Last week we talked about the validation of the Advanced NFL Stats WP model, and Brian Burke noted in his writeup that WP still failed to account for home field advantage. Now it does.

Although it’s clear that home teams perform better during a game, at least in terms of points scored, it’s not clear exactly how this translates into an increased chance of winning minute by minute. From simple win-loss records, all we know that at the outset of a game the home generally team ultimately has about a 56.5% chance of winning.

The problem, as should be fairly apparent, is that Burke only has WP available to test these win-loss probabilities. So what happens when you chart the home team win probability (go look!)? After extracting the results from the context from which they were derived (a model that learns over the course of the game), Burke found a WP curve with respect to HFA .

Starting with a 6.5% advantage at kickoff, and following the shape of the curve, we see the real, no kidding, actual HFA as the game goes on. This isn’t HFA in terms of yards per play, first downs, or points scored, or in terms of anything except the probability of winning.

The results are interesting in that HFA effect on WP decreases over the course of the game. Would you have expected this? Crowd intensity down the stretch of the game does continue to aid the winning team, but the marginal WP returns decrease. Why?

So there are (at least) two mechanisms at work. First is the decrease in performance advantage for the home team as the game goes on that I discussed above. Perhaps fatigue neutralizes the home team's edge, or perhaps it's visitor acclimation to a hostile, unfamiliar environment. Second, as the game clock ticks down, there is less time for the home team to capitalize on its advantage. By the end of the game the scoreboard doesn’t care which team is the home team and which is the visitor. A 1-point lead is good enough to win, period. So it’s a complicated thing to model. We just can’t add 6.5% to the win probability (WP) for the home team throughout the game.

The second point is the key from a WP standpoint. At the start of the game, the home team has 60 minutes of advantaged football ahead of them. As WP predicts the odds of winning the game from a given moment through the end of the game, you can't expect the same cumulative advantage at any point in the game. By the time a game has reached the final two-minute warning, home field advantage can only do so much.

It really is that sparse, so here's new NFL.com blogger Jason La Canfora's top 20 NFL players, in no particular order. Note that Walter Jones made the cut, which is fairly questionable at this point in time. Anyone else you guys feel should be on the list?

On an administrative note, here's a poll for all of you. This is a particularly dry stretch of the offseason, but I've tried to find something of NFL interest (Advanced NFL Stats and the like) even when there isn't anything remotely related to the Seahawks.

via media.thenewstribune.com

Between John and I, there have been a couple of posts at FG related to the Advanced NFL Stats Win Probability charts. If you've paid any attention, you know just how neat they are. If you are a generally curious person, you probably have wondered about the accuracy of the WP charts. Wonder no more. If you have no interest in probabilistic models, you should probably just stare at a wall for a few minutes.

For readers who are accustomed to linear regression models, you'd expect to see a goodness-of-fit statistic known as r-squared. And for those familiar with logistic models, you'd expect to see some other measure, such as the percent of cases predicted correctly. But the win probability model I've built is a complex custom-built model, using multiple smoothing and estimation methods. There isn't a handy goodness-of-fit statistic to cite.

We can still test how accurate the model is by measuring the proportion of observations that correctly favor the ultimate winner. For example, if model says the home team has a 0.80 WP, and they go on to win, then the model would be "correct."

But it's not that simple. I don't want the model to be correct 100% of the time when it says a team has a 0.80 WP. I want it to be wrong sometimes. Specifically, in this case I'd want it to be wrong 20% of the time. If so, that's a good feature of any probability model. This is what's known as model calibration.

Right, so that's it for the wall of text. If you are still reading, now go check out the charts in the article. The first shows a very nice relationship between actual results and the predicted results. There's a problem, however: The top chart shows the relationship between the 2000-2007 data and the model, which was built off of the 2000-2007 data. When building and subsequently testing a model, it's important to split the data into what's known as test and training data sets, part of the cross-validation process. If you test a model with the same data you created it with, the results will almost certainly show a very good model*. To ensure that this wasn't the case, Burke tested his model against the 2008 data, and the results look pretty good for a single-season sample.

