Monday, August 1, 2011

Rebuilding the Big Red Machine: Step 3 (Part 2)

Go Back to Step 3 (Part 1)

1. Converting a player's total on-field contributions into a single Run value

In order to properly value a player, you have to be able to accurately quantify his on-field production. I believe it was Bill James who originally determined that "Runs" were the currency of baseball. This brought about a statistical effort to more accurately value the contributions of players, which led to statistics like WAR (Wins Above Replacement). There are three layers to this wave of player valuation.

The first layer is converting the contributions of a player into a single run statistic. This has been done for both their total offensive production and their total defensive production.

The offensive component of WAR is based on wOBA. So, we have to talk just a bit about wOBA. To start, wOBA isn't based on any other statistics, but rather is based on each and every outcome of a hitter's plate appearances. It uses linear weights to value all the different outcomes relative to each other. So, every outcome has a run value that is proportional to the other outcomes. So, a homer is worth more than a triple, which is worth more than a double, etc etc etc. So, every outcome is weighted and rolled into a single number.

Additionally, once all the contributions are compiled, the wOBA can be converted into a single run value. Basically, you take the difference of the wOBA from league average and extrapolate it out over their number of plate appearances to get their offensive run value above/below league average.

As to defense, uses Ultimate Zone Rating (UZR), which is the number of runs above or below average (includes range and errors), for it's fielding component.

As with some other advanced defensive metrics, the field is divided into different zones which are assigned to the relevant fielders. And, of course, the balls hit into the zones are tracked. UZR is largely based on hits in the zones, outs in the zone, and the run value of the hits. The player's performance is compared to the league average for all balls converted in the zone. Obviously, he gets credit for plays he makes above the average and deductions for the plays below the average. A run value is applied to his performance on these plays and a total run value is determined. That run value is the defensive run component to WAR.

So, roughly speaking, that's how you get your offensive and defensive run totals.

2. Converting a player's single Run value into a Win Contribution Value
The second layer is converting a player's total run contribution into wins.

At this stage, the offensive run values are adjusted for park effects and a positional adjustment is added. Now, conceptually, the idea of positional adjustment is one that sometimes eludes me, so I'm not going to try to explain it. In essence, a player's performance is more valuable at the premier defensive positions, so an adjustment is made to give those players a boost. Hence, Hanley Ramirez's performance gets a boost, while Albert Pujols gets a deduction.

Now, converting runs to a win number is the simple part. A lot of statistical analysis has been performed to determine that generally speaking: 10 runs = 1 win. So, if a player generates +20 runs, than he's a +2 win player.

Additionally, WAR is tied to replacement level. So, the benchmark is wins a player would provide over a replacement level player. Here, replacement level is an AAAA type player, which includes the type of players available as minor league free agents, the Rule V draft, and MLB bench players.

3. Converting a player's Win Value into a Dollar Figure
Heading into the home stretch, the third layer is converting a player's win total into a dollar figure. Just how much was the player's contribution worth?

As for the value of a single Win, it's once again complicated. Different sources rely on different methods, but uses something along the lines of the following:

First, there are 162 games per season and 30 teams, which works out to 4,860 total games. Of course, there must be a winner and a loser, so half those games will be wins and half will be loses. So, there are a grand total of 2,430 wins at play in the regular season. Now, due to the fact that every team will field at least replacement level players, who will perform at a .300 win percentage clip, every team is assigned 48 wins. So, 48 wins for each of 30 teams means that 1440 wins are not in play. That means that there are only roughly 990 wins in contention among the 30 teams.

So, if you took the total salary committed to all the players in baseball and divided it by the 990 wins in contention, then you'd get the cost of a win. However, it's not that simple, as many players are cost controlled under the MLB financial structure. So, such a calculation would not reflect the market rate of a win, as players who are in their first 6 seasons or who have forgone free agency for contract security drag down the market cost of a win. You have to exclude players who are not available and focus on those who are. The price of a win is determined by market forces.

As a result, you look at the free agents who signed in any given year, determine their market driven salary, and then determine how many wins above replacement they created. Once that's done, you can determine the market price of a win by (basically) dividing the total salary of all free agents by the wins generated by those free agents.

Fangraphs has calculated the dollars per win as follows:

2002: $2.6M
2003: $2.8M
2004: $3.1M
2005: $3.4M
2006: $3.7M
2007: $4.1M
2008: $4.5M

So, if you had a 4-win player in 2008, he was worth $18M, which gives a more objective valuation that is not driven exclusively by the irrational decision of one or more teams. While this methodology provides a more objective player valuation, we need to take one more step. We need to make this general, league-wide valuation more specific and applicable to a specific organization. In order to do that, we need to examine the layers of revenue and how that impacts a player's unique value to an organization. Suffice it to say, a 4-win player may have a different value to the Yankees than he does to the Royals. But, we'll leave that for Part 3.

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