If you’ve been following me on Twitter (and you really should), I’ve been posting graphics of MLS Front-Office Efficiency figures for every club in the league.  I have made major changes to the formulation this year, and at any rate there are newcomers to this site all the time, so I will present Version 3 of Front-Office Efficiency in this post.

Front-Office Efficiency is a performance benchmarking tool that assesses a team’s performance relative to a baseline by calculating the ratio between a team’s usable payroll (its input) and league points won (its output).  The term “usable” is important because it communicates the resources available to a team that were actually used in the service of achieving its objective.  It is a simple metric, to be sure, and doesn’t explain everything about the relationship between resource and performance.  The goal of using such a tool is to identify organizations at the extremes so that more sophisticated analysis can be made on their practice and performance.

The Front-Office Efficiency expression is as follows:

\[ \mathcal{E}_{FO} = \frac{S_{av}U – S_0}{P – P_0} \]

where \(S_{av}\) represents the total payroll available to a team during the season.  Available payroll is defined as base salary expenditures for players who are on the roster at one point during the regular season — not loaned, released, transferred, or retired. Players who are injured, suspended, or on international duty are considered to be on the roster; the assumption is that the club continues to pay the player’s salary in these cases.  I know, these assumptions aren’t bullet-proof, but I believe that they are reasonable.

The major change in this expression is to multiply by the utilization factor instead of divide by it.  The utilization factor will never be greater than one (in most cases, it won’t be greater than 0.8), so it doesn’t make sense to divide a payroll number by utilization and come up with an even larger number.  Multiplying payroll by utilization results in the usable payroll of the team, from which we create the input-output ratio.

To calculate available payroll, the base salary for each player is prorated by the proportion of the season that the player was available for his team.  The league transaction records are used to calculate the number of weeks \(w_i\) that a player is available for a team, from which the proportion of the season (consisting of \(W\) weeks) can be calculated.

\[ S_{av} = \sum_{i=1}^N s_i \frac{w_i}{W} \]

The player utilization factor is expressed by \(U\) and it is the ratio of two weighted values: the sum of player’s prorated salary weighted by the number of minutes played \(m_i\) in league matches, and the sum of players prorated salaries weighted by their maximum possible minutes played \(M_i\) in league matches.  This factor asks, “Of the assets available to a club, what proportion of them were actually deployed during the competition?”

\[ U = \frac{\sum_{i=1}^N m_i s_i}{\sum_{i=1}^N M_i s_i} \]

This expression is different from the previous expression for player utilization factor, which used the maximum number of league minutes for all players.  I realized that that was not a correct expression of utilization because not all players were available with a team over the full season.

League points are represented by \(P\), of course, and \(S_0\) and \(P_0\) are baseline values of team payroll and league points, respectively.  The baseline figures represent some minimum attainable level that is used to calculate marginal expenditures, preferably kept constant so that results from multiple seasons can be used.  I prefer to set \(\left(S_0, P_0\right)\) for an initial year (2007) and calculate front-office efficiency from there.

Over time, the front-office efficiency will decrease in future years (i.e. the marginal payroll cost per point increases) as inflation increases. To remove the effects of inflation we use Bill Gerrard’s term for standard win cost, which is the inflation-adjusted payroll cost divided by the baseline payroll cost (which is from the year that we adjusted our payroll costs to).

I realize that there are a few equations, but they’re not complicated and they express what I’m attempting to accomplish pretty well.  I’ll continue presenting results on Twitter all this week, culminating with the infographic on Friday.