Dopamachine

Week 12 NFL Predictions (model v1.1)

2009-11-28T23:21:00.008-05:00

I tweaked the model somewhat. While I have not fully minimized the extremely high/low probability scenarios, those will occur less often in the current version of the model (1.1). This model will still tend to pick the same winners as the previous version, but the predicted scores and win probabilities are somewhat different.

The difference between this version and the previous is actually more of a bug correction than a substantive change. The previous version used each team's average score for the season to that point as a starting point. It then shifted that starting point up or down based on how well the team does relative to an overall average of teams along with factors related to the specific opponent. Therefore there was some redundancy such that a team that is better than average will start with a better than average score and then be further shifted up. So this version starts everyone at the overall average and simply shifts that value based on how well a given team has been doing and the specific opponent. It's a subtle distinction, but one that should predict fewer blowouts. That appears to be the case. Below are predictions using v1.0 and then v1.1. I added the predicted margin along with the point spread set by Vegas to see how the model does not just in terms of picking winners but against the spread (ATS).

Version 1.0

Away	Home	Away Score	Home Score	Away probability	Predicted Margin	Vegas Spread
Packers	Lions	39	16	0.97	-23	-10
Raiders	Cowboys	13	27	0.18	14	13.5
Giants	Broncos	28	18	0.8	-10	-6.5
Browns	Bengals	15	26	0.22	11	13.5
Buccaneers	Falcons	15	36	0.06	21	12
Dolphins	Bills	28	14	0.87	-14	-3
Seahawks	Rams	23	11	0.82	-12	-4
Panthers	Jets	16	23	0.26	7	3
Redskins	Eagles	10	28	0.07	18	9
Colts	Texans	31	19	0.85	-12	-3.5
Chiefs	Chargers	12	34	0.006	22	13.5
Jaguars	49ers	19	22	0.39	3	3
Cardinals	Titans	34	21	0.82	-13	3
Bears	Vikings	19	40	0.05	21	11
Steelers	Ravens	20	23	0.42	3	2.5
Patriots	Saints	35	46	0.23	11	2

These picks are not particularly controversial but several of the probabilities tend to be extreme.

Version 1.1

Away	Home	Away Score	Home Score	Away probability	Predicted Margin	Vegas Spread
Packers	Lions	35	18	0.93	-17	-10
Raiders	Cowboys	9	26	0.09	17	13.5
Giants	Broncos	23	22	0.56	-1	-6.5
Browns	Bengals	12	26	0.13	14	13.5
Buccaneers	Falcons	19	33	0.14	14	12
Dolphins	Bills	26	19	0.71	-7	-3
Seahawks	Rams	25	14	0.81	-11	-4
Panthers	Jets	17	24	0.29	7	3
Redskins	Eagles	14	23	0.2	9	9
Colts	Texans	26	18	0.77	-8	-3.5
Chiefs	Chargers	16	29	0.05	13	13.5
Jaguars	49ers	20	23	0.41	3	3
Cardinals	Titans	31	21	0.76	-10	3
Bears	Vikings	20	31	0.18	11	11
Steelers	Ravens	19	21	0.44	2	2.5
Patriots	Saints	28	32	0.41	4	2

In the second set of predictions the average absolute value of the point difference is 9.25 compared to 13.44 in the first version. Neither value is necessarily clearly better. The average margin of victory for the last two weeks were 9.38 and 8.19, but three weeks ago it was 13.92.

I hope to make a few additional changes soon, but I wanted to get these numbers up before the majority of the games were played.

Football Prediction Model v1.0

2009-11-22T18:12:00.013-05:00

Before going into the mechanics of the model, I want to examine the accuracy of the predictions this week:

Teams	Predicted Score	Actual Score	Predicted Probability
Dolphins	29	24	.72
Panthers	21	17

Redskins	9	6
Cowboys	26	7	.90

Browns	8	37
Lions	14	38	.74

49ers	18	24
Packers	28	30	.86

Steelers	27	24	.94
Chiefs	9	27

Falcons	31	31	.54
Giants	30	34

Saints	48	38	.95
Buccaneers	16	7

Bills	14	15
Jaguars	21	18	.69

Colts	30	17	.71
Ravens	22	15

Seahawks	20	9
Vikings	39	35	.93

Cardinals	35	21	.95
Rams	11	13

Jets	18	14
Patriots	32	31	.81

Bengals	26	17	.79
Raiders	15	20

Chargers	26	32	.83
Broncos	17	3

While the model correctly picked 11 of the 14 games played so far this week, I think there are some problems with the underlying assumptions. I'm not at all bothered by the Falcons/Giants result which predicted a close game (and nailed the Falcons' final score dead on) because it only had the Falcons win 54% of the time. But for the Steelers/Chiefs game and frankly the Redskin/Cowboy and Browns/Lions games, and others, I think that the win probabilities or at least the scoring distributions were way off.

