The Impact of MLS expansion on playoff qualification

In an earlier post I commented on the points and goals it would take to secure at least 8th place in the 2010 MLS table - the cutoff for the playoffs. I then wondered how those numbers would be affected with the addition of Vancouver and Portland in 2011 and Montreal in 2012. Luckily the response variable I used in the regression was generic:

-ln[p/(number of teams - p)]

Therefore, I can simply plug in the number of teams for the next couple of seasons, determine the response value that correlates to p=8 for each number of teams, and create the same 95% PI and CI values for each season. Figure 1 shows the results of that analysis up to the 20 teams everyone suspects is MLS's ultimate goal. I skipped the scenario for 17 teams given that the league will jump from 16 to 18 teams in 2011.

Figure 1: Goal differential and points required to make MLS playoffs based upon 16-20 teams (click to enlarge)

The net effect of adding each new team is to add one more goal and one more point to the minimum required to qualify for the playoffs.

There are a few assumptions made in this analysis. First, I assume that team performance holds to the historical average from 2005 through 2009. I will attempt to mitigate the impact of this assumption by updating the regression data set at the end of each season with the previous season's data. Second, it doesn't account fully for the additional points that would be available to a 18 to 20 team league running a fully balanced schedule. The most games any team played in the 2005-2009 time frame was 32 in the 2005 and 2006 seasons. If MLS were to keep the balanced schedule from 2010 in 2011, the league would jump to 34 games which means 6 extra points available to each time beyond the maximum available in my regression model to date. One might expect a shift upwards in the points required to finish eighth once teams are added.

It will be interesting to see how well the regression prediction plays out this season with the addition of the 16th team, and into the next two seasons as three more teams are added.

MLS Predicted Finish: May 9th, 2010

Predicted League Finish (click to enlarge)

This week saw many teams play two games as MLS attempts to bank matches ahead of the World Cup break in the middle of the season. This action also helps any prediction methods like the one I use, as a greater number of matches helps minimize errors associated with isolated hot streaks. Herewith is my summary of the impact of last week's action after a brief reminder of the background on my prediction methods. The background section will be a standard feature in each weekly post on MLS predicted finish, so regular readers of the blog can skip over it.

Background

In a previous post I noted three regression equations that I developed that have very good correlation to the last 5 years of play in MLS: finishing position vs. points, finishing position vs. goal differential, and points vs. goal differential. I use each team's current points and goal differential to project how they will finish the season in those categories, use those projections within the regression equations to predict finishing position, and then take the average of the three predictions to develop an average finish used to rank the teams.

Subsequently, I made a post explaining the range of values in goal differential and points that provided greater confidence in finishing position. This post set minimum values for goal differential and points required to achieve the 95th% confidence (CI) and prediction (PI) intervals. These minimum values are used to color code each team's projected season totals in goal differential and points, indicating the likelihood of the teams' finish in the Top-8 of the league.

Now, on to the impact of this week's action.

Galaxy continue to roll

I was fortunate (?) enough to witness the buzzsaw that are the LA Galaxy as they dismantled my Seattle Sounders for a 4-0 win. The team seems to have used last year's MLS Cup loss as a driving force in this year's campaign. Landon Donovan ran all over the pitch Saturday, keying three of the goals and then scoring his first of the year for the fourth. Seattle certainly contributed with their own bad plays on defense and in goal, but it took LA's killer instinct to take full advantage of them. This match followed LA's 1-0 win over Colorado mid-week, meaning they picked up 6 points and an average of a 2.5 goal differential per match. I didn't think they could get much better in season-ending finishing statistics, but they moved their goal differential up 3 (83) and goal differential up 9 (49) with last week's matches.

To give an indication of how well they continue to play, the only other two teams that are "all green" in the three key attributes are the Columbus Crew and San Jose Earthquakes. Neither team has played more than six games, which means they are greatly benefiting from a fast early season start with a high multiplier for total games (30) divided by games played (5 and 6, respectively). Even then, both teams are nearly 20 points behind and have less than half the goal differential of LA. Simply amazing!

Seattle continues to struggle

Of personal interest to me is the poor play of the Seattle Sounders. I mentioned before that their three ties from stoppage time goals would come back to haunt them. This weekend's loss to the LA Galaxy only made things worse. Seattle is now mired in last place in the hyper-competitive Western Conference (see discussion below). This week they stayed "all red" - their goal differential (-4) finally caught up with their low point total. Things won't get easier for the Sounders either - they face the East-leading NY Red Bulls this week at Red Bull Arena. It may be a long, hot summer for one of the league's most visible franchises. Seattle fans are a fickle bunch, and it will be interesting to see how many more sell outs the team records if their fortunes continue to deteriorate.

