Tomorrow morning we get geared up and start hiking the Inca trail that will end at Machu Picchu on Friday.  That was the main reason for this trip.  So no communication until Friday night at the earliest.

One Saturday I am leaving for Peru where I will be hiking the Inca Trail to Machu Picchu.   From Miami I’ll fly overnight to Lima and then on to Cusco on Sunday Morning.  We’ll tour through some of the sites of the Urubamba Sacred Valley on our way to the where we’ll stay in Urubamba.  You need to acclimate to the altitude so we don’t start the hike for a couple of days.  The second day will be white water rafting and more of the Sacred Valley sites.  Then we start the 4 day hike that ends at Machu Picchu.  We’ll spend a final day in Cusco, the former capital of the Inca empire.
I’ve been climbing stairs in preparation for the last 8 months so I am looking forward to getting to the real thing.  There certainly won’t be internet connections on the hike itself but I should be able to give updates from the hotels before and after as time allows.

So I was thinking about ways to test this belief.   Pondering that lead me to look at the line.  The line is approximately unbiased. If you look at the bias numbers they are historically centered around zero.  That in itself goes a long way towards explaining why it is hard to be much better than 50% betting against the line.  But then if  you look at the absolute error there appears to be a disconnect.  On average the bias is close to zero while the average absolute error is 10-11 points.   So even though the difference between the line and actual score is close to zero on average, the line is off by 10 points or more more than 50% of the time.  That is mind blowing when you think about it.  Shouldn’t that imply that there is a lot of opportunities to beat the spread?  If the line is off by so much so often then why can’t someone or some system consistently find those holes?  Personally, I think it goes back to my original theory, that the difference between the line and the actual score is random and centered close to zero.

So I started to think of any ways that you might at least be able to reduce the amount of this somewhat extreme variability or random error.  It seemed clear that the most likely candidate was turnovers, which are generally considered to be random bounces of the ball.   Hmm, random error, random turnovers, sounds like there could be a connection.  The problem was I don’t collect individual game statistics so I couldn’t investigate this idea.  I eventually  found a source of data so that I could look at the 2010 season.  What I found was that the turnover margin in a game explained roughly 40% of the difference between the line and  the actual outcome.  I got very excited.  The 2011 preseason was about to start so I needed  to   come up with a system that incorporated the turnovers along with the scores.  So what I did  was very simple.  I just added it as a new variable in the least squares regression model that I have been running for years. For these models the outcome is the score differential.  The variables are a matrix of the games.  For each game a variable for the home team is equal  to 1, and the variable for the road team is equal to -1.  All other team variables have a value of zero.  To this I added the turnover margin for the game.  I knew the results early  in season would be meaningless because this system is based only on games of the current year.   So it could take some time before it became stable.  When it did kick in it really kicked in.  As you can see from the NFL prediction tracker results page this new system came in first place in 3 out of the 5 categories over the second half of the season.

I’m digging into the numbers a little bit more here after the season is over.  Looking at the actual regression models for this season the turnovers explained a little less than 40% of the error in the line, but it was consistently in the 35-40% range all season long.  If you look at the regression models with and without the turnover variable.  The R-square of the model with turnovers is 0.60 and the R-square of the model without the turnover variable is 0.33.  That is a very large difference for only adding one variable to a model.  But of course predicting future games is very different from fitting prior games.  So I was never expecting to see the mean error in predictions to drop by 40%. That would mean reducing it from 10 points a game down to about 6.   So how well did it improve the original least squares predictions?  In straight up game winners it was 4 games better. Against the spread it was 11 games better. For absolute error it was a about a 6.8% improvement, and for mean square error it was an 11% improvement.  So all in all I think the results were very good.  Now it will be interesting to see if the results are repeatable year to year.

My original thought was to go another step in first trying to predict the turnover margin in a game and then plug that into the model to see if that further improved the predictions.  The problem was that I wasn’t able to find a way to reliably predict a turnover margin between two teams.  That does appear to be pretty random.  So for now the predictions from this model are predictions assuming that the turnover margin will be zero.  If you are curious, a turnover was worth an average of 4.53 points this past season.  So if a team was favored to win by 3 points and they were +1 in turnovers in the game the averaged a win by 7.5 points.  If they were a 3 point favorite and -1 in turnovers in the game then they averaged losing by 1.5 points.  So you see why the favorites don’t always win.  A 3 point favorite that loses the turnover game loses the game.  A touchdown favorite can loose a game by being -2 in turnovers.  The average turnover margin was +0.21 in favor of the home team, so I could have possibly tried adding .21*4.53=0.95 points to each home team.