My model samples 10,000 times from distributions which estimate the final score of each team. You can see that how my model came to the probability of .94 in favor of the Steelers.

It's hard to know if the failure of the model for this game to predict the winner is simply because this happens to be one of those 6% of games when the Steelers are more to the left and the Chiefs are more to the right of their respective curves.

My suspicion, however, is that very rarely should any team ever be given a probability greater than 90% to win any game. There are too many unpredictable factors. So I may introduce a fudge factor into the next version of the model when disparities are high. On the other hand, the Seahawks/Vikings game and Saints/Buccaneers games were also predicted to be blowouts, and the model was pretty close to the mark. I still question the distributions though, especially at the higher ends.

So how did I come up with this first version of the model? Well I was originally expecting to use many factors, such as yards/att for passing and rushing, interceptions, sacks, aspects of the offensive line, home/away status, and others. So I decided to run a stepwise regression with a dozen obvious factors, in which the predicted variable was Win-Loss record (I used 2008 data so that I had an entire data set to work with).

It's pretty clear from the beginning that some of the factors appear to be important (coefficient confidence intervals do not overlap with the vertical 0 line) and others are not. But this is what happens when I include in the model a simple factor that is simply the average points scored minus average points allowed:

Amazingly, nothing else matters. This one variable captures 83% of the variance for the entire season:
So while I would much rather make a model that is able to predict the outcome of games based on the underlying mechanics of the game, I'm starting by just focusing on how many points each team scores and how many points they allow.

In this version of the model I compare team performance with overall averages and then adjust the parameters for any given match up. For instance, a team that does much better on defense than average will shift the opponents' likely score downward. I then produce constants for each team based on their opponent. I then sample from a modified normal distribution 10,000 times with a standard deviation based on the sample standard deviation of that team. The win probability for a team is simply the number of times a higher score was sampled for them versus their opponent, divided by 10,000.

A few things I plan to consider (in addition to making large win probabilities and really high predicted scores appear less frequently):

1) What sort of distribution should I use? I've simply been sampling from normal distributions (telling it to redo any sample where a score is less than zero or greater than 65). Looking at the distributions of scores, it may make more sense to use a Gamma distribution or at least transforming the values first before sampling from a normal.
2) Should I weight more recent games more strongly to capture trends in these parameters?
3) What other factors should I include in the model? (e.g. does it really matter if a game is played at home vs. away? Also, what effects should coaching or historical rivalries have on games predicted to be particularly close?)

A new year, a new project

2009-11-22T00:58:00.003-05:00

So the election has come and gone. A year has passed and I have been itching to play around with other predictive statistical models. I decided to turn to professional football. I think that it will be difficult to produce a model that is very accurate for a couple of reasons. First, there are very few games in a football season (at least compared to other sports) so there is greater error in parameter estimation. Second, there is so much chaos in a football game; a few seemingly small decisions may determine the outcome of the game. Of course there are also the larger decisions or rare events that no one can foresee (e.g. the end of the New England vs. Indianapolis game). So I'm not really convinced that the model will do too well but it should be fun nonetheless.

Like the election forecast model, this operates using a parametric bootstrap. In the election model I used polls to estimate win probability for each state. In this model I use performance data from earlier in the season to estimate points gained and points allowed by each team in each subsequent game (along with win probability). The NFL is in week 11. So there is still time to tweak the model to improve its performance through the end of the season. Hopefully it will do as well as the "experts" at ESPN, which is not always too impressive.

Details about this model (version 1.0) along with predictions for week 11 will be posted soon.

Election Night Post-Mortem (I)

2008-11-11T21:26:00.015-05:00

Now that we have had a week to digest the election results, I would like to do a little post-election analysis of the results. My model predicted Obama would win with a probability > 99.9%. While I don't know how to verify this number, I can compare my electoral vote estimates with the actual result.

Not all of the results were immediately available. Several close contests included IN, NC, and 1 NE district (all went to Obama) and MO (probably will go to McCain). This brings Obama's final electoral vote tally to 365.

My first question is: Assuming that the actual outcome came from a distribution of Obama electoral vote probabilities identical to that of my model's (null hypothesis), what is the probability of having an actual Obama electoral vote count as extreme as 365?

To answer this we do a simple z-test: Z = 365 - 352.1 / 24.39 = 0.5289. This translates into a probability of p = 0.30. A typical significance threshold would be alpha = 0.05. Obviously the p-value obtained here is well above that so we do not have enough evidence to reject the null hypothesis, that the actual outcome came from my simulated distribution.