The West is dominating the early season

Six of the Top-8 teams are from the Western Conference. The Red Bulls loss this week lowered them to the sixth position, and two of their metrics (goal differential and points based off goal differential) turned red. The only other Eastern Conference team in the Top-8 is Columbus, who has only played 5 matches and is benefiting massively from a huge multiplier for their projected season-ending statistics.

This week also witnessed increased definition around the red-yellow-green statistics for each of the predicted attributes. There is now clear delineation around the eighth place position - those below it are now all red. The picture of possible league finish position is becoming clearer with the greater number of games played, yet we're only a third of the way through the season.

Biggest movers

Top three teams moving up in average predicted finish are:

• Real Salt Lake (+5): Real's 3-0 win over Philadelphia moved them up four spots based upon points, three spots based upon goal differential, and four spots based upon projected points based upon goal differential.
• San Jose Earthquakes (+4): San Jose's 4-0 win over the Red Bulls moved them up one spot based upon points, six spots based upon goal differential, and seven spots upon projected points based upon goal differential.
• Chivas USA (+3): Chivas' 4-0 win against New England helped mitigate the effects of a 2-0 loss to Houston on Saturday. More importantly, they benefited from the poor performance of others at the bottom at the table. They're now just two positions out of eighth, and are yet another Western Conference team beating out the bulk of the Eastern Conference.

Bottom three teams moving down in average predicted finish are:

• Chicago Fire (-5): Chicago's 4-1 loss to Toronto moved them out of the sixth position and down to eleventh. It cost them three spots based upon points, six spots based upon goal differential, and six spots upon projected points based upon goal differential.
• New England Revolution (-4): The Revolution's losses to Chivas and Columbus cost them three spots on points, eight spots on goal differential, and five spots based upon points from goal differential.
• New York Red Bulls (-3) and Colorado Rapids (-3): Losses by each team this week moved them towards the bottom end of the Top-8 spots in the league table.

Another interesting view of the table

Finally, I'd like to make readers aware of another awesome resource for ongoing table predictions throughout the season (HT: Boco_T). The guys at Sports Club Stats have a great prediction tool for any league you want to follow, including MLS. They use Monte Carlo statistical methods to project likely finish position, as well as the impact of a win, draw, or loss in the next match on each team's playoff chances. I'd suggest readers check out the website if they're interested in such data. I've added their EPL and MLS tables to my "Favorite Blogs and Websites" section to the right of this post.

What does it take to make the 2010 MLS playoffs?

In the last few posts I have explained how regression equations based upon 2005 through 2009 MLS data can be used to judge how well teams are performing in the 2010 season. Those posts culminated in this table, which I will update on a weekly basis with commentary throughout the season. I have done some further studies, mainly of the goal differential and points required to finish in the eighth spot in the table and make the 2010 playoffs.

Statistical Background

There are three ways to answer the question of what goal differential or points are required to finish 8th in the table. They revolve around the three statistical concepts below.

• Linear regression: A best fit line that represents the mean value of y for a given value of x.
• Confidence interval (CI): A range of values based upon the statistical spread within the data set and regression, often representing a range of values that are the likely distribution of the mean.
• Prediction interval (PI): A prediction of the range of future, individual observations based upon the data observed to date that is used to construct the regression.

In general, one can think of the regression as the single point mean of y for a given x value, the CI is the likely range of means for that same x, and the PI is the range of individual observations one would expect to see for the specific value of x. Those ranges, the CI and PI, are represented by the narrow and wider dashed lines, respectively, in the Figure 1.

Figure 1: Relationship of finish position and points from this earlier post.

Knowing the ranges of values expected for any value of x allows us to construct which values of x allow us greater certainty in finishing in the 8th position. In the case of my regression data, I have used the common 95th percentile distribution for constructing CI's and PI's. That means that for any value of x that I study, I will account for 95% of the expected values in the CI and PI when setting the bounds of any test.

Because the CI and PI involve distributions and not nominal values, the x-value that ensures the 8th place finishing position is below the range of potential finishing positions will be higher than that predicted by the regression equation.

Applying statistics to the League Table

In the case of my 2010 league table, I have constructed the following rules:

• Values are red if they fall lower than critical x-value from the regression. This means that they have less than a 50% chance of making the playoffs.
• Values are yellow if they fall between the critical x-value from the regression and the lower value of the 95% PI. This means that their chances of making the playoffs are between 50% and 95%.
• Values are green when they are greater than or equal to the lower end of the 95% PI. This means a team has less than a 5% chance of missing the playoffs.

