Lowering Expected Variance: Why the Eagles might be “better” but finish the same.

Quick post today.  We’ll start taking a detailed look at the upcoming season soon (hopefully next week), but I wanted to mention a high-level point today.  The over-arching question is: Are the Eagles better this season than they were last season?

I haven’t ventured a complete answer just yet; I still have a lot of stats to go through.  However, I have stated quite explicitly that, from a pure roster perspective, I don’t think the Eagles improved very much (and may actually have gotten worse).  There’s a problem with that statement, though.  It’s incomplete.  Here’s why:

When we talk about a team’s “true” ability level, we’re not really discussing discrete values.  Although many pundits (i.e. anyone/everyone on ESPN) views season projections this way, it’s a very bad method of forecasting.  In reality, ex-ante (before each season), the best we can do is put together an expected performance distribution.  In other words, before the season, we have no idea how many wins each team will produce.  Beyond our inability to fully quantify all the known controllable variables, there’s a HUGE degree of natural uncertainty (luck) in the game.

I touched on this a bit before last season.  In making my projection for the Eagles, I gave a range of outcomes before settling on 9.1 (if I remember correctly) as the average.  I ALSO explained that the Eagles were among the highest VARIANCE teams heading into last season.  Put simply, the team, prior to last season, had perhaps the largest range of expected outcomes.  So while I thought the team “should” win between 9 and 10 games, I also thought it was reasonably possible for them to go 4-12 or 12-4.  Chip Kelly was a big reason for that range; he brought with him a very large degree of uncertainty.  In hindsight, things works out generally as expected (at least on this site) and the Eagles finished with 10 wins.  Note that, given the point differential, the Eagles “true” performance last year was 9.4 wins (via Pythagorean formula).

So why am I telling you this?

Well, if we think about each team’s expected performance as a probabilistic distribution, then there are TWO main ways for the team to actually improve.  Most clearly, a team can increase it’s average win projection.  For instance, it could sign multiple impact starters, or take a great prospect very high in the draft.  Doing so might shift the teams entire distribution to the right, like so:

This is a graphic I used before the playoff game against the Saints.  The X-axis is wins in this example.  The values don’t really matter.  What matters is that the team has moved from left to right.  Clearly, the blue distribution represents a better team.  It’s average performance is much higher.

BUT, there is another way to improve (several actually but we’re focusing on the big ones), at least conceptually.  A team can keep its average win projection the same, but decrease its expected variance.  For example, the Eagles might still be looking at 9.1 wins this year, but the team’s range may have decreased.  That means our certainty increases.

Visually, it might look like this (again borrowing from this post from last season):

Notice the Cardinals; distribution is much narrower than the Eagles’.  Pretend that both have the same average (i.e. move the Eagles to the right so it’s centered on the Cardinals).

That’s better.  To borrow a finance concept, think of the distribution like a stock.  Many analysts/investors use volatility (technically standard deviation, not variance, but for our purposes they’re the same thing) as a proxy for risk.  When looking at an investment, you have to look at both the expected return AND the risk associated with the investment.  Here, you have to look at both the expected average win projection AND the range of potential outcomes.

It’s important to note here that, assuming a symmetrical distribution, narrowing the range ALSO decreases upside while minimizing downside.  Hence, sometimes it is better to have a wide distribution, like when you are a bad team.  However, since there are diminishing returns at the top end of the distribution (a 10 win playoff team isn’t much worse off than an 11 win playoff team), especially where the Eagles look to be headed (good enough to make the playoff but not good enough to challenge for a bye), a smaller range of outcomes is an improvement for the team.

Here’s the important part:

While it’s unclear whether or not the Eagles have shifted their distribution to the right (i.e. expect to win more than 9.4 games this year), it seems very likely that the team has narrowed its range of expected outcomes.

Chip Kelly is no longer huge unknown.  Nick Foles expected performance is undoubtedly higher this year than Michael Vick’s was before last season.  Personnel-wise, the Eagles have made significant improvements below the starters on the depth chart.  Obviously, injuries are a massive source of uncertainty.  Although the Eagles have not added any impact starters (making it tough to increase projected wins), they have made the roster more robust, particularly on the defensive side of the ball.

So yes, the Eagles likely are better this year, if only in terms of uncertainty.  Whether the team’s average win projection has improved is a separate issue that I’ll address over the next couple of weeks.


