Wins & Losses in the Valley of Mediocrity

Cleveland’s signing of the parrot-toting slugger Edwin Encarnacion was more than a savvy grab by a World Series runner-up looking to bulk up on home runs. It was also demonstrative of a Blue Jays front office that both comically misread the declining long-ball market and revealed the new regime's noncommittal strategic attitude that we all feared.


Now I get that a professional sports franchise is a business, and that I as a fan have no right to demand the firm hold a commitment to winning above maximizing revenues. To this end, while Encarnacion leaving will not make the team better, I can see how it could provide some relief to the bottom line. And so the decision to let EE walk and sign Kendrys-freaking-Morales was rational, and therefore at least somewhat defensible.


Noted curmudgeon and Rogers-apologist Andrew Stoeten certainly thinks so. Before Christmas he argued on Twitter that fans will pack SkyDome* regardless of whether or not the team wins. Loyalty to the brand, in other words, will outweigh any of this off-season's stumbles.


I've had a few weeks to think about this and I'm still not convinced. Is it not true that people like winners? If so, shouldn't this fact be salient to revenue?


The idea is intriguing and, it seems to me, should be a pretty clear matter of the empirical record. So let’s fire up the Stata and off to Baseball we go!

The Data

The history of the Jays seems pretty straightforward: big crowds at the start; drop off and rebound during the heady days of the late-‘80s; still more growth with the shift to the new stadium in 1989; and then a pretty big tail-off during the lean 2000s, followed by the steady growth of the last few years.


This graph hones in on the attendance aspect:

Say what you want about Alex Antholopoulos (who took over in October 2009), but AA knew how to put fans in the seats.**


The question, though, is whether winning had anything to do with it.  We start by plotting wins alongside attendance, and then draw a line of best fit.

A pretty clear pattern emerges, one confirmed by running a correlation.

A confounding factor however, is that the two stadia are not exactly like units—SkyDome can crowd in 49,282 for a baseball game, whereas Exhibition Stadium topped out at 26,680.  So we should pull out the smaller ballpark—and while we’re at it, the strike-shortened 1994 season as well—and then rerun the graph:

What’s interesting is that by doing this the pattern loses its fit a touch, a visual intuition confirmed with our good buddy Pearson’s R:

If we look closely again at the plots, the loss in explanatory power is because a few important outliers loom much larger in the sample.  A clear example is the figure from 1995, when the team was terrible but fans—still high on the back-to-back wins—came through the turnstile regardless.  Another big part are the modestly good teams of the ‘aughts, when the Jays were good but still not good enough to bring the wary fan back in.


On the other hand, a key lesson is that when the team is a smashing success, people will show up to watch them. That much is a lock.

This isn’t to say winning isn’t important. You can derive some pretty good policy inferences from R = 0.43.  Regressing the values brings even more evidence of the point:

An R2 of 0.38 is not something to jump up and down about, but the attendance-win relationship is statistically significant.  Thus we can be reasonably confident that assuming there are no extraneous forces at play and controlling for stadium size, each additional win adds another 32,162 fans.  


If we use Forbes' estimate of $23 for the average price of a ticket, and Statistia's MLB average concession revenue of $14.61 per fan ($5.90 for beer, $4.19 for soft drinks, and $4.52 for hotdogs; keeping in mind the numbers are actually denominated in USD), that works out to $37.61 per fan and  $1.21 M per additional win--even while being completely silent on merchandise sales and of course TV revenues, sponsorships, and other commercial tie-ins.


Winning might not pay all the bills, but it does at least pay some.

Digging Deeper

Even with the reasonable results above***, there is still the quirky results of some of those 2000s teams.  Good enough to win games, and yet seemingly unable to entice the casual fan to the ballpark.

One possible explanation is reflected in the broader sports economics literature—that competitiveness, rather than any absolute number of wins, is what matters.  People aren't interested in a cakewalk or a beat-down; instead they want close finishes, thrilling derbies, and to see their team win enough that each particular game matters (in, say, qualifying for the playoffs).


The variable I’ve chosen for competitiveness is divisional finish.  The jump from a continuous-type independent variable (wins) to an ordinal one (finish rank) means we have to use slightly more cumbersome quantitative tools, but we can still dig out what we need to.

Plotting finish and attendance for the SkyDome era highlights a rather interesting finding: yes, it’s good to win (or at least come 'close', assumed as the first two finish positions here). But it’s even worse to be a middling franchise.  Stay in the middle of the pack and it is reasonable to expect lower attendance than if you are the league’s doormat.


We can use the ANOVA technique to predict means for each finish position, then plot a 95% confidence interval on either side of the plots. In graphical form, the results look like this:

Again, rather than a gentle downward slope we get something like a fishhook. 


My guess is that this bend in the fit curve has something to do with diminished expectations. Losing on a hot day can be reasonably tolerable when you walk in with the expectation that you’re going to get trounced. Instead of worrying too much about the game, you sit back, enjoy your egregiously priced beer and hotdog, and enjoy the afternoon.


By contrast, seeing talent tread water in a divisional race—grinding out a win here and there, but ultimately falling short against the teams that matter to the playoff race--is an infinitely more painful proposition. 

In more concrete terms, the ANOVA results tell us that for a team jumping from third to second place, average attendance will bump up by more than a million fans!  Become a first-place finishing team and the jump is another 500,000.

Final Thoughts

The main take-away is that the 'middle of the road' strategy is a recipe for disaster. How Rogers can be so cavalier with an asset that is clearly a cash cow is beyond me.


As for the mediocrity theory advanced here, this is pretty much based entirely on my own anecdotal experience. If anyone has other ideas and more data for me to test, I’m all ears.


With the relative importance of gate receipts much diminished in recent decades, TV revenue is an obvious avenue for follow-up, provided that the necessary historical data exists.   



I also want to follow up with the relationship between payroll and wins. Does money solve the problem of winning--a question I'd like to address vis-a-vis other sports as well, particularly capped basketball. Here Baseball Reference has all the data we could want.  Next time, perhaps!


Stata code is here.  And the dataset is here.



*Strike 1 against Rogers.

**Strike 2 against Rogers.

***Strike 3 against Rogers.

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