Values for the goal differential and points that correspond to the CI and PI are shown in Figure 2 below. It shows that a team needs between a 3 and 16 goal differential and between 44 and 51 points to make sure they qualify for the playoffs.

Figure 2: x-values where lowest values in 95th% CI and PI are greater y-value that corresponds to 8th place in the table

The Modified League Table

Figure 3 shows the updated league table with the associated color codings. It gives a more complete picture of where teams are consistently performing at playoff form (LA, Columbus, and NY), the bulk in the middle that are showing mixed results, and those at the bottom who are already in danger of not making the playoffs. I have kept the average predicted finish from the three regressions shown in my earlier post, while collapsing the three constituent columns for those regressions to make the table easier to read.

Figure 3: League table as of May 3, 2010.

I will continue to update this table on a weekly basis, along with each of the columns and their colors. Hopefully it will shed some light on shifts in table position that will occur on a weekly basis - whether its goals or points.

Payroll doesn't win MLS Supporters' Shields

You can't buy this kind of hardware.

I made posts here, here, and here recreating the Soccernomics' pay-to-win regression, as well as highlighting some hidden results that the authors of that book didn't publish. Previous to that series of posts I highlighted the fact that MLS team payroll disparity isn't increasing, the average MLS team payroll is increasing at three times the rate of inflation, and teams with designated players (DP's) are the ones fueling that rise. The next logical question that arises is:

• Is there a correlation between MLS team payroll and finishing position like there is in the English leagues?

Background

For my international readers, I must take a few sentences to explain the Americanized version of the world's game that MLS plays. We don't award our championship to the team that wins the table. Instead, we give them what we call a Supporters' Shield which qualifies them for the CONCACAF Champions League, and then we break them and the next seven teams into a playoff. That's right - our domestic league uses a knockout round system to determine its champion. This bows to the very American way of determining championships in every other major sport - hockey, basketball, football, and baseball. In all of those other sports except football, playoff teams at least have to win a 5 or 7 game series to advance to the next round - that is, they have to win 3 or 4 games over their opponent. MLS and our football league - the NFL - have largely decided on a single game format. One match between two sides decides who advances to the next round of the playoffs. Pull off one above average performance, and you can easily send a team that consistently outperformed you all season into the off season wondering what all that hard work was for.

Not content to be like every other US sports league, MLS does throw in a home-and-away format in the first round of the playoffs. It's not clear to me why they do this in the first round but not the second round or the MLS Cup. Perhaps it is an attempt to prevent a large number of first round upsets, but it isn't exactly clear to me the purpose it serves.

To keep the playoffs interesting, MLS breaks eight teams every year into the playoff tournament. This presents some interesting challenges for a growing league. The total number of teams in MLS the past few seasons is as follows:

• 2005: 12
• 2006: 12
• 2007: 13
• 2008: 14
• 2009: 15
• 2010: 16

The teams added in 2007 through 2010 are not ones promoted from lower divisions - they are new franchises created for the explicit purpose of playing in MLS. This is another key difference from the rest of the world's game. Because of the rapid growth the last four years, this will be the first year that MLS will have not placed the majority of its teams into the playoff tournament.

All of these factors have a huge impact on the American game. Given that one just needs to make it into the postseason tournament to have a shot at a championship, a number of teams with losing records make it in every year. Indeed, last year's champion, Real Salt Lake, had a losing record and happened to flip a switch at the end of the season to make it into the playoffs and pull off an impressive run of wins once they were in the tournament. Also, given that there are a number of new franchises the last few years looking to make a splash, spending is way up for them yet they still struggle with the usual "expansion team" performance challenges. Finally, there is only the motivation of playoff seeding to push teams to compete for the top spots in the table. All these could potentially affect the drive of teams to spend money and resources to finish first rather than fourth or fifth in the table, thus making a relationship between payroll and performance harder to prove.

The Inputs

For this analysis I used 2005 through 2009 player salary data and MLS final table standings data.

As MLS is divided into two conferences (East and West) for the playoff format, I had to combine the two conferences for each season and assigned finishing positions based upon each team's total points for the season. Where ties in points existed, I awarded the teams the same position in the table and then skipped to the next finishing position for the first team after those that were tied. Once each team in each season had a finishing position assigned, I compiled the average finishing positions for each team.

I used the player payroll data to calculate each team's payroll as a multiple of the league average for the season. The team payroll multiple from each season was then compiled to make an average value for each team in MLS.