Perhaps a clearer way to see this is by simply marking the bin in my distribution which contains the actual outcome (Obama 365).

It's clear from this that the final outcome is right in the fat part of my bell curve.

It seems then, that these results suggest:

(1) The polls were quite accurate in predicting the outcome and (2) The model adequately translates accurate polling data into a valid prediction of cumulative electoral vote outcome.

(1) The polls were poor or modest predictors of outcome BUT (2) The simulation model is robust to somewhat inaccurate polls.

(1) The polls were so accurate that they made up for (2) a model that otherwise would have been a poor or moderate predictor of outcome.

All of these can be examined to some extent.

pollster.com, one of my two polling data sources almost immediately published a graph showing the relationship between their regression predictions and the actual outcomes

States above the line indicate where Obama over-performed the pollster trend margin. States below the line are those in which Obama underperformed the pollster margin. I haven't yet examined these data extensively (nor have I done a comparable comparison for the realclearpolitics data, the other polling source in my model). At a glance, however it seems that while the polls look like pretty good predictors, Obama seemed to over perform in more of the deep blue states (e.g. VT, HI, RI, MA) and underperformed in deep red states (e.g. OK, UT, AK, AR). Those designated as toss-ups seemed to fit the unity line quite well (states that hover near 0,0).

Off the top of my head it makes sense that the pollster trends would be the most accurate for toss-ups because these states tend to be more extensively polled, especially near the time of the election. The tendency for strong red states to become more red and strong blue to become more blue might reflect the superior ground game of the dominant party in those states leading to higher voter turnout for their party. This explanation is somewhat unsatisfying to me though, as likely voter models (which many pollsters use) are generally designed to account for turnout discrepencies. Also, if the results happened to be in the opposite direction I would have said that this too would make sense, as I would expect greater complacency of democrats in strong blue states and republicans in strong red ones. I guess that's a problem with any post-hoc explanation.

I intend to examine some of these issues more fully later. One last point though. I had mentioned that the site fivethirtyeight.com seemed to have the best election model out there. The sophistication of Nate Silver's model has actually won him a great deal of publicity lately, including interviews on cable news channels and a recent NY Times article. His final prediction had Obama winning 98.9% of the time with an average of 348.6 electoral votes. As I mentioned before, I know of no way to evaluate the accuracy of win probability. His electoral vote prediction of 348.6 was similar (slightly less accurate even--although not a statistically significant difference) than my simple bare-bones model. I wonder whether my model was as accurate as his because of the particular electoral landscape in this election, or whether the added sophistication in his model (with demographic information and weights associated with each pollster, etc.) simply reach a point of diminishing returns and does not affect the outcome that much.

Whatever the answer, this whole experience has reinforced my novice interest in playing with statistics and modelling and I intend to continue doing this sort of thing in the future.

2008 Presidential Election Simulation (IV): Election Day Eve

2008-11-03T20:26:00.005-05:00

With the polls showing Obama with a commanding lead, including leads in the swing states (all former red states), tonight's simulation is more of an academic exercise. My model, which relates polling margins from realclearpolitics.com and pollster.com to win probabilities has Obama winning 9,997 times out of 10,000. The mean Obama EV count is now at 352.1, with a standard deviation of 24.39. Therefore, if these polling data, and this model relating polling margin to win probability are accurate, the 95% confidence interval for Obama EVs is (303.3, 400.9). Don't forget to vote!

2008 Presidential Election Simulation (III): One Week To Go

2008-10-27T23:26:00.020-04:00

With one week left, Barack Obama seems to be holding on to his lead. For this simulation I decided to average the state-by-state win probabilities based on realclearpolitics.com and pollster.com polling aggregates.

The results: Obama wins greater than 99.9% of the time. I have him averaging 345 electoral votes with a 95% confidence interval of (298, 392).

All data to the right of the vertical dotted line represent Obama simulation "election" wins. Those few results to the left of the dotted line are wins for McCain. As with my previous simulations, these data represent the results of 10,000 simulated elections.

The chart below represents the current status of the race based on the win probabilities computed from my model. The states are ordered by probability from most likely Obama wins to most likely McCain wins. This demonstrates the challenge McCain faces. The states colored in green are places where Obama currently leads but are the likeliest of this group for McCain to pick off. In order to get to 270, McCain must either win all of those green states: NM, NH, CO, OH, NV, FL, NC, and MO or some other combination of even more strongly blue states, such as PA (which despite this week's broadcast of This American Life, McCain is at the wrong part of the normal curve winning just 5% of the time).

From Chart

These data are a snapshot of what would happen if the election were held today. Who knows what events will occur to change the dynamics of the race in the next week. I am skeptical that McCain can do much of anything at this point to win. Only a low probability crisis or surprise about Obama would likely change the outcome. I will crunch the numbers on election day and examine how close my electoral vote projections are to the election results.

