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The OFFER formula: Win-curve factors

This is the third of four posts in a series explaining the O.F.F.E.R. statistic: On-Field Financial Efficiency Rating.

(Credit: John Rieger-USA TODAY Sports)
(Credit: John Rieger-USA TODAY Sports)

This is the third 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 1: The value of a postseason appearance for an MLB franchise]

Part 1 of this series estimates the actual dollar value of a postseason birth by exploring the value that winning can create on two levels; revenue-per-win in a season with a postseason appearance, and revenue-per-win in a season without a postseason appearance.

Win-curve 2 Levels

[Part 2: OFFER formula: Salary efficiency factors and on-field productivity variables]

Part 2 of this series laid the foundation for the OFFER formula and explained the salary efficiency and on-field productivity variables (X, Y, Z and A, B, C). The basic OFFER formula and variables are as follows:

OFFER formula basic

= MLB average team salary

= Individual team salary

Z = Regular season games played

= Regular season wins

= 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, or 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 = Aw/Cw – Penalty value for missing postseason

a2 = Bw/Aw – Bonus value per win in postseason year

a3 = Cw/Aw – Bonus value per win in World Series year

(authors note: a1 and a3 were accidentally switched in Part 2. Variables above are correct.)

Part 3: The win-curve factors

In this entry we dig back into the different levels of value on the win-curve. The average revenue-per-win derived from the three levels of the win-curve represent the third dimension of the OFFER formula, financial productivity.

Gennaro’s win-curve

Let’s briefly recap what we already know from Part 1. The win-curve analyzes four different layers of value associated with winning.

1) Win dollars – Revenue per win in a season where a team fails to make the postseason.

2) Postseason dollars – Revenue per win in a season where a team makes the postseason but does not win the World Series.

3) World Series dollars – Revenue per win in a season where a team makes the postseason and wins the World Series.

(Note: The fourth layer measures chronic winning or losing over the course a 3 year period. Since the purpose of the OFFER formula is to evaluate efficiency for a single season alone, this fourth level of value is not relevant.)

photo

The specific values and slopes along individual team curves can vary drastically based on market size, the popularity of the team brand, the history of the franchise in the market, and ticket pricing…amongst other reasons. 

These non-universal factors (market size, brand, etc.) dictate the slope of the curve for each individual team, and provides a framework for ownership to know the point where financial output against profits returned equals upmost efficiency for that particular organization.

The discrepancy between big and small market curve extremes is illustrated by the “steep” and “flat”  2006 win-curves for the New York Yankees and Atlanta Braves.

Screen Shot 2014-10-08 at 6.20.58 PM

The advantages and disadvantages facing different teams with regards to market size, consumer appeal, and ownership are neither consistent nor temporary.

The purpose of the OFFER statistic, however, seeks to find a common ground for valuation between these big and small market teams, irrespective of non-universal factors. 

In order to generate a universal formula for all thirty MLB teams, free of prejudicial valuation, the variables and factors accounted for must be equal in scale and objective by natureSince market size and ownership financial worth can never be equal in scale, they cannot be factors for consideration, at least not individually, in the OFFER formula. 

What can be used to measure the financial efficiency of an organization based on the league average for revenue per win (the win-curve); a pure measurement of dollars spent → wins produced → average revenue generated in return.

Since Gennaro’s win-curve chart averages out the progressive slope of all 30 MLB teams, ratios taken from the curve can serve as constant variables for revenue production per win.

The w-factors (Aw, Bw, Cw)

The OFFER statistic is three dimensional; 1) Salary efficiency, measured by comparing the individual team payroll to the MLB average for total team payroll, 2) On-field productivity, measured by the number of wins a team accumulates over the course of a single season, and        3) Financial Productivity.

The third dimension of the OFFER formula representing financial productivity are the w-factors; Aw, Bw, and Cw (Aw is substituted for in the formula by either a1, a2 or a3).

