers always seem to get the lines within 0.5-1.5 points of the actual results.

What do you mean 0.5-1.5 points? The standard deviation of pointspread and the actual spread is around 9 or so (in the NBA).

[GOJONNY]

Yeah but that SD would be skewed by the amount of dogs that get up. What are the stats whenever a favourite wins?

And that's not taking into account the over/under lines on NBA - ridiculous how many times that falls within 1 point. I just hope it never happens in other European sports, but I guess it will soon and betting will no longer be profitable.

[LT Profits]

NBA Favorites that have won straight up this season have gone 594-213-17, 73.6% ATS with an average Pointspread Variance of +5.43 points.

[jstblaze]

question?

LT?

Just to clarify so i dont misunderstand, you are saying that for the favorites that won ATS, they won by an average of 5 points greater than the spread?

thanks.

[LT Profits]

Correct jst.

[LT Profits]

Actually, hold the phone jst.

That +5 variance was for all games where the favorite won outright, whether they covered the spread or not. If you took only the games where the favorite covered, the variance would be much higher.

[jstblaze]

wow, thats pretty significant variance. more than i would have expected.

but i have been betting many heavy favorites this year, like the Lakers and Boston (more so in the first half), and I have ebeen surprised how often these heavy favorites are consistantly covering -11 point lines, by winning by 17-20.

from a non-cappers perspective (i try soemtimes, but just am not adept enough) so if you think you can weed out the the game where the favorite is to be upset, then betting with the favorite on the rest of the games, provides you a statistical advantage.

obviously this banks on you being able to cporrectly pick which underdogs are going to be able to win outright, and not bet on those games. (or bet the other way i guess)

[LT Profits]

Actually the variance makes sense when you consider that the variance for all NBA games this season regardless of winner is around 9 points, as Arnold has already pointed out.

[Ganchrow]

The term "variance" has a very specific meaning in statistical analysis, namely the sum of the squared deviations of each observation from the mean.

You guys appear to be talking about the average margin of victory, which is completely distinct from the variance.

[jstblaze]

i dont htink they were talking margin of victory. we are comparing margin of victory to the spread.

so that would be average deviation from the actual point spread.

so it is along the same lines as variance and is represenattive of a similar purpose, just not the same thing.

[Ganchrow]

i dont htink they were talking margin of victory. we are comparing margin of victory to the spread.

so that would be average deviation from the actual point spread.

so it is along the same lines as variance and is represenattive of a similar purpose, just not the same thing.

Excuse me, "the average deviation of margin victory from the spread".

This is still completely distinct from variance, which has a very specific meaning.

Now if you were to take the sum of the squared deviation of margin of victory from the spread, then you'd be dealing with the same units as variance. This known as the "sum of squared errors" or simply SSE. Take the square root of the average and it's called "root mean square error" or RMS.

[Ganchrow]

The difference between summing the errors and summing the squared errors is two-fold:

1. When you square a real number the result is always positive. This means that observed values on opposing side of the mean (or in this case on either side of the spread) won't cancel one another out. For example, if given a spread of 11, half the time the favorite won by 1 and the other half the favorite won by 21, then by taking the simple sum of deviations the two would cancel one another out ((21-11) + (1-11) = 0), implying a level of precision of where none actually existed. By taking the sum of the square deviations ((21-11)² + (1-11)² = 200) the error in the estimate of the spread 11 becomes apparent.
2. By squaring deviations you're including what amounts to a penalty term to the variance measure, where the further an observation is from the mean, the more it impacts the SSE. So while an observed MOV 1 point from the spread will impact the variance by 1² = 1, an observed MOV 2 point from the spread will impact the variance by 2² = 4, or 4 times as much.

[donjuan]

Just to clarify, a game that lands on or close to the point spread for the game does not necessarily indicate that the spread was efficient ("correct") for the game.

[GOJONNY]

Interesting stats guys - thanks for the research. Favourites that win SU win 73% ATS is still pretty sharp, much lower I imagine than in other sports like rugby.