2008 Presidential Election Status (Compared with 2004)

2008-10-24T10:32:00.012-04:00

In the preceding post, I discussed the commanding lead that Obama has sustained and alluded to a changing electoral landscape in which (at least this time) the outcome will not simply hang on the results in FL, OH, and PA.

To provide context for where things were immediately before the 2004 election, I decided to dig up state polling data from Real Clear Politics. This page gives the RCP Average polling margin for 18 states (those states for which the race was somewhat tighter) in the 2004 election. Those states were FL, OH, PA, WI, IA, MN, MI, MO, NM, NV, CO, NH, ME, WV, OR, NJ, AR, and HI.

Below is a histogram of the margin of error. Negative values indicate states where Bush polled ahead of the actual result and vice-versa for positive values.

From this we can see that the RCP Average was generally pretty accurate, with the notable exception of HI (far left of the histogram) which RCP predicted for Bush by 0.9 points but Kerry won by 9.

Since not all states have equal value, I decided to normalize these errors based on electoral votes to give a theoretical RCP error impact (simply, percent margin * state electoral votes)

Again, we see no major bias in the data, with the average theoretical error impact near zero (0.07) and the cumulative error impact is 1.32. This indicates that the polling theoretically overestimated Kerry's electoral vote total by 1.32 votes. This positive value is almost entirely due to FL which was polling at Bush +0.6 but was won by Bush with a margin of +5. Of course this error did not affect the outcome in FL, so it is important to not misinterpret these theoretical error impact scores as reflecting actual differences in electoral votes. In fact, there were only two states for which the polling data chose the wrong winner: HI (4 EV) and WI (10 EV), Kerry won both and they were predicted for Bush. While polling for HI was way off (see above), the RCP Average for WI was Bush by 0.9 while Kerry won it by 0.4. Although the outcome was wrong, the RCP Average was still somewhat accurate. Together the actual impact of Polling error was therefore Kerry +14 EVs.

So what did the polls look like in 2004? Below is a histogram of the state margins (Kerry - Bush) based on the RCP Averages for 18 competitive states just prior to the election:

The average margin in 2004 for these states was in slightly in favor of Bush by 0.3889 percent. Kerry led in the polls of 7 while Bush was ahead in 11. Again, because these states have different EV values, the predicted electoral vote count among these 18 states was: Bush 109, Kerry 78. The actual outcome for these states was: Bush 95, Kerry 92, a large enough margin for Bush to still win the election.

Below is a histogram of the same 18 states indicating the current RCP Average margin for the 2008 election (Note: states like VA and NC, which may flip to the democrats this year were not among those included in the 2004 list of 18 and are therefore not included here either.

One obvious difference between this histogram and the one above is a rightward shift in polling margin to an average Obama lead by >9 %. Based on state electoral vote values, this predicts that of the 18 states Obama wins all but two of them, receiving an amazing 176 electoral votes to McCain's 11.

In summary, the 2004 polling data indicates RCP Averages are pretty close to the actual results.

If the current pattern, or anything close to it holds up for the 2008 election, Obama will win far more than the 270 EVs he needs, with a high probability for a landslide.

Obama doesn't need Ohio or Florida (although he may still get one or both of them)

2008-10-16T20:41:00.007-04:00

In the past two weeks, the numbers have become far more favorable for Obama across the board. This includes leads in Florida and Ohio as well as previously red states like Virginia, North Carolina, and others.

The most recent polls seem to have the race tightening somewhat in Ohio in particular and to some extent in Florida (graphs created by pollster.com, using trend lines that are maximally sensitive to local changes as well as noise).

Nevertheless, Obama still wins if he is able to hang on to New Hampshire (Obama + 7.3 to +10.4), New Mexico (Obama +7.5 to +8.4), Virginia (Obama +7.7 to +8.1), and Colorado (Obama +5.8 to + 6.2) (ignoring all other toss-up states)

Of these, the margin in New Hampshire may be tightening somewhat, although Obama still has a healthy lead.

Additional toss-ups which lean in Obama's direction (when smoothing is maximally sensitive to local changes) include Nevada, North Carolina, Missouri, and still of course Ohio, and Florida. In recent days, North Dakota and West Virginia have also become toss-ups, and Obama still threatens to pick up Indiana. With the four I mentioned and graphed above (NM, NH, VA, and CO), however, all these other states, which include the ostensibly critical Florida and Ohio simply become gravy for Obama.