The w-factors represent the average revenue-per-win (RPW) generated by a team that either 1) fails to make the postseason (Aw – Blue curve), 2) makes the postseason but fails to win a World Series (Bw – Green curve), or 3) makes the postseason and wins a World Series championship (Cw – Gold curve).

In order to differentiate the revenue-per-win averages in each of the three season-types, the three curve slopes must first be analyzed individually.

To account for slope variations on an individual curve, the w-factor averages are computed by taking the total revenue over total wins (RPW), at five separate win-total intervals across the bottom axis.

Win-curve 3 Levels

The first win interval is set at the 87 win marker, since threshold for playoff qualification in the 2014 MLB season was 88 wins (A’s, Prirates). The final interval is set at the apex of the curve at the 105 win mark, and the other three are set at somewhat equal-distant markers in between (91, 96, 100).

By following the slope of one individual curve, then taking the revenue total (on the Y-axis) and dividing it by the win total at each of five corresponding intervals (on the X-axis) of that curve; and then taking the average of those five interval RPW averages (by adding them together and dividing them by five), the resulting figure is the average revenue-per-win for each of the three season-type win-curve levels…the w-factors.

The table below should help for clarification on how the w-factors are generated.

WC Tables

The numbers in bold on the right of the chart will serve as constant values in the OFFER formula for the MLB average revenue generated per win in each of the three levels on the win-curve;

$1,513,264.18 million per win in non-playoff season (Aw)

$1,837,364.46 million per win in a playoff season (Bw)

$1,997,832.51 million per win in a World Series season (Cw)

Dual-function of w-factors (a1, a2, a3, Bw, Cw)

The w-factors serve dual-purpose in OFFER formula calculations. The first is that described in the section above, the win-curve function; where the total number of wins multiplied by the applicable w-factor represents total revenue generated on the regular season.

During the beginning stages of developing this formula, the w-factors initially were meant to function only as a representative value for revenue generated per win. 

However, after several trial and error calculations yielded inconsistent results in measurement. Teams with extremely low payrolls who failed to reach playoffs had OFFER scores higher than it reasonably appeared they should), so the main formula was adjusted to correct the imbalanced results by using the w-factors for another purpose.

The second function of the w-factors in the formula is to serve as either a increase variable (a2 & a3 > 1) for making the playoffs, or decrease variable (0 < a1 < 1) for missing the playoffs; which is thereafter multiplied by the team’s total number of regular season wins (A).

To better understand the w-factors and their dual-function work in the OFFER score, the main formula can be “simplified” by breaking it down according to the three win-curve value levels. Depending on the outcome of an individual team’s season, their OFFER score will be generated by plugging the relevant numbers into one of the following three equations:

Screen Shot 2014-10-16 at 5.48.13 PM

The value for variables a1 (penalty for missing the postseason), a2 (bonus for postseason appearance), and a3 (bonus for World Series season) is calculated by fractioning the w-factors to represent the missed opportunity or bonus opportunity gained for revenue generation; which is then substituted in the formula where in place of the Aw variable.

a1 = Aw/Cw (Decrease variable — in a season without a postseason appearance)

1.513264178/1.997832513 (a1 = 0.75745297)

a2 = Bw/Aw (Increase variable — in a season with a postseason appearance only)

      1.83776446 / 1.513264178  (a3 = 1.21443729)

a3 = Cw/Aw (Increase variable — in a season with a postseason appearance and a World Series championship)

1.997832513/1.513264178 (a2 = 1.32021393)

Now, with all OFFER variables defined, and with all constant variables calculated, we need only plug in the individual team payroll, individual team regular season wins, and individual team playoff wins+series (if necessary) into the applicable equation below.

OFFER.3

(The fourth and final entry in the OFFER series will chart the resulting OFFER scores, and will attempt to calculate a pure measurement of revenue return per win for each of the 30 MLB baseball organizations in the 2014 season.)

 

 

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