This is Part II of a series that examines the Texas Rangers 2009 revenue outlook in a rough version of the framework laid out by Vince Gennaro in his fantastic book Diamond Dollars. Check out the Offline Reading list for other great reads.
In Part I, Texas Rangers Win-Curve Part I: Wins vs. Attendance, I walked through a model for predicting 2009 home attendance based on the team's on-field success as measured by wins.
Part II aims to add another piece to the puzzle by determining a team's chances of making the playoffs for a given number of wins.
WHAT EVERYONE KNOWS
Two types of teams make to the playoffs: 3 division champions and 1 wild card team.
The more games a team wins, the better its chances are for making it into the playoffs by either method.
In reality, for a given number of wins, a team will either make it to the playoffs or not. There are only two outcomes: 'yes' and 'no'.
MODELING THE DATA
Because there are only two outcomes, the data can be modeled with a logistics curve. The curve is created by a generalized binomial regression. Basically, using an independent variable (wins), it determines the probability that the dependent variable (team makes the post-season) is true.
I gathered 11 years of historical data for the American League in its current alignment - since Tampa Bay's inaugural season in 1998.
I ran regressions for each division and for the American League as a whole.
One hypothesis that I was eager to test was that for teams in smaller divisions, like the 4-team AL West, the odds of winning the division (and therefore the odds of making the playoffs) are greater than for teams in a 6-team division like the NL Central.
I tested this hypothesis by comparing the curves for each of the three divisions against the American League curve. Essentially, all 4 curves are the same but shifted either to the left or to the right.
The AL West curve, surprisingly, is shifted right, meaning it is harder to make the playoffs in the AL West than in the AL as a whole. The AL Central curve is shifted left, and the AL East curve showed a right shift approximately equal to the shift in the AL West curve.
At 92 wins, an AL team has had a 66.96% chance to make the playoffs. The AL West, AL Central, and AL East have had 62.69%, 78.24%, and 61.94% chances, respectively, at the 92-win level.
Since it has been easier to make the playoffs in the 5-team AL Central than it has been in the 4-team AL West, the hypothesis does not hold up. The difference between the AL West and AL East was barely noticeable.
TEXAS RANGERS POST-SEASON PROBABILITY
The two curves that apply to the Rangers, the AL curve and the AL West curve, are fairly similar. At 80 wins, the AL curve shows a 0.35% chance, and the AL West curve shows a 0.24% chance.
In what appears like it could be a weak division in 2009, 85 wins might be enough to get the Rangers in. Historically, though, 85 wins has resulted in only a 4.70% chance on the AL curve and an even smaller 3.58% chance on the AL West curve.
If the Rangers make the improbable jump from 79 wins to 95 wins, the AL curve gives them a 90.88% chance of making the post-season, while the AL West curve gives them an 89.59% chance.
Based on the 2009 outlook, if any AL West team can get to 95 wins, it should win the division handily. One team reaching that level would have a fair amount of shock value by itself, but if two teams hit the 95-win mark, it would be absolutely stunning.
APPLYING THE POST-SEASON EFFECT
When a team makes the post-season, the fan response typically includes increases in season ticket sales, television ratings, and merchandise sales. This post-season effect has a tangible benefit on team revenue for current and future seasons.
According to Gennaro's model, a net present value (NPV) is calculated for the post-season effect. For each win, the NPV is multiplied by the post-season probability for that win total, and the resulting value is added to that point on the win-curve.
In Part III, the dual focus will be on turning attendance figures into attendance dollars and assigning a value to the post-season effect.