Here's a wonderful graph from Charles Franklin, that puts this into perspective. Read his full article here.
So the story line of the last two elections (namely, that it all comes down to who can win 2 out of Ohio, Pennsylvania, and Florida) has changed. There are many ways Obama can win whether or not he gets Ohio or Florida, and with a double-digit lead in Pennsylvania, it is unlikely to be a deciding factor (any more than, say, New York or Maryland).

Presidential Tape Measure

2008-10-06T22:13:00.009-04:00

The New York Times recently published a chart with all major party presidential candidate heights and weights since the 1896 election. They explicitly ask:

Does candidate height and weight play a role in electoral success?

I decided to run a linear regression using height and weight to examine the role of each variable. It seems that while neither significantly contributes (p > 0.05), there is a trend for weight (p = 0.10). Adding height to the model does not improve it, which makes some sense given the highly significant correlation between height and weight.

In the group, the average weight of winners was nearly 12 lbs heavier than that of losers, although again, this is not enough to reject the possibility that this difference is due to chance.

One last note: I looked to see whether heights and weights have changed much over time. It seems that there is absolutely no change in average presidential candidate weight since 1896. However, presidential candidates have gotten significantly taller (statistically speaking) through the 20th century. from 1896-1960 (beginning of the TV era) presidents were about 5'10.6". Since then, they average 6'0.5". I suppose that these data suggest that modern presidents have been more physically fit than early-to-mid 20th century ones.

2008 Presidential Election Simulation (II)

2008-10-04T02:55:00.010-04:00

I last posted election simulation results a few weeks ago. At that point Democrats were holding their heads in their hands as McCain coasted through a post-convention bump and the dominant news stories were about the "lipstick on a pig" comment and Obama's supposed kindergarten sex ed program. Since that time we have had a financial crisis, McCain "suspended" his campaign, we have had presidential and vice presidential debates, and today a wall street/economy bail out plan finally passed in the House, after it was initially rejected. In all of this time there has been a great deal of movement in poll numbers, generally in a favorable direction for Obama.

Here is another presidential election simulation based on current polling data, predicting what would happen if the election were held today. Keep in mind that as polling numbers change in the next month, so too will these probability values.

When I previously explained my methodology, I may have glossed over the details a little bit. Here is hopefully a clearer explanation of my procedure.

By taking the current polling margins I compute a win probability for each state based on a normal cumulative distribution function approximating that of Charles Franklin's. His curve can be found here. Below is my approximation of his curve, using the parameters mu=-1, sigma=6.8.

I then use the current state-level polling data to determine win probabilities for each state. I create two separate models, one based on the Real Clear Politics averages and the other based on the latest regression analysis margins from Pollster.com.

I then simulate 10,000 elections based on these probabilities. The percentage of the time Obama gets more than 269 electoral votes is taken to be his overall win probability if the election were held today.

Here are the results:

Based on the margins of polling averages from Real Clear Politics, Obama wins an astonishing 98% of the time (average 328 electoral votes). Note that results to the left of the dotted line are McCain wins while those to the right of the dotted line are Obama wins.

Based on the margins of pollster.com regression lines, Obama wins 93% of the time (average 312 electoral votes).

So at this point the race is Obama's to lose. Nevertheless, after seeing such dramatic movement in the polls in the last three weeks we might expect that these numbers could shift back. In fact, I expect Obama's lead to decrease in the next month if for no other reason than the fact that races tend to get tighter as elections get nearer.

Will Power: Dopamine and Temporal Discounting

2008-10-01T11:58:00.016-04:00

Temporal discounting (a.k.a. delay discounting and hyperbolic discounting) is a concept in psychology and behavioral economics that describes the tendency for animals and people to prefer smaller rewards that will happen sooner (SS) over larger rewards that will occur later (LL). This concept has been developed by George Ainslie, who wrote Breakdown of Will, a book I recommend. This approximates the concept of "impulsive choice," which is integral to our understanding of drug addiction. It is also why we may value being healthy and physically fit over eating that piece of chocolate cake, but we still end up eating the cake when it's in front of us.

Temporal discounting is not just associated with pathologies, although it does describe a normal tendency to behave irrationally. For example, most people offered $50 now versus $100 (inflation adjusted) in two years, would choose the $50. On the other hand if they could choose between $50 in five years versus $100 in seven years the vast majority would choose the latter option. How is this possible? In five years, after all, they would be in the identical situation as the first scenario, in which they make the opposite choice.

The rate (shape) of a value curve as a function of delay can explain this discrepancy. Most behavioral data indicate that the change in value as a function of delay follows a hyperbolic function (as opposed to exponential, for example) function.

This figure, from Ross et al. (University of Alabama) shows that when a delay is short, the hyperbolic function allows a SS reward to be more strongly valued than a LL reward, even though the smaller reward is less strongly valued most of the time.Depending on the individual and the reward involved, the value curve can look dramatically different. A smoker, may be certain they are smoking their last cigarette and feel very much in control. Hours later, that same smoker, because of a sharply scooped out hyperbolic value curve, may find himself lighting up once again. This is one way to understand "will power": The sharper the hyperbola, the more impulsive the behavior appears.

