irregularstats

In my first post, I laid out and briefly discussed my team rating (named ‘SUM’ for now) that combines 5 metrics:

• Shots on Target Ratio (SoTR) weighted *6.3
• Passes per Shot (PPS)
• Danger Zone shot % (DZ%)
• A very simple Expected Goals model (xG)
• Shot on Target Save % weighted *2.5

I compared it to end of league standings for the 14/15 English Premier League and found a decent correlation between the two, with an R2 of 0.754.

Since, I realised it would be more representative to judge my team rating against points scored rather than league standing and goal difference, because these offer a slightly higher level of accuracy – e.g. Everton and West Ham finishing on the same amount of points isn’t captured by league standing, which ranks Everton (11th) higher than West Ham (12th).

Going with the same calculation:

SUM = (SoTR*6.3) + (Save%*2.5) + PPS + DZshot% + xG

SUM correlated against points scored:

R2 jumps from 0.754 to 0.852, simply by judging against points rather than league position. Of the two that stand out, Southampton and Tottenham, I am more annoyed by Tottenham being undervalued. Southampton had a great season, playing excellent football, and this is recognised here. I don’t think many could convincingly argue that Man Utd played significantly better than Saints. SUM does rank Spurs as the 8th best team last season, however there is a considerable gap between the mid-table and the top 5 teams. Is this representative of these team’s performances? Maybe so for the likes of Everton and Swansea, but I am not convinced Spurs were that much worse than Liverpool and Southampton. Looking at the data, the reason for Tottenham’s low team rating is their comparatively low SoTR – the 8th best in the league compared to Southampton’s 4th best and Liverpool’s 5th best.

Also, Chelsea performed much better than Man City over the course of the season, finishing with 8 points more, yet City are rated higher. A possible reason for this is discussed later.

I am happy with the clustering at the bottom of the table. It is hard to differentiate between the performances of these teams, although QPR ran away with it at the bottom.

Let’s now correlate SUM with goal difference.

R2 jumps again, up to 0.934. The clustering at the bottom of the table is broken down a bit more, and the rating difference between Southampton and Tottenham starts to make more sense – despite being only 4 points between them in the table, Southampton’s goal difference was markedly better, 21 vs 5. Similarly, City’s GD was superior to Chelsea. This makes it clear to me that the metrics used to create my team rating are more representative of goals than actual results, which I guess is an issue in general amongst the analytics and wider community.

Let’s move over to this season. After 13 games, Leicester are the surprise package, and they stand out the most in the left plot below:

SUM underrates their current performance, and you can deduce from this that their current run is surely unsustainable. They are rated exactly the same as Everton (who have been excellent in the last few weeks), and this shows on the right graph, with them both having the same goal difference. Also interesting to note is Spurs who many acknowledge to have been amongst the most impressive teams thus far. SUM rates them as much, with no difference between them and Man City at the very top.

West Ham and West Brom are overperforming according to SUM, which is not an unreasonable claim (ahem). And Villa and Sunderland deserve to be at the bottom according to their underlying numbers, although over time, Big Sam could/should improve the Mackems position.

It is clearly fairly easy to get high correlation between team rating and points scored/goal difference by combining just a few metrics – starting with just SoTR gives you an R2 of 0.77 on its own. However I am convinced there are other metrics out there that will improve SUM and I will continue looking to find them.

Please feel free to criticise/suggest possible improvements.

 

Yes, another postgrad who thinks he knows a thing or two about football and statistics come to jump on the analytics moneyball merry-go-round, hoping to one day be in charge of all Liverpool’s transfers – you caught me.

Disclaimer – I don’t reeeeaaallly have an idea what I’m doing, statistically speaking. And on that reassuring note, lets begin.

Over the last few days I have been trying to ride the crest of the defensive metric wave, the increased attention paid to the side of the game generally considered harder to measure than attack. Many really interesting pieces have been written recently; I won’t link them as you’ve already read them, right? Metrics like passes per defensive action (PPDA), passes per shot against (PPS) and save % are excellent (oh go on then). I, blindly, wanted to combine these metrics with SoTR and an *extremely* crude xG model. Could these 5 base-metrics be combined to create one ‘super-metric’ that scores a teams skill/ability? FitbaFancyStats did something very similar here. I wanted my own.

Using the 14/15 Premier League as my blind, unwitting Guinea Pig, I created the 5 metrics (replacing PPDA for danger zone shot %). Soon enough it became clear that the data were all measured in different scales – they needed to be normalised. The process of feature scaling/min-max scaling/normalisation scales each data point to a range between 0-1. Now, the worst team in the league for, say, SoTR, scores a big fat zero (Sunderland), and the best (Man City) scores 1. Great. Add these together to create my super-metric and I’m done…? Lets see:

A simple correlation of the ‘super-metric’ (SUM) and final league position is a decent start – a highly significant p-value shows…significance? It’s been almost 6 months since I left uni OK?! At least the best teams are near the top and QPR are at the bottom. Stoke, Palace and Tottenham overperformed whilst City and Southampton are underperformers. An adjusted-R2 of 62% is good.

I was pleased with myself initially, smugly grinning to myself over a lunchtime bacon sandwich. Until I remembered that SoTR itself is supposedly highly correlated with final standings. Quick, check it:

FFS. Sure enough, SoTR is highly significant on its own, with an R2 of 71.6% – more than my super-metric! None of the other 4 metrics have such high explanatory power for final league standings. Thus, most of the explanatory power in ‘super-metric’ Mark I. is coming from SoTR. Surely it is not representative to give SoTR the same weighting as the other 4, less powerful metrics.

I decided to play around with weights. This is where my method gets very, I don’t know, crude/simple/amateurish etcetc. Trial and error was my gameplan, initially randomly attaching weights in excel to the normalised SoTR metric. The effect this has is to further punish those teams with low SoTR scores (0*10=0), and boosting the teams with the highest scores (1*10=10). After playing around with different weights, I settled on 6.3. Now my super-metric looked something like this (remember, all metrics have been normalised to range between 0-1):

(SoTR*6.3) + Save% + PPS + DZshot% + xG = SUM

Its correlation with the league table looks like this:

You can see the SUM is much higher now for the top teams compared to before with no weightings attached (Fig. 1). Still highly significant. However the R2 has risen to 75.4%. All that has changed is SoTR has been given more influence. R2 falls if the weight of 6.3 is increased or decreased, thus 6.3 is deemed optimal for maximising R2 – whether this should be my aim or not, I genuinely don’t know.

I also experimented with attaching weights to the other variables – the only metric that marginally improved R2 when weighted was save %, from 75.4% to 77.7%. No overall model improvement when weighting xG, apparently the hallowed metric doesn’t carry the same explanatory power as SoTR or save %, although I expect this is because of how simply calculated it is in my model.

The maximum R2 I can achieve from all possible combinations of the 5 base-metrics is by combining just weightedSoTR and Save%, giving an R2 of 80.2%. According to this, that is a more accurate describer of team ability than my ‘super-metric’ – the one with all 5 metrics included. Which is more useful – a metric with the highest possible R2 but made up of only 2 metrics, or one that includes all 5 genuinely valuable and descriptive in their own right metrics like those used presently?

Like I said, I don’t really know what I’m doing.