Perhaps you can add a "shiny new/classic old ballpark" factor. As a whole, it looks likes the teams with nice ballparks are on the positive side, and the teams without one are on the negative side.

Rather disappointing analysis in my opinion. I believe Derek Zumstead's most recent look at actual market advantages did a much better job of looking at this issue. I'm incredibly skeptical that the value of marginal wins should be considered linear. That flys in the face of common sense. Using your formula one concludes that almost none of the trades that happened this year made any economic sense from the sellers perspective. Sure the Brewers ditching Alex Ochoa for 700K in savings probably mades sense since it didn't likely cost the team a win, but dealing Ray Durham was worth between a win or two for the WS and they saved a pitance without getting much for talent. And at those marginal rates they'd have needed to get talent equal to 2 first round picks to even come close to making sense. Similarily clearly the Brewers were better off not dealing Jose hernandez and getting a couple of extra Ws instead of paying his salary and only getting a decent prospect or two. No I imagine that there is little value in revenue for marginal wins between 70 and 80, a certain value in getting to 70 (and making it to the mediocre level). After 80 wins there should be a steady increase in the value of a win peaking somewhere around 90 where the playoffs become likely, and then declining slowly as winning the division handily becomes no big deal.

Which ballparks that are old fall under your definition of classic? Wrigley is the only one that jumps to mind.

An interesting point that Voros brought up is that the marginal value of a win has the same total dollar impact, regardless of market size. This sounds pretty strange to me. This means that if you have a 2 million person market and an 8 million person market, then the benefit of an extra win is the same in either market.

I wonder if this is due to other entertainment avenues that baseball competes with. There's alot more to do in NYC than in KC. If one market is 5 times as large, but there are 5 times as many things to do, the "marginal market" that each city is after is the same total number.

Voros: maybe getting data from the various Tourism boards might allow us to account for this. Just a thought...

Um, I think Fenway is a classic old park.

Interesting that the two teams that replaced classic old parks with shiny new ones, Detroit and the White Sox, are on the negative side.
Perhaps the Red Sox should think more than twice about replacing Fenway.

Most of the other negative teams play on fake grass or in football stadiums. The anomalies are Anaheim and Baltimore, which Voros addresses above.

Excellent article. One very, very quick-and-dirty stat/implication. If each NY market team has an inherent $37 million revenue advantage, each win costs $3.5 million, and we assume (unrealistically, as you note) that all costs other than salaries are fixed, such team could spend the extra money and win 91 games a season. Furthermore, there is a *dynamic* aspect to this. The additional wins result in more revenue, which then permits more money to be spent on salaries, which creates more wins, etc., etc. In other words, the effect over time of inherent metropolitan market advantages might be greater than one would see in a static regression model. I don't know what the point of equilibrium/diminishing returns over time might be, but I would suppose the Yankees may have reached it. I also agree, however, that any revenue sharing approach must not penalize teams for being better at exploiting their market (i.e., intelligently building a better team that brings in more revenue). The Mets have certainly proven the point that the success of the Yankees is not inevitable.

Having thought about it more there's actually a second implicit constant term in the equation. By using raw winning percentage and the historical precedent for even the worst teams winning at least 33% of their games there's a built in cushion in that term. Since that's positive and the explicit constant term is negative they reduce each other in magnitude, but it certainly throws off any simple calculation of marginal win values.

I'm not really worried about the constant term. The theoretical Springfield Isotopes example is just a warning not to extrapolate beyond the bounds of the observed data. There's no model that will tell you what the expected revenues are for a team that doesn't win located in a town with no people in it -- or at least, since such a thing has never been observed, we have no means of assessing how accurate that prediction would be.

As to the national revenue, I would rather just see it subtracted out of the left-hand side. A team's share of the national revenue isn't a function of its population size, per capita income, etc. The left-hand side should really just be locally-generated revenue.

Two quick comments,

Remember that by last year's numbers, the Montreal Expos brought in over $52 million in revenues from the league alone, so that one could assume that if a team were allowed to exist while generating _no_ local revenue, they would probably take in somewhere around the $55 million mark.