The results of these two compilations can be seen in Figure 1 below.

Figure 1: MLS average league position and payroll, 2005-2009

Just like the Soccernomics analysis, the data above is non-normal and must be transformed to perform any correlation studies and regression analyses. To do this, I initially tried the Soccernomics transformations of translating finishing positions to percentages as well as using natural logs and found that they worked. See Figure 2 below, where the p-value is greater than 0.05 and the assumption of normality is a safe one.

Figure 2: Graphical Summary for ln(p/16-p)

The team payroll data was also transformed by a natural logarithm, and we can now explore if there is any relationship between the data.

Correlation Test Results

As in my previous post on regression, the first attribute to check is the Pearson coefficient statistic before doing any regression analyses. Doing so will tell us if there is a statistically significant correlation between the two data sets. Figure 3 shows the results of the tests.

Figure 3: Correlation test between average team finish and team payroll multiple (with and without DP salaries included.

As Figure 3 indicates, there seems to be little chance there is a statistically significant correlation between team payroll and where the team finishes in the table as the p-values are not less than 0.05. What's interesting is that if the DP salaries are excluded (Team% no DP), the correlation statistics actually improves.

I did try a number of other transforms to the data to see if there was one that would generate improved fit. Unfortunately, none of the other transforms I tried improved the correlation statistics. Thus, I conclude there is no relationship between team payroll and table finishing position in MLS.

Reasons for the Lack of Correlation

Given the prominence of the Soccernomics analysis and the different conclusion drawn for MLS, here are some explanations why we might see such a difference in outcomes between the leagues.

• The poor cost/benefit equation of the DP: While the DP sucks up a ton of available pay-roll (MLS salary cap guidelines not withstanding), it represents only a single player on the pitch. As we saw in the correlation statistic comparison, the statistical score actually improves when the DP's salary is removed. This is especially true of the LA Galaxy, whose blowout purchase of David Beckham and his $5M+ annual salary has resulted in two bottom table finishes followed up by an appearance in the MLS Cup in 2009.
• The volatility in the league's makeup: There have been three expansion franchises added to the league in the last three years of the data used in the analysis. Two out of the three have tried to make a big splash by signing DP's, with one experiencing wild success in table position (Seattle Sounders FC) while the other has been in the league basement (Toronto FC). The Soccernomics study used a relatively stable list of teams that fought for positions in a mature league structure, which would provide less "special cause" variation seen in MLS's results the last few years.
• Low sample size: As with all statistical tests, sample size is key. The greater the number of samples, the more forgiving the test is and the lower the threshold for concluding a statistically significant relationship exists. See Figure 4 below for an example of how the number of samples affects the critical test statistic. The highlighted column indicates the critical correlation values that a test must be equal to or greater than to ensure less than a 1% chance of error in assuming a correlation exists between two data sets. In the case of the MLS data I used, n=15 so one must observe a correlation statistic of 0.5923 or greater. As I stated in my regression post, the Soccernomics study had 58 teams included and thus only needed to observe a correlation statistic between 0.2948 and 0.3218 to make a conclusion of correlation.

Figure 4: Critical correlation value vs. sample size and significance level

• The league's salary cap structure: Outside of the league's DP rule, MLS does try to maintain some form of a salary cap like most other American leagues. While America tries to pride itself as one of the most capitalistic societies, it's exactly the opposite in its sports leagues. In some ways, it makes sense. Capitalism fosters a system of cutthroat competition that eventually leads to a few winners and many losers. This can be counterproductive to providing a healthy, competitive league of 20-30 teams. Providing a ceiling on team payroll may help league parity, but it does make it difficult to rationalize expenditures in hopes of future success.

Ultimately, as MLS moves towards a stable 20 team league in the next few years (increased sample size) and the use of DP's becomes more rational with experience (improved cost/benefit equation) we may see the correlation statistic improve.

Next Steps

If the the main goal in MLS is not to win the table but to win the playoff tournament and the MLS Cup, what attributes could be considered in understanding the likelihood of winning the Cup? I will explore this topic in my next post. Until then, enjoy some soccer this weekend!

Why the MLS owners fought the players so hard

Note: This is a repost from March 8th, 2010 at my other blog, which is a mix of politics, economics, and containted a few soccer-related posts before this blog was created. I made this post in the middle of the MLS labor turmoil. I have reposted this here as it will provide the background for the first few posts I make of new analysis.

Figure 3.1 from Soccernomics, which shows a substantial

correlation between wage expenditure and where a team
finishes in England's top two soccer leagues.

