This should be a pretty quick analysis, but I wanted to see how the betting community felt about the title race because, let's face it, bookies make money for a reason.
Initially I wanted to compare the current title winning odds (which suggest we're favorites for the title over City) to the "title odds" you could generate by examining the results of the top teams game-by-game. Essentially, by examining how many points a team is expected to gain in each game they play (I'll showcase how I did that later), you can get an end-of-season table generated from the individual game betting odds.
If that final table is different than the current betting odds (or if the points gaps are larger or smaller than would be expected from the outright title winning odds given by various bookie websites) then you could see if there's an arbitrage betting opportunity (ie betting on outright title odds instead of game-by-game odds). More importantly for me (since I don't gamble and I'm pretty sure it's illegal in my state anyways) you could get a feel for the public's perception of the title race.
For instance, City has title odds (outright) of 31.3% (see the table I've provided below), but if City is expected to get more points on a game-by-game basis than Chelsea for the rest of the season, then it would be a good idea to bet on City's outright title odds now (since they should be favored to win the title). These title odds come from bet365 via oddschecker.
Graph Explanation and Example Calculations
The 'Fraction' column is what the oddsmakers list as the probability. How this works: if you bet the second number, you get the first number plus the second number (your original bet back). So, if you bet £8 on City to win the title, you'd get your £8 plus £15 in winnings.
These values can essentially be converted into probabilities. Take City again: if you add the denominator to the numerator (8+15 = 23) then divide by the denominator (8), you get the fractional odds of 2.875 (preferred in a lot of European betting systems).
Then, if you divide one by the decimal odds you get the expected probability of the event happening. Again with City's numbers: 1/2.875 = .3478. Now, when you add all the probabilities up using this method (NB: no teams below Everton have title odds) you get a number bigger than 1 (here, 1.1114). That's called the 'vig', which is how bookmakers make money (I could be wrong; that's how American odds systems work).
So, if you normalize all the raw probabilities by the total probability that's greater than 1, you end up with the expected probabilities of winning the title. Chelsea, theoretically, have a 50% chance of winning the title. City, from these odds, are listed as having a 31.3% chance of winning the title.
But Wait... There's More
Unfortunately, I couldn't get game-by-game odds past March. Using oddschecker.com (link includes full page needed for odds) I managed to get odds through the end of the month. These take values from many different bookmakers and give a single value. I don't know how they did it, and I also don't care. I took those odds, threw them into a table, then did analysis. Results:
The legend at the top should give a rough idea of what each colored cell means. So, by taking the game by game odds (which were fractional) and putting the decimal values down in the table, I could get a sense of what each team was expected to do in each game for the rest of the month. Let's look at Liverpool's data to explain.
Liverpool at United had the odds to win of 2.90 (fractional: 19/10), draw odds of 3.5, and loss odds of 2.5. By dividing each of those numbers into 1, you could get percentage likelihoods that each outcome would happen (NB: in my table I already normalized the odds to add up to 1 to remove the vig).
Then, the lightish purple cells are the expected points that game should generate. Since Liverpool would theoretically win 33.7% of their games against United, that would generate 33.7% * 3 pts = 1.011 points. With a draw giving 1 point, and at 27.9% chance, that adds another .279 points to Liverpool's expected points for that game for a total of 1.29 points.
By doing this for each game you can see how they should perform in each contest. Against Sunderland, Liverpool are expected to win 73.9% of the time and generate (with draws) a total of 2.387 points. That is very good. Our highest expected points total in any game is 2.191 against Crystal Palace, while City's highest expected total is 2.617 against Fulham (that's a lot).
Final Table for the End-of-March
Here we see that Chelsea are expected to hold the top. We currently have a 7 point lead over Liverpool and Arsenal, but that gap is expected to decrease at the end of the month; however, both teams will also lose their game in hand, meaning our point gap effectively increases during that time. The same occurs from City.
To get a feel for whether the gaps are supposed to shrink or grow, look at the yellow highlighted cells in the calculation table above. Due to the relative ease of our fixtures (Arsenal at home instead of away like City) we are expected to get the most points per match. Liverpool (who have an easy four game run) are second. Arsenal have a horrid four game run, reflected in their expected points per match.
- United seem to get some love from the bookmakers. The odds of beating them seem lower than you might think given their position in the table. They are likely a public team with a lot of action from squares, inflating their odds of winning (similar to the Cowboys or Packers in American football).
- Liverpool have a stupidly easy March. They will probably look pretty good, but wouldn't be surprised if they have a hard fall in April.
- Poor Arsenal. They can really do themselves some favors with some key wins, though.
- City's three games in hand look like they might be a disadvantage. We've seen this season that all the teams are capable of slipping up against poorer opposition, and I'm glad we already have the nine points from those games.
- We actually look pretty good here. I still think City's odds are a little low; if I were a betting man, I'd bet their title odds straight up here, because their game-by-game odds should potentially give them a more than 30% shot at the title.