Anyone got stats on the over/unders and how far they deviate (on average) from the lines? Also, is there any site I can use to test parameters on data myself?

What's the % like of wins ATS on favourites and underdogs overall?

[donjuan]

Favourites that win SU win 73% ATS is still pretty sharp

This has nothing to do with the sharpness of the lines but rather how evenly matched the teams are. If you get the Crusaders playing the Lions, Cheetahs or Reds in Christchurch every weekend then they're going to win less often ATS when they win SU than if it's Brumbies vs. Waratahs in Canberra.

[GOJONNY]

How about when there is a mismatch between two teams - say NY @ Boston in a 100% motivation match and the line is set at -19.5 - bookies would never offer say 25.5 or 30.5, even if their analysis concludes that it would be a fair line. So I dunno, maybe one-sided matches see the faves more likely to cover.

But yeah the over/unders analysis would be good - which sites do you guys use to analyse such trends quickly and effectively?

[bettilimbroke999]

I agree the over/unders stats would be nice to see, the NBA totals have been absolutely razor sharp in the past few months hitting within .5-1 pts on half lines at an incredible pace, makes you feel like you scalp a point you've got a great chance of winning lately.

[donjuan]

the NBA totals have been absolutely razor sharp in the past few months hitting within .5-1 pts on half lines at an incredible pace

As I stated earlier in the thread, this has nothing to do with how sharp (efficient) the lines are.

[Data]

As I stated earlier in the thread,

The earlier statement, where you said "not necessarily", was technically correct yet somewhat pointless. The statement below, where you said "nothing", is plain wrong.

this has nothing to do with how sharp (efficient) the lines are.

[Ganchrow]

I agree the over/unders stats would be nice to see, the NBA totals have been absolutely razor sharp in the past few months.

From the 1990/1-2006/7 season the root mean square error of the deviation between closing total and actual realized total score has been 17.45 points over 19,939 games.

For the 2007/8 the same statistic has had a value of 17.99 points over 1,237 games which is nominally higher (implying generally less "accurate") than that of the immediately preceding 17 seasons.

[donjuan]

Data,

It is a common misconception that a line was "correctly set" if the final score lands on or very close to the O/U or spread when in reality the final score is simply a point on a probability distribution. As well, "sharp" lines aren't meant to predict the final outcome but rather to have the final outcome land on both sides evenly (or x% of the time for MLs).

[Data]

Data,

It is a common misconception that a line was "correctly set" if the final score lands on or very close to the O/U or spread

Perhaps you were referring to the NFL lines but for the NBA lines discussed here, this is not a misconception.

when in reality the final score is simply a point on a probability distribution. As well, "sharp" lines aren't meant to predict the final outcome but rather to have the final outcome land on both sides evenly (or x% of the time for MLs).

True. Due to Gaussian nature of basketball scores distribution that means that the sharper the line the more likely the game will land on/close to it.

[donjuan]

Perhaps you were referring to the NFL lines but for the NBA lines discussed here, this is not a misconception.

For NBA lines it is as well. I'm talking about single games or small sample sizes, not over a long season. You'll see people say the line for a game was sharp if the final score lands on it for that game. That is ridiculous as it is just a point on a distribution for that particular game. Now if you are saying that lines at one book land on the spread (for NBA) 5% of the time and at another book 3% of the time over a reasonably large sample size, then of course the one that lands on the number 5% of the time is sharper. However that is not what I disagreed with. What I disagreed with was this:

the NBA totals have been absolutely razor sharp in the past few months hitting within .5-1 pts on half lines at an incredible pace

[bettilimbroke999]

From the 1990/1-2006/7 season the root mean square error of the deviation between closing total and actual realized total score has been 17.45 points over 19,939 games.

For the 2007/8 the same statistic has had a value of 17.99 points over 1,237 games which is nominally higher (implying generally less "accurate") than that of the immediately preceding 17 seasons.

I appreciate your input Ganchow you're clearly an intelligent individual. Perhaps the lines aren't as accurate as I thought and I have just been wagering on some of the more accurate totals and my opinion is skewed based on those games.

