Putting Arsenal’s start into context

Commenter Bart (see comments below) has pointed out a whole host of errors in this post. The tables have subsequently been updated (11Nov12)

As usual, one of the top four from the past season has started somewhat poorly. The past two seasons this has also happened, to Arsenal in ’11-12 (link), and Spurs in ’10-11 (link). Incidentally Arsenal finished last season 3rd, and Spurs were 5th at the end of the ’10-11 season.

This has led to stories about Arsenal’s decline and questions as to whether Wenger is losing his control at the club, but how deviant has this ten game stretch been compared to Arsenals historical performance in the Premiership?

I have 466 Arsenal games on record, 12 full seasons plus the ten games played thus far this season. By taking ten game samples (i.e., games 1-10 being sample 1, games 2-11 being sample 2 etc.) that gives me 457 ten-game samples to look at.

Let’s start with the 14 points they’ve accrued thus far:

So, in the vast majority of the ten-game samples, Arsenal picked up more than 14 points. They pick up an average (mean) of 18, so they’re a significant distance behind that, but random fluctuations occur due to random chance. So if we take the sample as a whole then what are the chances that they’d be this bad by chance as opposed to the result of them being a worse team?

As such, the number of points they’ve scored over the first ten games suggest that we can be about 85% sure that they’ve been worse than their average performance over the prior ten years.

Let’s delve in and take a look at some of the other factors that may be driving their results (I can’t explain the crappy resolution on these next two tables, if you click on them the picture files are far clearer):

Their goal differential is almost exclusively better, although that’s not surprising given the correlation between goal differential and points. However it’s the next two numbers that are, to me, the most telling. In terms of driving the play and controlling the ball in the attacking areas of the pitch Arsenal are behind, in one case significantly their usual standards (the mean values for STR and TSR are 0.649 and 0.625 respectively).

In terms of the luck-driven components they’re actually not doing too bad, their sh% is below historical levels but that’s being compensated for by their higher than usual sv%, but again, they’re so luck driven that it’s pretty pointless reading too much into those. Ditto PDO.

Finally what is the probability that Arsenal have been this bad (or, in the case of sv% and PDO, this good) compared tho their historical performance through chance alone?

The two numbers I’m paying the most attention to here are those associated with STR and TSR, the pair of which are telling the same story, albeit with differing degrees of certainty. Basically Arsenal have been somewhere between somewhat and significantly worse than their historical performance.

That being said they’re still a pretty good team and the number of points they score should still regress upwards somewhat as the season progresses (a TSR of 0.621 projects to ~74 points over a full season, an STR of 0.598 projects to ~71), however some damages has already been done, and, in very simplistic terms, you’d have reduce any projections for Arsenal by ~4 points simply because of their start to the season.

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3 thoughts on “Putting Arsenal’s start into context

  1. Don’t mean to be too critical of your first post in a while but …

    Something doesn’t read right:
    You state that Arsenal have a better save% than usual, which is offsetting their poor shooting%.
    Looking at the tables I might conclude that the exact opposite is true.
    They have a save% of 83.7 … and 82.1% of the time that number is actually better in your data over 10 games! I might conclude from those numbers that their save% is significantly WORSE than the historical average.

    Furthermore, Arsenal would seem to be about right where they should be when considering their historical number, as you’ve stated many time that TSR is the best indicator of quality (of which they are almost bang on mean) and the luck element PDO is also very near historical mean. Thus they’re about as good as they normally are and don’t have significantly more of less luck. i.e. they’re pretty much where they should be.

    On top of that … I thought they picked up 15 points from their first 10 games with a goal difference of +7?

    Finally … what is really interesting is the following (if we take the top table into consideration) … their TSR is almost mean … their STR is darn bad (i.e. they can’t seem to get a shot on target these days) but somehow that doesn’t really matter as they manage to score an incredible amount of goals/shot on target (very high shooting% compared to historical data) … does that rhyme with the striker issues that are apparently having, putting Gervinho up front or trying to incorporate the new striker Giroud into the team?

    cheers.

    ps – didn’t look at the second table … 2 of the bottom 3 STDEVs don’t seem to rhyme with the top table.

  2. One other thing, TSR and STR are pretty much interchangeable in terms of their predictive ability over the course of a season, I simply choose to use TSR because of the larger volume of events

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