How much does a win in women's college basketball cost?

One of the great complaints of followers of women's basketball is that it's a game of the haves and have-nots, and the haves own the casino.

It has now been nearly 24 years since a school not belonging to the half-dozen power conferences (ACC, Big East, Big Ten, Big Twelve, Pac-12, SEC) has won a women's basketball national championship. How is a team like, say, Northern Arizona supposed to compete with teams like Tennessee or Connecticut, schools which have a massive amount of resources?

But as anyone who follows women's basketball for even a little while knows, big budgets do not necessarily lead to big wins. Take Illinois and Washington, two schools which should have decent budgets to compete but which somehow come up short in terms of winning. Take Texas, which undoubtedly has money to spend and has Gail Goestenkors to boot, but hasn't broken into the Big Twelve elite. You could then look at all the mid-major powerhouses like Wisconsin-Green Bay and Middle Tennessee, which must be short on money but still somehow yield great results on the court.

In other sports - baseball comes to mind - this leads to calculating something called the marginal cost per marginal win (MC/MW) as a means of evaluating decision-making. In professional sports, players have to be hired through the signing of contracts. There is a minimum amount of money that one must spend on each player because most agreements with player unions mandate a minimum of spending. Obviously, stars receive much more than the minimum amount.

So what is marginal cost? Marginal cost is the cost above the minimum cost for a team. Take the WNBA, for example. The Tulsa Shock (why are they such a great example?) could decide to trade all of their players for racks of used basketballs and sign an all-Rookie squad for 2012. This squad would be paid the minimum WNBA contract. The marginal cost of this imaginary all-rookie squad would be $0.

marginal cost for a team = (total salary - (number of players) x (minimum salary per player))

The MC for a team basically indicates how much money is being put into the team. The minimum has to be spent, anything above that is a decision by the owners regarding how to allocate resources. Some owners might not spend very much money beyond the minimum; the New York Yankees might spend zillions beyond the minimum. But the MC simply discounts that part of total team salary which ownership is required to spend and just considers it the cost of doing business, a cost that doesn't have much to do with winning games.

So if one were to take MC and divide it by total team wins, we could get some idea what benefits were reaped by spending cash beyond the minimum. If Team A goes $50,000 beyond the minimum salary and gets 15 total wins, and Team B goes $200,000 beyond the minimum salary and also gets 15 total wins, then Team A must be doing something right. (Or Team B is doing something wrong.)

Makes sense right? Almost. It turns out that there's one crucial element that we're missing. This is the idea of a marginal win.

Let's suppose you're running the Tulsa Shock. Suppose that after their lone exhibition game, the players all get septicemia from eating some bad burritos after the game and are out for the 2012 season. The WNBA says, "okay, we're going to hold you to these contracts but we will make the medical exception for your entire roster and allow you to sign 11 players at minimum salary so that you can field a team for 2012."

So what kind of players can the Shock get? The answer is "the players that no one wants". Every other roster is set, spring rosters have been culled and no one is going anywhere. However, there are a bunch of castoff players that Edwards could pick up off waivers. We'll call these players replacement players, or if you want to keep the terminology consistent, "marginal players".

The question then becomes "exactly how good is this group of marginal players?" After all, if we're discounting part of the team salary as "the cost of doing business", we might have to discount a certain number of wins as "the cost of playing basketball". This team might not be very good - it might be horrible, in fact - but it might win some games if not very many. There appears to be a small number of wins that even the worst teams can earn on their own. (Historically for the WNBA that number appears to be three WNBA wins.)

We subtract the wins that a team of marginal players would stumble into from the team's total season wins and call every win above those wins a marginal win.

marginal wins = total number of wins - (wins earned by a hypothetical squad of marginal players)

Marginal wins are the wins beyond those that a team of scrubs ought to be able to get. These wins represent real accomplishment.

We now determine the marginal cost per marginal win as MC divided by MW.

marginal cost per marginal win = (cost spent above minimum cost)/(wins earned beyond minimum wins).

With this fraction, we are looking at the real value teams get from spending money. How many extra wins beyond the minimum are those extra dollars beyond the minimum purchasing? With this tool, we have a way to determine how effective a team is at spending money. One could even create an imaginary graph with marginal costs on one axis and marginal wins on the other and categorize those low spending but high performing teams.

This kind of analysis can be done in every sport except the WNBA, which treats player salaries like they're nuclear launch codes. With the WNBA, we are missing the total amount spent for our calculation of the formula. (The marginal cost would just be the CBA minimum.) Maybe we'll have better luck with women's college basketball.

In order to find MC/MW for any sport, we need four items:

a) the total amount spent for each team
b) the total amount of wins each team earned
c) the minimum cost for each player
d) the average expected wins for a team in the sport composed of marginal players

With the new WBBState.com website, we now have Part A - the total amount of the athletic budget for each of the teams in women's college basketball. We don't know where WBBState.com is getting its information, but part of this exercise shall be to assume that it's accurate.

Part B is also easy to get. No problem there.