I’d be interested in hearing anyone’s thoughts for or against my theory of the winner against the spread being random or any other ideas the explain even more of the error in the line.

For the season, when p(cover) was > .55 the record was 61.5%, when p>.60 the record was 65.8%,
when p>.65 the record was 70.3%, when p>.70 then record was 74.7%.
Definitely good results. Hopefully next season can duplicate this. But I do remain skeptical. Overall the mean prediction was 58.1% which is unusually high. So I think a large part of it was that it was just a lucky year.

home           p(win)   p(cover)      road       p(win)   p(cover)    line    lineavg                                                   

N.Y. Giants   0.53170    0.41657   Atlanta      0.46830    0.58343     3.0    0.82229
Denver        0.27348    0.57908   Pittsburgh   0.72652    0.42092    -8.5   -6.38467
New Orleans   0.79020    0.42735   Detroit      0.20980    0.57265    10.5    8.55825
Houston       0.67296    0.52623   Cincinnati   0.32704    0.47377     4.0    4.68853

 home           p(win)  p(cover)  road            p(win)  p(cover)   line   lineavg                                                     

 Green Bay     0.74835   0.84077  Detroit        0.25165   0.15923   -3.5    7.1342
 Houston       0.71324   0.80163  Tennessee      0.28676   0.19837   -3.0    5.9335
 New Orleans   0.86991   0.64128  Carolina       0.13009   0.35872    8.0   11.7889
 Oakland       0.49489   0.38231  San Diego      0.50511   0.61769    3.0   -0.1341
 Minnesota     0.43551   0.39824  Chicago        0.56449   0.60176    1.0   -1.6993
 St. Louis     0.10937   0.40242  San Francisco  0.89063   0.59758  -10.5  -13.1400
 Arizona       0.51827   0.40405  Seattle        0.48173   0.59595    3.0    0.4762
 New England   0.88977   0.58790  Buffalo        0.11023   0.41210   10.5   12.8252
 Atlanta       0.89942   0.58358  Tampa Bay      0.10058   0.41642   11.5   13.7745
 Jacksonville  0.70473   0.58012  Indianapolis   0.29527   0.41988    3.5    5.6071
 Denver        0.66462   0.55512  Kansas City    0.33538   0.44488    3.0    4.4514
 N.Y. Giants   0.57280   0.45760  Dallas         0.42720   0.54240    3.0    1.8984
 Cleveland     0.23363   0.47898  Pittsburgh     0.76637   0.52102   -7.0   -7.5473
 Cincinnati    0.43904   0.51570  Baltimore      0.56096   0.48430   -2.0   -1.5916
 Philadelphia  0.79943   0.51173  Washington     0.20057   0.48827    8.5    8.8084
 Miami         0.58301   0.48860  N.Y. Jets      0.41699   0.51140    2.5    2.2000

 home           p(win)  p(cover)  road            p(win)  p(cover)   line   lineavg                                                     

 Indianapolis  0.14238   0.33667  Houston        0.85762   0.66333   -7.0  -11.5531
 Kansas City   0.51407   0.41908  Oakland        0.48593   0.58092    2.5    0.3682
 Buffalo       0.46267   0.57666  Denver         0.53733   0.42334   -3.0   -0.9794
 N.Y. Jets     0.67304   0.56366  N.Y. Giants    0.32696   0.43634    3.0    4.6692
 Tennessee     0.73163   0.45831  Jacksonville   0.26837   0.54169    7.5    6.4131
 Washington    0.69951   0.45875  Minnesota      0.30049   0.54125    6.5    5.4255
 Pittsburgh    0.94527   0.53214  St. Louis      0.05473   0.46786   16.0   16.8491
 New England   0.83880   0.53074  Miami          0.16120   0.46926    9.5   10.3032
 Dallas        0.58295   0.52631  Philadelphia   0.41705   0.47369    1.5    2.1901
 Green Bay     0.88152   0.47753  Chicago        0.11848   0.52247   13.0   12.4087
 Seattle       0.38655   0.48012  San Francisco  0.61345   0.51988   -2.5   -3.0227
 Carolina      0.77352   0.51927  Tampa Bay      0.22648   0.48073    7.5    8.0163
 Baltimore     0.89135   0.51585  Cleveland      0.10865   0.48415   12.5   12.9159
 Cincinnati    0.66302   0.51379  Arizona        0.33698   0.48621    4.0    4.3581
 New Orleans   0.72538   0.48773  Atlanta        0.27462   0.51227    6.5    6.1826
 Detroit       0.58328   0.48962  San Diego      0.41672   0.51038    2.5    2.2247

I’ll be heading home for the holidays Tuesday night. So things could get updated slowly.