In the July 30, 2008 issue of the Journal of Neuroscience Kobayashi & Shultz publish a paper showing that dopamine neurons, which are known to be associated with reward prediction error and incentive salience, also encode temporal discounting in a Pavlovian conditioning task. This suggests that prior to making the choice, our dopamine neurons are likely firing less to the idea of $100 in two years compared than to the idea of $50 now.
If you believe in "free will" (I will do another post on this topic sometime), how do you square away the potential role of dopamine neuronal activity in constraining value? In fairness, it remains to be proven that the activity of these dopamine neurons causes the behavioral phenomenon. Nevertheless, future work will undoubtedly examine how well we can predict subsequent choice based on the early activity of dopamine neurons to differently valued and differently delayed rewards prior to their presentation as a choice. If we are able to do this accurately, it seems to me we will have strong neurobiological evidence for value constraints that precede choice and will.

Heads I win, tails you lose

2008-09-29T18:05:00.008-04:00

It seems that John McCain took credit for the successful passage of the bailout earlier today, while speaking in Columbus, OH. He was a true leader who brought all parties together.
From Politico:

"I've never been afraid of stepping in to solve problems for the American people, and I'm not going to stop now...”

Obama, on the other hand, was supposedly too afraid to put country first:

“Sen. Obama took a very different approach to the crisis our country faced. At first he didn't want to get involved. Then he was monitoring the situation.” McCain, grinning, flashed a sarcastic thumbs up. “That's not leadership. That's watching from the sidelines,” he added to cheers and applause.

After the bill failed to pass in the House, McCain's campaign blamed Obama and the Democrats, even though two thirds of the Republicans voted "no":

“This bill failed because Barack Obama and the Democrats put politics ahead of country.” — McCain-Palin senior policy adviser Doug Holtz-Eakin

So if the bill had passed, it would have been because John McCain is a terrific leader who put country first and brought everyone together. But since the bill failed it must be because Obama and Democrats were too partisan to put country first-- even though most Democrats voted for it, and most Republicans voted against it.

Hmm. In the words of David Letterman, "This doesn't smell right."

Our Happiest Age

2008-09-27T17:09:00.010-04:00

Today I stumbled on to an interesting website displaying a graph that relates survey answers of believed or expected happiest age to age of the responder. The data were made available and above is a scatter plot with a best fit line and 95% prediction bounds.

While the R-square is low (0.1354) the positive relationship is very highly significant, as the 95% confidence interval for the slope of the fitted line is (0.3688, 0.5481), which obviously does not include 0.

This means that as people get older, their stated belief regarding the best year of their life increases. While this initially struck me as reflecting optimism, the fact that the slope is less than 1 means that at a certain point people begin to believe that their best year is behind them. This happens at age 27-28 on average. Earlier than that people think their best year is ahead of them.

I'm 28 years old now, so I guess I'm supposed to believe that this is the best year of my life. In truth, the data are so variable that 95% of the time I would believe that the best year of my life is somewhere between 2 and 53, which is a huge range.

While it's sad that we become less and less optimistic with age, the good news is that according to this fit line and prediction bounds, the time when one's current age creeps outside the 95% confidence intervals for their believed happiest age is 74. After that at least 95% of the time people think their best year is behind them.

This figure simply shows the mean and standard error of those responding. The overall average expected "best year" was age 31 (sem 0.55). The average age of those responding was 35 (sem 0.44).

As a final note, these data are not quite normally distributed (both in terms of age of responder, and in perceived best age), but are pretty close.

Government Bailouts

2008-09-25T11:55:00.006-04:00

If the proposed $700 billion Wall Street bailout passes, we will have spent about 7% of our 2008 GDP on bailouts. Everyone is talking about this new bailout proposal, but with those already done the government will have spent over a $1 trillion on bailouts this year. This site has an interesting graph showing the various bailouts since 1970 (in 2008 dollars). It sounds like both Democrats and Republicans believe that some sort of intervention is necessary, although it is not yet clear to me whether the government's purchase of nearly worthless pieces of paper to "restore confidence" will prevent major economic collapse. It is also not yet clear to me how much time we have before a collapse is imminent, and for that matter, what the realistic effects of such a major recession will be. Many are comparing what is going on now to the Great Depression. Could we really see unemployment hit 25%? How difficult will it be for people to borrow money if there is no intervention?
I would really love to hear quantified predictions rather than simply that the economy is at serious risk (and that we need to do this as soon as possible), as Bush told us last night. I would also like to see what the cost of spending $700 billion (as well as the total $1.01 trillion) on bailouts will have on the value of our currency and other economic indicators.