Part C is a little difficult. What is the minimum cost for a Division I women's college basketball player? One might say "it's the cost of the player's scholarship". However, we don't know if that cost counts against the total budget in Part A, so we shall assume without grounds that it's taken care of by the university and costs the athletic budget nothing.

"Aha!" you might say. "I'll grant you that, but surely all those phone calls and home visits and illegal shoes must cost something. The minimum cost for each player has to be the minimum cost of recruiting a player. Isn't that what college basketball is about? Recruiting?"

Okay, let's perform a thought exercise. I'm a college coach and I wish to recruit a replacement player for Big State. The theory above states that there's a pile of replacement players out there that can't get on with a Division I squad and are there for the taking.

BRRRRING!

Replacement player: "Hello?"
Me: "Hi, I'm head coach at Big State. We need a replacement player. Are you interested? It comes with a full scholarship."
Replacement player: "Sure!"
Me: "Fine. Fax the NLI over to our office Welcome aboard."

CLICK.

Total minimum cost of recruiting a replacement player: the cost of a phone call and some toner ink for your fax machine. The minimum cost of recruiting is approximately $0.00. And now, if you don't mind me, I'm taking my wife and part of my recruiting budget and going to Cancun.

Note that I've performed some slight-of-hand here. The magic trick is in realizing that the concept of a replacement player *does not exist* in women's college basketball. If MaChelle Joseph of Georgia Tech loses a player, that conversation above will never take place. The NCAA won't allow it. Joseph will just have to deal with having one less player on her team for the season. Even so, the idea of a replacement player is a useful one and we'll keep it. We shall hand-wave away scholarships and the idea of minimum recruiting cost and claim (without proof) that the school's budget for women's basketball is in effect the allocated "salary" of our women's basketball team.

The part which is missing is Part D: if there were such people as replacement players in women's Division I basketball, how many wins would a team composed entirely of these players get? We'll have to do some guessing. Let's say that a women's basketball team has 13 players on it. Each player has a differing level of value. Some of the players are players like Skylar Diggins or Brittney Griner who are obviously not replacement-level by any sense of the term - if Brittney Griner gets hurt there probably wouldn't be a player that could replace her even if Kim Mulkey was able to offer a scholarship.

Take UConn's starting five. Not a replacement player in a bunch. Starters - for the most part - are not replacement players. For most decent teams, starters have value.

Likewise, for decent teams, the sixth woman has value above the average player. I'd claim that on an average team, players #7 and #8 have a level above replacement.

The problem concerns the players riding the tail end of the bench. On any team - even a Notre Dame or a Texas A&M or a Baylor - there are players stuck at the bottom of the roster that barely see any minutes. (Some coaches call them "20-20-20" players - they only see time when you're 20 points ahead, 20 points behind, or if there's 20 seconds left in the game.) If these players aren't replacement level, they might as well be. You could certainly replace them with other players, because the players at the end of the bench are seen so infrequently that replacing them wouldn't impact the team.

So where does replacement level begin on an average team? The #9 spot in the rotation. The #13 spot? Where?

I'm splitting the difference and claiming that #11 is the replacement level spot on a college roster. What could a team of players that were the #11 players from various college rosters be like? How many wins would it get.

Let's take the 343 or so Division I teams and split them into 13 groups of about 25 or 26 teams each. We'll look at the teams that make up group #11 from the top and see what the average number of wins for that group was. I used the values from RealTimeRPI.com from 2007 to 2011. The average number of wins associated with the #11 cluster (out of 13 total clusters) is slightly above nine (9).

Therefore, we claim that nine wins is the number of wins from a group of marginal players. It seems very high, particular since the difference in quality between the best college team and the worst is much greater than the difference between the best pro team and the worst, and we've already assigned three wins as the marginal number of wins for an WNBA team. However, if you think about it, nine wins makes sense because most of the teams at this level come from weak conferences who play teams from either their own weak conference or teams from other weak conferences. The rule becomes "you ought to be able to add enough cupcakes to your diet of teams to get nine wins no matter how bad you are."

So given the above, which teams paid the least for their wins? And which teams paid the most for them? (Note that wbbstate.com doesn't have information on some schools, like the service academies.)

Leaders in Marginal Cost Per Marginal Win - NCAA Division I

Let's now limit the list to only teams from power conferences.

All of these teams have something in common - they don't have much of a budget (Tennessee and UConn supposedly have budgets of over $5 million) but they won a lot of games. It just goes to show you how valuable Tara VanDerVeer is to Stanford, making miracles happen with the Stanford budget.

(* * *)

So which power conference teams got the least bang for the buck? The big losers are those who finished the season with nine or fewer wins - basically, these teams had zero marginal wins and a team of scrubs would have done just as well. The MC/MW value is basically undefined or negative.

There's an old saying that the most expensive army is the one that is the second-strongest. In this case, the most expensive Division I teams are the ones that can't get nine wins.

Do these numbers prove anything?

The problem is in obtaining accurate information upon which to base the concepts of marginal costs and marginal wins. We've had to make a lot of guesses and assumptions; the reader is left with the exercise of picking away at those. Maybe someday, a team of crack reporters will get the accurate numbers we need; sadly, that day is not today.