[Data]

What I disagreed with was this:

the NBA totals have been absolutely razor sharp in the past few months hitting within .5-1 pts on half lines at an incredible pace

I am not arguing with you on this but with what you said below:

this has nothing to do with how sharp (efficient) the lines are.

The irony is that these two statements are very similar as they both completely disregard one of the two possible causes of the observed phenomenon - randomness and line sharpness. Since we cannot reject any of these two causes due to the small sample size, we must conclude that both statements are wrong.

[Data]

From the 1990/1-2006/7 season the root mean square error of the deviation between closing total and actual realized total score has been 17.45 points over 19,939 games.

For the 2007/8 the same statistic has had a value of 17.99 points over 1,237 games which is nominally higher (implying generally less "accurate") than that of the immediately preceding 17 seasons.

I think that does not account for the change in year-to-year actual results variances. The year with higher variance will produce the higher RMSE as well but that does not mean that the sharpness of the lines decreased.

I like comparing correlation coefficients between the actual results and the lines. Are there any pitfalls in this method?

[Ganchrow]

I think that does not account for the change in year-to-year actual results variances. The year with higher variance will produce the higher RMSE as well but that does not mean that the sharpness of the lines decreased.

So feel free to net out the realized score variance if that's what you need. It's akin to the difference between the the residual sum of squares and the total sum of squares. Take 1 minus the ratio of the former to the latter and you have a theoretical coefficient of determination (R²).

There are obviously numerous other possible measures of the nebulous concept of "accuracy". A practitioner's ultimate choice of measure should be dependent on the reasons for which he's trying to gauge "accuracy" in the first place.

I like comparing correlation coefficients between the actual results and the lines. Are there any pitfalls in this method?

I can't say that I immediately see any particularly compelling advantages of using such a metric.

[Data]

A practitioner's ultimate choice of measure should be dependent on the reasons for which he's trying to gauge "accuracy" in the first place.

Lets stick to the example you provided. We want to compare the accuracy of this year lines and previous year lines. What method should we use? Again, it seems that your example with RMSE tells us nothing.

[Ganchrow]

Lets stick to the example you provided. We want to compare the accuracy of this year lines and previous year lines. What method should we use? Again, it seems that your example with RMSE tells us nothing.

You are certainly entitled to your opinion.

[Data]

You are certainly entitled to your opinion.

That did not help much. Well, at least you gave me a push to learn that whatever I did not like in your example is called a violation of homogeneity of variance.

[Ganchrow]

I provided one possible measure of "accuracy". There are many. My goal was not to write a definitive treatise on how one should judge "accuracy" but rather introduce the very widely used notion of taking the root mean square error as a metric for the total "value" of an estimator. If you're looking for an in-depth discussion of this topic I'd probably recommend an econometrics textbook. This is a very good one.

The concept to which you're referring is known as heteroscedasticity and it may or may not be of concern depending on how one wishes to judge "accuracy". (Let's also not forget that heteroscedasticity would come into play insofar as we'd expect the variance of a higher total to be greater than that of a lower total.)

If you did take into account differing tranche variance then you'd be measuring the value of the estimator qua estimator. If you didn't take into account tranche variance then you'd measuring the overall value of the estimator as a predictor of the event in question without regard to the particular attribution of variance.

Consider the science of meteorology. It's generally easier to predict the weather in certain locations than others. Imagine two locations, A and B, where location A has much more easily predictable weather measurement than location B. However, the weather prediction technology used at location B is slightly more advanced than that at location A implying less residual variance (i.e., after adjusting for the variance of the regressor, which is the inherent variability in the weather at each location).

So ... where is weather prediction more accurate? Location A or location B? Well it depends on which you mean by "accurate"? From the standpoint of "goodness" of the estimation methodology the answer is clearly at location B. However, from the standpoint of where you'd feel more comfortable scheduling a picnic based on a weather forecast, there answer may well be at location A.

Within this framework there's no royalty to the term "accuracy". The way you choose to measure accuracy will be a function of your intended usage of that metric.