I mentioned in a previous post that I am reading the book Soccernomics, which is chock full of statistics that clarify or challenge conventional sports wisdom. The authors do a very good job of not only comparing differences in soccer leagues, but also across other sports with a special emphasis on baseball given it's similarly lenient financial rules. One of the more interesting aspects of international soccer versus traditional US sports leagues is the financial and transaction rules governing the game.

Most US professional sports leagues are governed by some form of salary cap to prevent runaway spending by big market teams that translates to widening disparities in competitiveness. The most successful model of this behavior is the NFL salary cap and it's resultant goal of "league parity". Transactions between teams nearly always involve player trades, and are often executed as much for salary cap management as for overall team improvement. This is due to the fact that the teams are often required to assume the terms - both financial compensation and duration - of the contract. This model minimizes costs, and provides a predictable and somewhat stable source of revenue and cost for owners.

International soccer, governed by FIFA rules, is completely different. Largely, there are no salary caps - although that may change as an emerging soccer debt bubble may cause governing bodies like UEFA to place "break even" financial requirements on clubs. Teams are free to spend what they want, where they want. When it comes to transactions, player swaps do not take place. Rather, a "transfer" will take place where the club and player are paid a one time compensation for the transferring of rights from one club to another. Transfer fees can be huge, as speculation plays a big part when rival clubs are bidding for a player's talents. They can be the difference between profits and losses for clubs.

The authors of Soccernomics have found out some interesting things related to transfers and team payroll.

First, there is very little correlation between the money a team spends in the transfer market and their success in the league.

But much of this [transfer] money is wasted on the wrong transfers. In fact, the amount that almost any club spends on transfer fees bears little relation to where it finishes in the league. We studied the spending of forty English clubs between 1978 and 1997, and found that their outlay on transfers explained only 16 percent of their total variation in league position. By contrast, their spending on salaries explained a massive 92 percent of that variation.

What's interesting is that even given this data, clubs still go out and blow huge sums of money on transfers. Soccernomics goes into many reasons why transfers largely fail to improve a club and why clubs continue to pursue them, but I will save readers from me regurgitating all of Chapter 3 of the book. Rest assured - transfers present a bad ROI, and you need to read the book to get the full story why.

Second, there is a good bit of correlation between the money a team spends on annual total player payroll and their success in the league. The graph at the top of this post shows the author's regression results when studying payroll and club success. While there is a substantial correlation, the graph must be deconstructed to understand the true magnitude of the trends given that logarithmic functions had to be used to get the linear fit. If one is to look at what it takes to move from mid-table on average to the top 4 positions, we could examine points that correspond to 0 and 1 on the x-axis. Adjusting both the payroll data and the finishing position data by their logarithmic functions, one finds that a club must spend about 3 times more money than the league average to achieve an average finishing position 5 places higher than the average club. Given a table of 20 teams, that means one must spend 300% more than the average team to move up 25% of the table - diminishing returns indeed! Given that finishing in the top of the league effectively means promotion - either from the Championship to the Premier League or the Premier League to the Champions League - and ever growing revenue, there is huge pressure on team finances to compete for those top few spots.

And thus, we get to the rub of soccer in the United States. The MLS player's union and ownership is locked in a stalemate over the terms of the next collective bargaining agreement (CBA). Players are asking for fundamental changes to the way the league manages their contracts - they are asking for free agency, terms closer to the rest of the world's players when it comes to transfer terms, and for an eventual dissolution of the league's single entity structure so that players can sign contracts directly with teams. The league's ownership is steadfastly refusing these terms - and for good financial reasons. No one expects MLS to turn into the Premier League overnight, but the failure of the NASL looms large as the cautionary tale of what happens when US soccer leagues don't run a conservative financial house. Given the expectation of US sports franchise owners that they should run their team like a business and make a profit (an assumption Chapter 4 of Soccernomics ultimately destroys), the owners can look at results like those from the English leagues and see what the end game is - large sums of money, often spent irrationally, producing unpredictable results and destroying the financial health of the league's teams. Teams like the Seattle Sounders, with deep pocketed owners and fans who set the league record for attendance in the team's first season, would look to use that financial position to build a permanent place at the top of the league for themselves.

As a Libertarian, I can't say I agree with the owners' position. There's a legitimate point to be made for workers' rights and against the business collusion of a single entity. But as a growing soccer fan that wants the MLS to be a stable, long-term venture I also can't disagree with the owners' approach of limiting the financial commitment required of teams. They are doing the rational thing of following the statistics, and recognizing that the league can't support such an arrangement at this time.