The second comment is that there are a few problems with the revenue/win is not linear argument: one is that representing it as linear makes analysis before the season or at the very start of the season possible. You might figure a team is an 84 win team before the year starts, but that really means that the team migh have chance to win anywhere from 69 to 94 games with the chances of any one win total occurring increasing as it converges to 84. Therefore getting at that "curve" precisely can't be done because you don't know whether two extra wins gets you to 90 wins or to 78 wins. So the curve is "flattened" out considerably when you take this into account. Another point is that the win% numbers only affect revenue in subsequent years in the model. The only aspect of current year success that affects the model are the number of home playoff games played. Finally, and most importantly, curves that were bent, logarithmic, hyberbolic, exponential, and all sorts of other weirdness were tried and none of them improved the accuracy of the formula. I'm assuming because there are all sorts of different kinds of 84 win seasons, that the effects of these 84 win seasons differ greatly as well. Meaning that to get at the "average" effect from an 84 win season, the various different effects get averaged out to where we once again get a flat and average looking rate.

Finally, in order to use more complex functions, we'd probably need a much higher sample size than I have available (90 teams) in order to get at them. With only the 90 teams, all we're going to get are the simple trends and the important variables. If we try and get complex, the system doesn't become more accurate and becomes harder to work with.

I'm still having trouble getting past "Another point is that the win% numbers only affect revenue in subsequent years in the model. The only aspect of current year success that affects the model are the number of home playoff games played." The fact is that the Twins attendance went from 12K to 22K last year and you're saying that was due to the 69-93 fifth place finish in 2000. It may be an isolated event that doesn't model well, but like the marginal wins value not being linear, big improvement does have a larger impact on attendance for bad teams.

Nice piece of work. Some of what follows is quibbles and I know you're more interested in broad factors than specific details.

A few things that should push up the accuracy of your model.

There's a strong upward trend in revenue. You can take this into consideration by including the year in the regression (well I actually used year-1994)

I can't understate the importance of either having made the playoffs the previous season or in particular having won the World Series in the previous season.

Once you include these in the regression, the marginal value of a random win in previous seasons goes down a fair bit.

Likewise, making the playoffs and winning the world series in the season under consideration is very important. And including this in the regression lowers the value of a random win by quite a bit. (I know why you didn't include this in your model. In looking at what to bid on a player his impact on your potential playoff chances are very difficult to assess -- particularly years down the line. And that's before getting into how long he rates to sustain that rate of play. Way easier to work with in a marginal revenue produced versus value over replacement study than what I have. )

I'm surprised that you found the marginal value of a win to be more or less constant across markets. I found winning percentage* market size to be both positive and significant. Makes for a right messy equation though. If you opted for a simplifying assumption, I can see why.

"the lowest belongs to the Expos (due to the fact that the Per Capita Income in their Area is easily the lowest of the 30 teams)"

I don't know much about Canada, partly due to living in Florida. I'm curious whether Montreal is impoverished or something. However, any extra social services provided would increase the portion of people's money that they could spend on entertainment. If I make less money, but don't have to buy health insurance...

"There's a strong upward trend in revenue. You can take this into consideration by including the year in the regression (well I actually used year-1994)"

I did do this, in a more simplified way. I simply scaled up the revenue numbers to 2001 levels for each year.

As far as making the playoffs and world series, it is more or less in the model under the "home playoff games" heading. If you make the playoffs you get at least one home playoff game. If you make the World Series you could get as many as 10 or 11 playoff games.

I decided to use games instead of artificial levels, since that's more or less how the revenue is generated for the individual teams.

As far as the revenue per win/market size relationship, I was equally as surprised but I'm just not finding it.

It _could_ be that I'm estimating total revenue instead of local revenue and the revenue sharing combined with the error rate of the regression combined to reduce the difference to insignificant levels. I'm going to work on trying to compartmentalize the numbers a little more (breaking down how each revenue source is generated individually and then putting it back together), and maybe try and do a little bit more work on the right way to split two team markets (there could be significantly different revenue generating functions for two team markets than a one-team market).

Art,

Well obviously with last years winning percentage being a key variable, making the playoffs is going to be contained within that. The problem I had with trying to add more playoff and WS data was simply that it didn't make the model more accurate, only more complex. If I do a few things different with the model than Ron, then whether a certain variable shows up as significant could be affected.

As for revenues, I simply scaled up the revenues in 1999 and 2000 to where the total league revenues were the same for all three seasons. This is a bit of a kludge for some questions such a model could work with (say overall revenue growth or something) but for my main purposes I figured it was the best option. YMMV.