6 thoughts on “Lowering Expected Variance: Why the Eagles might be “better” but finish the same.

  1. I think conceptualizing wins in terms of variance is really useful, especially at this point. The shaded bubbles are clearly stand ins for real outcome distributions, but it’s also worth thinking about how and why they might not actually be so symmetrical. E.g. A high upside/low downside team may be look a little off in some cases. I’d be pretty interested In seeing how you think about the factors that structure not just the projected wins and spread along the x axis, but also how the factors influence the entire shape of the distribution.

    • That’s a good question. I’ll see if I can put anything of value together. In general, I think any good team’s distribution is skewed left simply because of the injury risk. There just isn’t a corresponding upside event to balance out losing a starting QB or other major contributor. I also think the distributions are mostly playkurtic (in comparison to a Normal curve). There’s so much luck in the game and teams are close enough that it’s pretty easy for a team to fall 2-3 games short (or win 2-3 more) than its “true” level.

      Good idea for a full post though.

  2. your analysis isn’t taking into account the possibility of Foles dramatically improving.

    Sure, we know that his numbers will regress this season, but his numbers were a mirage in the first place. Once teams got a handle on the Foles-Kelly offense (post Raiders game) the eye-test says that Foles did not play particularly well with the exception of the Bears game, regardless of what his numbers were. Even his redzone stats were partially a function of being is so many goal to go situations. So even though his numbers will be worse, it is very possible that Foles actual level of play will be much higher.

    Also, if we look at the defense post-Broncos game they allowed merely 21.5 points per game (if you take out the flukish “Snow Bowl”). If they are able to sustain that level of effectiveness than the offense will only need to generate about 26 points a game to have a projected 10 wins based on point differential.

  3. Brent: off track, but don’t you think Vegas is under valuing the Eagles? They are 15:1 to win the NFC. I would think they are (or should be) big favorites to win the division. Perhaps this is under valued too, I see 3:2. Let’s assume they win the division. They need to win 3 (or 2 games) to win the conference. If it’s even odds, that’s 1/8 right? Now maybe they are underdogs for a game or even two, but they could also be favorites. I would think maybe you take the 1/8 and discount a little for the off chance they do not win the division. So 10:1? but 15:1 seems materially low to me. They won’t have 3 road playoff games.

    Not that I live in Vegas, but it’s just fun for me to think about who has odds better than their true odds. the division could all far apart around them.

    • I haven’t yet come up with a final projection (and I’ll do an odds column before the season starts), but my first reaction is that Vegas is actually pretty on point here. I don’t think the NFC East is good, so I certainly agree with you there, but we have to remember just how big a gap there is between the Eagles and Seattle/San Fran. That’s why you see the odds where they are. If the Eagles play Seattle in Seattle, they’ll be BIG underdogs. Now, they might still be undervalued. Given the recency effect, the public is probably overweighing Seattle, which would inflate their odds beyond the “true” measure. If Seattle’s goes up, everyone else’s should go down. I’ll keep an eye on that and see if I can find any actual evidence beyond the conceptual logic. However, I think 15/1 is both a reasonably fair line and a potentially attractive one for Eagles bettors. Remember, though, that I think this year is not going to go as well as many currently believe. I’m thinking 9 wins and a division title, which is a good season, but that doesn’t lead to great Super Bowl odds.

      • thanks for the response. I think you yourself may have a recency effect. If the Eagles play Seattle in Feb, it’s not like they play a week after we last saw them. We will have won once (and had a great record and a bye) or won twice. And same with predicting SF is a big gap ahead of us. They rarely would have to play both, and if they do SF is likely in Philly. And if Seattle is say 5 point favorites (they wouldn’t be, say, 10 point favorites), then maybe the Eagles are 5 point favorites in their first playoff game.

        I think in our division, 9 wins is…good but I’d take the over. the division could be really bad. Romo and Eli could be awful.

        What is a “BIG” underdog to you? Enough to shift our winning outcome from 1:1 to 1:2 b/c that is 1/8 to 1/15. That would, to me, seem like a really big underdog, I don’t know how to translate it but what, 8-10 points?

        obviously I am bullish. I am making the bet thru a friend in Vegas.

        I look forward to seeing how you predict out to 9 wins. I think when you go step by step you will shade towards 10 (or 12!!).

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