So right now I think I have to be agnostic on the of issue bailouts. Even after reading newspaper articles and watching the news, it is still not clear to me what the relevant cost-benefit analysis looks like. I should also mention that in addition to impact estimates, I would like to see some sort of measure of the accuracy of these estimates based on either previous forecasts or a model of the uncertainty of these effects. After all, what suckers we will all be if we spend an additional $700 billion on bailouts and STILL have economic collapse along the added mess created by spending huge sums of tax dollars on it.

Minimum Wage

2008-09-18T22:22:00.004-04:00

The U.S. federal minimum wage was raised for the first time in a while in 2007 to $5.85 and then in July, 2008 to $6.55. In 2009, it is scheduled to increase to $7.25. I recently downloaded minimum wage data from the Bureau of Labor and Statistics and graphed changes in the minimum wage over time. I also converted each year's value to Consumer Price Index-adjusted 2008 dollars. From this we see that the minimum wage was actually greatest (in purchasing power) in 1968 (over $10/hr in 2008 dollars), when the actual wage was raised to $1.60/hr. This goes to show the impact of inflation: approximately an order of magnitude reduction in dollar value since 1950.

Fun with maps

2008-09-17T22:33:00.014-04:00

I've always loved this map, demonstrating the population density of the US. I downloaded this from the US Census website, which has a lot of interesting demographic maps.

This map really shows just how sparse much of the western US is (one dot = 7500 people). Playing with Photoshop's distort tool, I overlaid the next map onto this one.

This is Tornado Alley and "Dixie Alley" from NCDC
Many states have 25-30% obesity (BMI > 30) rates, with those in Tornado Alley and Dixie Alley leading the way.

And finally, an interesting US map showing the distribution of religious affiliation.

Not that there is any causal relationship between these data sets. It is fun to look through this stuff though.

Problems with Democracy

2008-09-13T09:59:00.001-04:00

Chruchill famously said, "Democracy is the worst form of government except for all the other forms that have been tried." One of the supposed benefits of democracy is the idea that by allowing all citizens to have their say, policies will better reflect the people's interests. This is intuitively true when we compare modern democratic republics to the autocracies of Europe in past centuries.
Nevertheless, when we examine the political process in modern America, several practical problems emerge related to the psychology of the people.

Voter Turnout
While in theory every individual has the right to vote overall turnout since 1964 has never been above 65% of the voting age population. Midterm congressional elections usually draw only about 35%. Therefore, election results do not necessarily reflect the people's interests as a whole.

Some would argue that individuals who choose not to vote had the opportunity to have their say, and therefore it is not the fault of democracy as a system. Others may suggest that refusing to vote is, in itself, making a political statement. While I concede both of these points to some degree, we currently do not know to what extent they are true. For example, the fact that election day is held on Tuesdays means that some individuals probably do not vote because of work or other obligations.

A friend of mine has been following the 2008 presidential election with great interest. He has a clear preference for one of the candidates, but when I asked him about it he told me that he is not going to vote. To him, and I think many people, voting is a hassle. "What's the value of a single vote?" one may ask. In the 2004 election one vote constituted 0.0000008% of the popular vote. To go to a polling place during a work day and potentially wait in line for hours to cast a single vote, seems like a waste of time. The problem is, millions of people may think this way. The 2000 final tally giving Bush a win in FL (and therefore, overall) was 537 votes (larger than the margin of counting error). In 2004, the election was decided by a difference of 118,000 votes in OH. I should mention that in OH, individuals in particular precincts had to wait in line for 4-10 hours (in the rain) to cast a single vote. While people are willing to wait in such lines for concerts and next-generation iPhones, I wonder how many people thought it was not worth their time for a single vote. My point is that while one person's vote has a miniscule impact, the fact that millions will use this fact to justify not voting could have an enormous impact. It is of relevance to both 2000 and 2004 that registered Democrats seem to have somewhat lower turnout than Republicans.

Incumbency
High congressional incumbency rates suggest a couple of points. One potential issue is name recognition and comfort with the familiar. This, in itself, is not necessarily bad. However, if elections are about voters getting their say to represent their interests, it is curious that they believe the best person for the job is already in office 80-95% of the time. An alternative interpretation is that most areas simply are lopsided in voter affiliation. Perhaps a district that is 60% republican will seldom vote for a democrat. Even if we took this to be true, it says something about the influence of voter party identification on the ability for incumbents to hold on to power. Thus, it would seem that identity rather than job performance could determine the outcome of many congressional elections. This might be a plausible explanation for why the congressional job approval rating is just over 20%, as most districts will undoubtedly reelect these individuals in November.

