## 49ers-Jets Statistical Review: Raining on the Parade

The Niners have won two games in a row. Awesome! We have cause for celebration, right? Well, perusing some of Ninjames's Golden Nuggets this week, I've gotten the feeling that I'm the Grand Marshall of a parade, and it's starting to drizzle. The analysis has gone something like this: "Singletary's 49ers have won a couple of meaningless late season games, but Nolan's squad did that too." In making this assertion, proponents cite wins against the Rams and Texans in 2005, the Seahawks and Broncos in 2006, and the Bengals and Bucs in 2007. Now, we all know that the 2005 and 2007 wins come with a bit of a caveat  in that the 49ers' opponents were either crappy (i.e., the Texans and Bengals) or were resting their starters (i.e., the Bucs). So which side is right? Are the Niners' back-to-back wins against the Bills and Jets a sign of change or are they more of the same? In this week's statistical review, I'm going to answer that question using a bit of PG-rated hardcore stat analysis.

BLAME IT ON THE RAIN

The question at hand is, "Do the Nolan era 49ers perform better during the second half of the season than the first?" Since Mike Nolan took over to start the 2005 season, the 49ers have played 32 games (9-23 record) in the first halves of their seasons and 29 games (12-17) in the second halves of their seasons. If you look only at the records, that's a 4.5-game difference, or a little over 1 game better in the second half per season. However, as we all know by now, 4 season-halves per group is a pretty small sample size, so this 1-game difference basically tells us nothing. In order to come to a meaningful conclusion, we have to somehow increase our sample size. The easiest way to do that is to look at each game rather than each season-half. Doing so gives us group sizes of 32 and 29. To make the conclusion even more valid, we also need to account for the 3-game difference in number of games per group. Because that difference is entirely due to the fact that the second half of the Niners' 2008 season is incomplete, we can equalize the group sizes by cutting back the first half of this season to 5 games. But which 5 first-half games should we choose? Well, the best way to do that is to choose them randomly, so that's what I did.

So we have our sample: 29 games played in each half of the season. Now we need to figure out how to measure "49ers performance." Well, you know what I'm going to use for that: the tried-and-true DVOA statistic. For each game the Niners have played since 2005, I obtained their total, offense, defense, and special teams DVOAs from Football Outsiders. Below is a table showing the averages for each half of the season and the differences between them:

 Nolan Era TOT DVOA OFF DVOA DEF DVOA ST DVOA First Half -46.94% -32.93% 16.86% 2.84% Second Half -24.81% -21.10% 5.71% 2.02% Difference 22.13% 11.83% -11.14% -0.82%

After the jump, I'll go hardcore on these stats, and review the 49ers' performance in their 5 SVW situations against the Jets...

OK...So there seems to be quite a difference in the 49ers' performance between the two halves. The only performance consistency they show from one half of the season to the other is on special teams (Remember: Negative values for defensive DVOA mean better defense). Now, that's all well and good, but we need to go one hardcore step further with this analysis: Are these differences - gasp - statistically significant?

To determine statistical significance in this situation, we have to do what's called an Analysis of Variance (ANOVA), which basically tells you whether the average difference between two groups is greater than what would be expected by chance (aka dumb luck). Because we're not trying to cure cancer here, I'm going to use a rather liberal statistical significance level of .10, which means we can be 90% confident that an average difference is, in fact, a meaningful one.

It turns out that the overall and defensive DVOA differences are statistically significant, while the offensive and special teams DVOA differences are not. Specifically, we can be 93.1% confident that the Nolan Era 49ers perform better overall during the second half of the season, and 93.0% confident that they perform better on defense during the second half of the season. In contrast, we can't be sufficiently confident that the offense and special teams perform any better or worse during the second half of the seasons as compared to the first.

So what is there to say about the Niners' second-half performance this season? Is this year change or more of the same? Below is a table showing the averages and differences for this season:

 2008 TOT DVOA OFF DVOA DEF DVOA ST DVOA First Half -28.46% -27.62% 6.68% 5.80% Second Half -7.94% -17.40% -5.10% 4.34% Difference 20.52% 10.22% -11.78% -1.46%

If you ask me, that right there is pretty (site decorum) consistent. Comparing this table with the previous one, the overall and defensive DVOA differences are nearly identical. So what does this all mean?

THE DEVIL IS IN THE DETAILS

Just to refresh our memories, I identified the following strength vs. weakness (SVW) matchups for the 49ers in their game against the Jets:

 Situation SF Rank NYJ Rank SF RED ZONE OFFENSE VS. NYJ RED ZONE DEFENSE 31 5 SF RUSH OFFENSE VS. NYJ RUSH DEFENSE 26 7 SF RUSH OFFENSE VS. NYJ RUSH DEFENSE ON 1ST DOWN 28 6 SF PASS OFFENSE VS. NYJ PASS DEFENSE ON 3RD DOWN 30 8 SF DEFENSE VS. NYJ OFFENSE ON 2ND AND SHORT 27 6

So, aside from the redundant 1st-down rushing SVW, how did they do? See below.

Red Zone Offense - In one word, splendidly. The Niners were successful on 6 of their 13 plays in the red zone, with 1 first down, 1 field goal, and 3 touchdowns. This is even more impressive given that the Jets were the 5th-ranked red zone defense going into the game. Score: Eagle.

Rushing Offense - In one word, shabbily. Of their 33 running plays, the Niners were successful on 13 (5.3 ypc), of which 6 produced first downs and 1 produced a lost fumble. In their 20 unsuccessful plays, they averaged a piddling 1.6 yards per carry. I'll give them a pass though due to the caliber of their opposition. Score: Par.

3rd-Down Passing Offense - In one word, stupendously. The Niners were 7 of 13, with a touchdown. Score: Eagle.

2nd-and-Short Defense - In one word, eh-ly. I wasn't even going to evaluate this one seeing as how the 49ers only had 4 of these situations during the Jets' meager 20:11 of offense, but one of the Jet touchdowns came on 2nd and short. Just had to bring it up. Score: Par.

Using my golf scoring system, the Niners were 4 under par over 4 holes. Like last week, the 49ers' SVW performance reinforced what we already kind of knew about their overall game performance. I like this week's "they played better than the other team" version though.

Next up on Friday...a preview of the once-in-a-blue moon home game for me: 49ers vs. Dolphins in Miami. Frank Gore's not the only one that might to be out of commission this week.

**For any statisticians out there who feel that ANOVA is not the correct analysis here because of non-independent groups, I found the same conclusions via a paired samples t-test with 29 randomly assigned game-pairs. I chose to report the ANOVA results instead because they were easier to articulate and present to a non-statistician audience given the same conclusions. The only noticeable difference between the two sets of results was that offensive DVOA change was closer to statistical significance using the paired samples t-test.

**DVOA statistics used to produce this article were obtained from Football Outsiders.

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