The OFFER formula: Salary efficiency factors and on-field productivity variables

Credit: Tommy Gilligan-USA TODAY Sports
Credit: Tommy Gilligan-USA TODAY Sports

This is the second of four posts in a series explaining the O.F.F.E.R. statistic: On-Field Financial Efficiency Rating. The OFFER statistic is a comprehensive yet imperfect formula developed by the author as a loose measurement for MLB franchise financial efficiency. Factors include individual team payroll, regular season wins, playoff games/wins and projected revenue production per win. The OFFER statistic values organizational productivity without factoring irregular variables such as city/market size or the financial worth of individual owners.

Part One of this series explored the value of a postseason appearance for an MLB franchise by using approximate measurements on Vince Gennaro’s win-revenue-curve. The win-revenue-curve (win-curve) shows the different levels of revenue that a win during the regular season and playoff can generate on average for MLB franchises.

In this entry, we build a foundation for the OFFER formula by exploring the constant factors in an MLB season and the outcome-dependent variables that are generated as a result (i.e. individual win-loss records and playoff results).

The following are universal constants in every Major League Baseball season which we can use together with Vince Gennaro’s win-curve model (below) to generate variables and find a base for a working statistic:

1) Every team pays their players an annual salary, which combined, equals their total team payroll for that season.

2) Each team is scheduled to play a total of 162 games in the regular season.

3) Each team will generate a win-loss record as a result of the 162 games played during the regular season.

4) Ten teams will advance to the postseason.

5) One team will win the World Series.

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The OFFER statistic intends to work on a three dimensional scale by assigning value for salary efficiency, on-field productivity and financial return in the form of:

1) individual team payroll compared to average MLB team payroll;

2) total regular season wins, postseason wins, and World Series championships; and

3) the potential revenue generated on average as a result of wins produced (three levels of win-curve: win dollars, postseason dollars, World Series dollars).

OFFER formula

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OFFER variables

X = MLB average team salary

Y = Individual team salary

Z = Regular season games played

A = Regular season wins

B = Postseason wins + postseason series played (in a season without World Series championship)

C = Postseason wins + postseason series played (in a season with World Series championship)

Aw = Win-Curve ratio: average revenue generated per regular season win in a non-playoff season (substituted in the equation with a1, a2, and a3)

Bw = Win-Curve ratio: average revenue generated per regular season win in playoff season

Cw = Win-Curve ratio: average revenue generated per regular season win in World Series season

a1 = Bonus value per regular season wins in postseason year

a2 = Bonus value per regular season win in World Series year

a3 = Penalizing value for missing postseason

Salary efficient variables: (X and Y)

The variables for payroll efficiency, X over Y, represent the average MLB team payroll (X) divided by the individual team payroll (Y). The number produced has high determinate effect on a team’s OFFER score.

It’s important to note that value scale for the OFFER statistic is low-to-high (i.e. the lower the OFFER score, the lower the level of financial efficiency, and vice versa). That’s why it’s necessary to use the average MLB payroll as the X variable, and to make it divisible by the individual team payroll — the Y variable — in order to keep the formula consistent with the scale.

In the 2014 season, the average total payroll for all 30 MLB teams was $103,291,137. This number will serve as the constant X variable in the OFFER formula, to be divided by the individual team salaries as the Y variable.

On-field productivity variables: (“Win variables” A, B and C)

The second dimension of the statistic is the number of wins produced in both the regular and postseason. No statistic is more reflective of on-field productivity than a team’s win total. The win-curve approximates a dollar value for each regular-season win (beginning at 75, ending at 105) in three potential types of season outcomes: missing the playoffs, a playoff appearance (without winning the World Series), and a World Series championship.

As a natural measurement for on-field production and as the most significant factor in overall revenue production, regular season wins (A), postseason wins without a World Series (B) and postseason wins with a World Series Championship (C) are the appropriate variables to analyze in measuring on-field organizational efficiency.

While every MLB team will have an assigned value for A (regular season wins), only nine of the ten teams who reach the postseason will have positive values for B, and only one team (World Series champions) will have a positive value for C.

It should be noted that the variables B and C should never both have positive values when calculating an OFFER score for one team; the World Series champions are the only playoff team that will have a zero value for B. Furthermore, for teams who fail to make the postseason entirely, their values for and will always be zero.

The B variable stands for postseason wins in a non-World Series championship season plus the number of postseason series for which the team participated or received a bye. Division winners will get an automatic +1 in value for their wild-card round bye.

The value assigned for B can only range between 1-15; 1 being the scenario that the A’s and Pirates experienced this year (one playoff series with zero wins), 15 being the the maximum number of combined postseason wins and series played/bypassed a team can go through without actually winning the World Series (11 wins + 4 postseason series).

The C variable represents the total number of postseason wins + the number of postseason series bypassed in a season that a team wins the World Series. When applicable, C has a constant value of either 15 or 16 (11 or 12 +  4): the total number of wins necessary to win the World Series for a wild card team or division winner plus the 4 total series participated in or bypassed (wild card round, divisional round, league championship round, World Series.)

The reason the C variable is calculated separately from B in the formula is because C is multiplied by a separate win-revenue-curve factor (Cw) than B is (Bw). We’ll get further into that in Part Three.

Common denominator variable: (Z = 162)

The common denominator in the formula, Z, is an important variable in understanding how and why the OFFER formula is measured the way it is. Each MLB team can count on consistent revenue production for wins generated the duration of the 162-game regular season.

As mentioned in Part One, any additional revenue the team receives as a result of making the postseason is a bonus revenue stream for organizations. Logically, the further a team advances in the playoffs, the greater the amount that organization profits from any further on-field production.

The value of Z is set at 162, the total number of games played in the regular season, so as to generate a statistic that places an increased value on postseason appearances and wins.

Again, only ten of thirty MLB teams advance to the postseason. Therefore, calculating the OFFER score for the other twenty teams that don’t play in the playoffs should be comparatively simple, as the only win variable in the numerator of the OFFER equation with any value other than zero would be A — regular season wins — assuming that every team records at least one win over the course of a season.

The ten postseason teams will all have assignable values for and either B or C. Since only ten teams will have positive values for B or C, plugging in the number 162 (total regular season games) for as the denominating factor distinguishes the increase in revenue an organization stands to generate from additional wins throughout the postseason.

Filling in all the variables discussed above, the OFFER formula looks something like this:

Screen Shot 2014-10-09 at 4.18.58 PM

(Part Three of the OFFER statistic series will analyze the win-curve w-factors Aw, Bw, and Cw; These w-factors represent the third dimension of the OFFER formula, estimating the approximate revenue production in correlation with the on-field productivity and salary efficiency factors.)


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