Also, Burke charted out the model confidence, which is pretty interesting to look at from a fan perspective. It makes sense that the average game should start out with a roughly 50/50 split at kickoff. As late as the ten minutes from the end,  however, there is generally only about ~80% confidence in a winner. That leaves a lot up for grabs.

*Unless you screwed up.

It's not easy to keep track of every single roster move by every team in the NFL, especially when your vested interest lies with one team. That's why I was somewhat surprised when I saw this list of free agents from Jason La Canfora's blog. Pretty impressive set of names, isn't it?

It's not surprising why several of those guys have not been signed. Edgerrin is on the wrong side of 30 and showed his age last season. Shaun Alexander. Marvin Harrison has the combination of age, injury, and some mysterious allegations following him. Mark Tauscher tore a knee ligament in week 13 last year and comes in at age 32. I was a sophomore in high school when Willie McGinest turned 30. DeWayne Robertson can't even keep a website running:

At this point, pretty much anyone on this [list] is looking at a one-year, veteran-minimum-type deal, so it’s not a tremendous investment, and a lot of teams have ample space after the salary cap jumped this offseason.

With injuries such a part of the game, most teams will be looking for free-agent help by the first few weeks of August, with two-a-days chipping away at their rosters by then, and these guys are worth watching.

Barring a bunch of injuries, these guys won't be Seahawks. However, some teams will be desperate enough or at least willing to take a chance in signing some of these fellas. It's amazing how quickly NFL players go from stardom to the unemployment list.

Here's a quick hit and run, as I left for SF several hours before this piece automatically published. Being the magnanimous soul that I am, I didn't want to leave you without something to read just because I'm getting further from my computer with every word you read. Danny O'Neil brings you aggregate payroll over the last five years. This isn't much other than the knowledge that Paul Allen is not pinching pennies with the Hawks, as we already learned that payroll doesn't correlate with winning. That's a lot of money. 

Friday discussion question: If you could attend one and only one Seahawks game this year, which one would it be? Play nice and don't insult any mothers. 

Let's try a little game. I'm going to pose a series of three questions, and you will answer them one by one in your head. Don't follow the link until you've answered all three.

In your head, picture a football game. The offense has the ball and is about to pass. Don't consider YAC, but only the position of the catch itself relative to the first down line.

1.) It's third down. Where, relative to the televised yellow first down line and within +/- 2 yards of the line,  is the most difficult distance to complete a pass to? I'm looking for a distance from the first down line, so horizontal distance from the quarterback is irrelevant at this moment.

2.) It's second down. Same question.

3.) First down. Again.

The answers can be found here. 

How did you do?

at training camp. Well, sort of free. Transportation to and from the facilities will cost $5 a head. Details courtesy of the PI.

The team announced Tuesday that fans can attend practices at the Seahawks' waterfront headquarters on Lake Washington beginning on Aug. 3 and ending Aug. 20. They must first register through the team's Web site, seahawks.com, on a first-come, first-served basis beginning July 16 at 10 a.m.

This will be the first time since the team returned camp to the Seattle suburbs from Cheney, Wash., in 2007 that fans can watch the Seahawks practice.

The team will also hold two practices at UW in August.

If you've never been to a training and have a moment or two to spare in August, I recommend going. Firstly, you'll have the chance to see the new facilities in person, and the grounds are supposed to be fantastic. You may also enjoy watching Seahawk players in action and in person, both of which are pretty neat. A few summers ago, some friends and I drove up to Green Bay to catch a Packers training camp, figuring we'd get a chance to see Favre in action in what would likely be his last season. We were half right. Even though I am not in any way a fan of the Packers, I enjoyed watching NFL players go through a practice fifty feet away from where I was sitting. Watching a game on TV or even from up in the stands leads to a bit of a disconnect, in that you really don't appreciate just how incredible NFL athletes truly are. Kabeer Gbaja-Biamila, while on the smaller side for a defensive end, was huge. Ahman Green was jacked beyond belief. Even more impressive is the level of talent. Watch players you've only barely heard of perform amazing feats and still not make the roster. So again, if you have $5 and a day in August, go to training camp.