Manipulation of Public Perceptions
The most damning and perhaps obvious practical problem with a democratic system as it exists today in the US, is the role of propaganda. I'm using Webster's 3rd definition:
Propaganda: "ideas, facts, or allegations spread deliberately to further one's cause or to damage an opposing cause."

Setting aside the negative connotations of the term, propaganda is obviously the purpose of political campaigns. The content of propaganda can be true and useful for voters to make informed decisions. Propaganda can obviously also mislead. Think of the hundreds of millions of dollars spent on political advertisements this year. What is the content of those 30 second ads? Do we really learn more about candidates' policies? In the last week, McCain has put out ads stating that Obama is in favor of "comprehensive sex education for kindergarteners." Is this true? Well, no. But that does not matter to the McCain campaign as long as the ad is effective in raising Obama's negatives. The tactics do not need to be so direct either. Beginning with Tony Schwartz's "Daisy" cartoon, designed to play on the fears that Goldwater would have been trigger-happy with nuclear weapons, all presidential campaigns market their candidates to some degree as heros or champions and their opponents as incompetent or untrustworthy. In the 2008 campaign, such imagery has been perhaps more blatant and direct, but thematically no different.

Selling candidates as consumer goods (but with greater passion) degrades candidates, showing what is both necessary to be elected in the age of visual media, and the depths to which these candidates will sink for a win. In the past 50-60 years advertisers have learned a great deal about what works. Simply stated, billions of dollars are spent on ads because they affect behavior. Period.

Many of us are annoyed to sit through commercials, but are not really angered by them. After all, it is up to us consumers to choose to purchase products in the end. We have free will, right? Well, if effective techniques are used to bend our perceptions, attitudes, and desires so that as a group we probabilistically behave in a particular way, our will is constrained.

Thus, autocratic rulers of the past controlled their subjects directly. It ultimately did not matter what the people wanted. Today, with elections, the power is given to the people to choose their leaders. Only, now, with effective campaigning, and "issue ads" the views and desires of the people are molded. I know this sounds quite dark. I would not go so far as to say we are entirely controlled by the ads on television. But if they were not a determining factor in election outcomes, why else would it be essential for candidates to spend hundreds of millions of dollars on advertising?

Summary
So maybe Churchill was right. I can't think of a just system in which the governed have no say. However, the idiosyncrasies inherent in the psychology of the people, and the manipulation thereof, seems to hinder our ability to realize some of democracy's noble ideals.

Model results in pictures

2008-09-12T22:57:00.000-04:00

Because the last post only gave the end results, I thought it might be a little more informative to see what percent of the time McCain or Obama won each state in the simulation. The picture here shows the percent of the time Obama won from 0-10% (Full Red) to 90-100% (Full blue).
This was based on the data from pollster.com. Ultimately, Obama won almost 90% of the time with these polling data.

2008 Presidential Election Predictions

2008-09-12T21:27:00.001-04:00

There are a number of sites out there that run simulations based on polling data to predict the result of the presidential election if it were held right now. I think the best one is at www.fivethirtyeight.com. Before I knew about this, I started playing with the polling data myself. I found a curve presented by Charles Franklin, relating polling margin to win probability. For example, a candidate ahead in a pre-election poll 55% to 45% will win around 90% of the time. Based on his curve, which I approximate with a normal cdf, I ran a simulation of 10,000 "elections" based each on the polling data on realclearpolitics.com and pollster.com. I did this a few weeks ago and Obama had an overwhelming lead (90-97% win probability). Given the recent shifts in polling trends, I decided to run the analysis again.

Although the national data is trending slightly toward McCain since the republican convention, my model still predicts Obama wins 71% of the time (realclearpolitics.com) or 90% of the time (pollster.com).

This model is incredibly basic. It does not take into account national trends, and many of the state polls lag behind McCain's recent bounce. For these and other reasons, I think these simulations over-estimate Obama's probability if the election were held today. Fivethirtyeight uses a much more sophisticated model, and has each candidate winning about 50% of the time. It will be interesting to redo this analysis over the next 55 days.

As a caveat, this analysis is likely to only be accurate immediately prior to the election. I did run this simulation using the polling data of battleground states immediately prior to the 2004 election. This simulation gave Kerry a 22% probability of winning with an average number of electoral votes of 250. He actually received 251. So although this model is about as simple as it could be, it may be a decent predictor immediately prior to the election.

Inaugural Post

2008-09-12T21:05:00.000-04:00

Welcome to dopamachine. My name is David Sturman, and I'm a medical student and neuroscience PhD candidate at the University of Pittsburgh. While I really love to think and talk about science, I thought that I would use this blog to post about a range of topics. I hope you enjoy.