"...And Then We Went To The Etihad".

Manchester City entertain surprise package Leicester in the mid day televised Premier League game on Saturday in the first of five, potentially high leverage head to head matches involving the current top four teams between now and May.

It is unusual to have four teams in genuine contention for the title with just 140 matches remaining, so although the outcome of the early kick off will move the dial it won't be as dramatic as if there were fewer title hopefuls.

The current market odds favour Manchester City followed by Arsenal, the respective second and third favourites in the preseason. So August liabilities may be still skewing the market's February estimation of either lifting the title.

By contrast, Tottenham and Leicester where available respectively at triple and quadruple digit odds.

Numbers are oblivious to any monetary balancing of the books and even the fluctuating levels of future performance that a high profile manager in waiting may inspire. They simply rise or fall as the matches are played out.

Not so very long ago, Leicester were just Championship FA Cup cannon fodder for the Premier League Big Boys.

Manchester City has averaged 1.83 expected goals per game and allowed 1.09 in the season so far compared to Leicester's 1.58 and 1.21 respectively, which gives the hosts a 53% chance of winning, 23% the draw and 24% the visiting Foxes.

The market is more bullish about the hosts (five Premier League losses so far) beating the twice defeated upstarts. It puts Manchester City's chances at nearer 60%.

There will be around 20 minutes to digest the result from the Etihad before the probabilistic projections of Spurs entertaining Watford and Sunday's trip to Bournemouth by Arsenal begin to turn into real points.

There'll also be ample time for the North London fan base to root for the best case scenario for their respective sides in the early game.

So how will the three possible outcomes alter, not only the title chances of the two Citys, but also those of Arsenal and Spurs?

How a Manchester City win might change the title odds at 3 o'clock on Saturday Feb. 6th.

How a draw might change the title odds.

How a Leicester win might change the title odds.

Obviously a win is the best possible outcome for either Manchester City or Leicester.

The host would draw level with their visitors with a win, the most likely outcome. Viewed purely in terms of the relative strengths and remaining schedule of the four challengers, Manchester City's likelihood of winning the title would remain below 50%. Although  in a potentially skewed market they are likely to move to odds on.

A Manchester City win is also marginally the worst outcome for Arsenal.

Spurs can root for a Man City win or a draw. Although the latter would turn their Valentine's Day game at the Etihad into a high leverage game.

A Leicester win would eat into the chances of each of their three competitors, particularly Manchester City's.

Although their underlying inferior defensive and attacking expected goals would mean that even a six point lead would be insufficient to overturn a title win by someone other than the Foxes as still the most likely outcome come 3 o'clock on Saturday.

Using Excel To Simulate Villa's Demise.

In the previous post, I described a simple method to use expected or real goals to estimate the average number of goals each team might score and allow in a single game at a certain venue and hence derive the win/draw loss percentages for the game via a Poisson.

It's a handy trick, particularly if you want a method to frame you own match odds and compare them to the market. But the goal ratings can also be used to create passable odds for games that are due to be played over the remainder of the season.

The table above shows the home/draw/away odds for the final weekend of the season using team ratings from the first 230 matches of the season, expressed in expected goals.

It is likely that the abilities of the 20 Premier League teams will change over the remaining 150 matches, but often the change is gradual. Regression towards the mean may be used along with season to date trends to extrapolate each side's future ratings. But on this occasion the ratings from week 23 have simply been used throughout.




To download the estimated home win/draw/away win probabilities for the remainder of the 2015/16 Premier League season just click on the download icon above.

There are two worksheets. One with match odds, both home and away and a second which lists win/ draw (and loss) odds for each team's final 15 games.

We've now got the available ammunition to simulate the range of points that might be won by each of the 20 sides and eventually join up all the interconnected results in each iteration of a season to project final league positions.

But first we'll just use excel to simulate the range of final points a side might expect to get based on these match probabilities.

Here's Villa's final 15 games with their predicted win% in column D. In column G take their predicted draw probability from 1 and drag this formula down to G16.

Insert a random number in column H and again drag down to H16.

We need two columns. One for three points should Villa win and one for a single point should they draw. A win is assumed if the random number is less than the corresponding win probability in column D.

We've taken the draw probability from one in column D. So a draw is assumed in proportion to it's likelihood if the random number is greater than 1 minus the draw probability. We've also ensured that we don't get a win and a draw in the same game.

Now add up all the points won from wins and draws in Villa's final 15 games. Sum(I2:J16)

Now we need the data table/What if to run the simulation, in this case 1,000 times. count column L up from 1 to 1,000 and paste K16, the total points won by Villa from our projected odds into M1.

Select M1000 to L1. Click "What if", then Data Table, then Column input cell, then select an empty cell, K1 in this case. Click "OK" and the simulated points for Villa will auto fill into column M.

For a step by step screen grab for this stage refer back to this post.

Add the points Villa currently have to each iteration. With 15 games left it was 13. I've done this in column N. And then use =Countif($N$1:$N$1000,Q14) to sum the number of iterations from the 1,000 (or more) you've run to see Villa's most likely final points total.

It's 26, which is also around the mid point of the current quote on the various spread betting sites.

Next time I might get around to simulating league positions in excel, GD tie breakers and all that.

How To Frame An Individual Match Outcome.

A simple method to frame your own match odds using historical goal or expected goal data. We'll look at Sunderland's upcoming home game with Manchester City. City unsurprisingly are strongly favoured.

Here's what you need.

1) The average number of goals or expected goals scored by the home and away teams in the competition.

So you can take data from this season or last season or a weighted average of a number of seasons. Your choice, you can validate your model against out of sample games later to see what works best.

2) The average number of goals or expected goals scored and allowed by Man City and Sunderland. Again time frame is up to you. I don't differentiate between home and away goals, that comes later. Why would you want to chuck half your data away or risk over fitting a "home or away specialist"?

Also the team figures haven't been regressed by adding a proportion of league average. We're just looking at the basic process here.

That's it.

Here's some representative figures. Home teams are scoring 0.25 goals per game more than visitors, 1.49 compared to 1.24. The average game has 1.37 expected goals per team. (Basically just the mean of the first two figures).

Sunderland are scoring few and allowing lots. Vice versa for City.

We want to find Sunderland's average expected goals at home against Man C. So these figures are more usefully expressed as rates.

Sunderland score 1.09/1,37 or 0.79 times the rate of scoring in the competition.

Man C allow 1.16/1,37 or 0.85 times the rate of conceding in the competition.

Sunderland are at home and home teams score 1.49/1.37 or 1.09 times the average rate for this competition.

Multiply these three rates together 0.79*0.85*1.09 = 0.73

Sunderland are likely to score at 0.73 times the league average number of goals at home to City. The league average expected goals for the competition is 1.37 goals.

So in terms of expected goals Sunderland might average 0.73*1.37 = 1.00 expected goals.

Do the same for City.

City score 1.92/1.37 = 1.40 times league average.

Sunderland allow 1.91/1.37 = 1.39 times league average.

Away teams score 1.24/1.37 = 0.91 times league average.

Man C are likely to score 1.40*1.39*0.91*1.37 expected goals = 2.43 expected goals.

So Sunderland have an expected goals average of 1.00 goals and Man C has 2.43 expected goals. We're in Poisson territory now and a plain, non-tweaked Poisson gives the following match predictions.

Compared to the current Oddschecker % of 13% Sunderland, 21% the draw and 67% Man C.