*Before I begin I’ll say, as the title suggests, this is simply a thought experiment. The thoughts are also all mine, which is kind of dangerous in science, so I’m looking any input/thoughts/suggestions you may have. I like this idea and think, as a community, we could take this somewhere.*

As I’ve mentioned previously the idea of a replacement level team is one who’s performance is essentially the minimum you could reasonably expect from a team in a given league. To determine replacement level for the Premiership I took the ten teams with the worst TSR and looked at how they performed.

~~I’ll throw a table in here later but to sum up their season statistically~~ As per the table below these teams have an average TSR of 0.377 (i.e., they take ~38% of shots in the matches they play) and score a combined total of 315 points, resulting in relegation on each and every occasion. Importantly they also get pretty average luck, ~7 Premiership teams a season will finish the season with a PDO below the combined 980 these teams recorded.

*An explanation of total shots ratio can be found here and here, for PDO see here and here.*

So far so salient. This is where the thinking starts.

In theory we can then take this information and suggest that ‘replacement level’ performances account for about 630 points per Premiership season (31.5 points multiplied by 20 teams). We also know that each year Premiership teams collectively accumulate approximately 1040 points. Subtract the ‘replacement level points’ from the ‘total points’ and you essentially have the points that teams are playing (and paying) for here.

Basically I’m intimating the 20 teams are fighting for a share of ~410 points (1042 – 630). The best teams will typically take 50-60 of these, the worst will typically take a number around zero.

So how many of these ‘points above replacement’, or ‘PAR’s’ (hat-tip to baseball) are required to finish in a certain position in the Premiership?

Let’s leave it there for now. As I said at the start I’m looking for any comments or suggestions you have. Does it at least sound like I’m following a lucid thread of thought here?

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Cool! The soccer analytics holy grail. Immediately what jumps to mind is that PAR is a whole team measure, so not as useful as its baseball equivalent.

It is for now. I’ll have a play at splitting it up a little bit next week. Someone with access to far more data than me could have a much better stab

Hi,

A couple of thoughts popped into my head while looking at the chart and reading the post …

1) I assume that you got the PAR numbers by adding up all the scores for teams in that position, dividing it by ten and subtracting 31.5? Or was there some difficult mathematical formula used? 🙂

2) What struck me as interesting was the difference between two positions that lie next to each other, e.g. 3rd and 4th have a difference of 6 points, 11th and 12th only 1 point.

The biggest gap is 7 points, between 19 and 20 and 2 and 3. Meaning that over the past 10 years the top 2 teams (even though they have been different over that period) have always been quite a lot better, on average, than the rest of the pack.

Now here is where I do some thinking but mathematically don’t know if I’m doing it right, will explain why not in a sec.

If a team would want to climb from position 3 to position 2 they need to improve by 9.4% (7 point difference on their projected end of season total of 74.5 points) … if a team wants to climb from position 20 to 19 they have to improve by 27.5% (7 pts, projected 25.5).

Now, I’m sure I’m missing something as points are 0,1,3 and not 0,1,2. Therefore, I don’t know how to answer the following … hypothesis; in a season that is halfway and going exactly to predicted PAR two coaching positions open up, that of the team in 18th and that of the team in 5th. All things being equal (no injuries, transfers etc.), which coaching position has the more difficult task to improve the team by one position?

3) Instead of just looking at teams lying next to each other in the tables … For the Premiership there is talk of a Big4 or 6, is there evidence of this in the PAR numbers? By the way, I mean position-wise and not related to team name (e.g. Everton). Are there groups of positions on the league table that share the same quality/stand out from the rest?

4) What are the average TSR numbers associated with the positions? Is there a relationship in deltaPAR and deltaTSR between league positions? This comes back to point 2 above, because if TSR is related to how good a team performs then I assume one can see how to improve TSR to improve league position, the points improvement associated with a TSR improvement.

5) Fun fact …

2011/12 position 20, pts 27, diffPAR +1.5, TSR 0.360, PDO 979.

2010/11 position 12, pts 46, diffPAR -0.5, TSR 0.486, PDO 975.

2009/10 position 16, pts 39, diffPAR -0.5, TSR 0.439, PDO 990.

Now this is for Racing in La Liga and of course La Liga’s PAR values will be different, but if the team is related to position/PAR in the Premiership you’re spot on. 🙂 diffPAR being the difference between projected points and actual points. Added in the TSR and PDO values for fun, but notice how they fit well in 2011/12 (relegation) with the 10 teams you looked at.

Stopped at 09/10 because I don’t have numbers for before 2009/10 yet.

Well … nothing really insightful, basic stuff. I like looking for relationships.

cheers,

b.

ps – oh I almost forgot …

6) You looked at a 10 year period and got the figures above … is 10 years long enough to make a definite PAR chart? If so, after next season, if you remove the first season from the numbers and add that next season do you expect the values to change?

Changing values could indicate a widening quality gap between average teams and the top teams for example (what many are saying is happening) and thus after an X amount of years in the future could we see the gap between the PAR of #4 and #5 be huge while the PARs between the positions under that come closer together?

On a wild tangent, but we could then be witnessing what the difference in prize money does for teams going to the CL and teams with EL or nothing. I know there are a million other factors at work, but still. 🙂

1) You’re spot on, but I used twelve seasons so divided by twelve

2) Great question. My hunch is the team in 5th but I’ll think about it some more

3) I think you could suggest that there is some evidence of a big four and big six due to the gaps between 4th and 5th and between 6th and 7th. Other than the team in 20th though there’s really not that much between the teams in 8th and 15th but once you hit groups that size your basically saying half of the league is the same

4) TSR will come another time. I think it’ll be more illuminating

5) That’s kind of promising but I don’t think we can read too much into cross league measurements. This really isn’t perfected for the Premiership yet

6) You’ve hit the nail on the head here and it’s something I hadn’t considered. If I was able to run simulations then this is exactly what I’d be investigating. And money definitely plays a part here – there’s definitely a £ value for 1 PAR.