Last time we did Saber-Terms, I discussed replacement level, which is a convenient baseline to which we compare the performance of baseball players. One of the stats you’ve seen bandied around here on this site by John and I is **Wins Above Replacement**, or WAR. Today I’ll introduce the various parts that go into calculating wins for *position players* (pitchers may come a little later), and I’ll begin by talking about the offense part of WAR.

**Introduction**

Wins Above Replacement, as it will be described here, was initially constructed by Tom Tango as a total player evaluation system. There have been a few in the past, particularly Pete Palmer’s Total Player Rating and Bill James’ Win Shares, and WAR is somewhat derived from that work. I won’t go into any history beyond this, but know that there have been predecessors to WAR that also evaluated players in terms of wins.

Why would we want to evaluate anyone in terms of wins? Well, isn’t that all we care about, wins? It makes intuitive sense: measuring a player in terms of wins is more logical than any other denomination because wins are ultimately what teams are gathering and what fans want to see. A player’s value ultimately has to be seen in terms of wins.

WAR is a total player evaluative stat, so that means it is supposed to take into account all aspects of a player’s performance. This includes not only offense with the bat, but offense with the feet (baserunning), defense, and playing time. Those components are all measured and added to compose the total WAR. Today, we’ll start by discussing offense.

**Offense**

Offense is the aspect of the game which seems most obvious to everyone. Non-pitchers hit all the time, and a record of their PA is kept that shows the results of each appearance. Thus, it would seem simple to measure this kind of performance, and it is. Unfortunately, for years now the game has been measured by inefficient numbers like batting average or RBI.

So what kind of offensive numbers do we use for WAR? Well, the truth of the matter is that you can use *anything* to measure the offense part of WAR as long as it follows these two rules.

1) The stat is measured in runs or wins

2) The stat is taken against the league average

The first rule is an obvious necessity: we want this measure to be in wins. Runs are easily convertible to wins via Pythagorean expectation, and wins are, well, wins. The second rule is there due to how the replacement level part is calculated (more on that later in this series).

So, we can use anything, as long as it’s in terms of runs or wins and it’s measured against the average. Where can we start? How about the simplest, most crude method of estimating run production available? Let’s use good ol’ R+RBI-HR! The very things I despise indeed.

**League Average (R+RBI-HR)/PA**: 0.207

**Hanley Ramirez (R+RBI-HR)/PA**: 0.281

**Hanley Ramirez (R+RBI-HR) above average**: 48 runs above average

If you chose to do your calculations that way, that is what you would come up with. Pretty good considering the restrictions on the system, but we can do much better than that. For reference, **Dan Uggla** came in at 4.6 runs above average, and **Jorge Cantu** came in at 17.8 runs above average.

That system is very contextually based. The common system that we use is something called linear weights. Linear weights essentially assigns an average run value to each batting event, then tallies all of those totals and gives you the total runs above average for a given player’s stats. In order to make players more comparable, we often display this information as wOBA, a rate stat scaled to OBP that uses linear weights. The reason why we use this is because we do not want to give credit to the hitter for the situation in which he steps to the plate, as so much of that is out of his control. For example, Cantu’s performance is going to look better if he has Hanley on base all the time when he steps up, while Uggla’s performance will look worse if he has less people on base for him.

Here are the linear weights run values as measured by FanGraphs for the 2009 season for the three players in question:

Ramirez: 43.8 runs above average

Uggla: 14.2 runs above average

Cantu: 7.5 runs above average

But what if you do want to include context in a big way? The polar opposite of something like linear weights, which strips all context, is Win Probability Added, which keeps all context. WPA credits or debits a player for the changes in the win expectancy of his team. Thus, higher leverage situations will have more of an effect on the team’s winning and be worth more, while lower leverage situations will have significantly less effect on the team’s winning and be worth less. WPA is the only stat we’ve mentioned so far that is already measured in wins; the other stats would have to then be converted from runs to wins.

Ramirez: 3.09 wins above average

Uggla: 0.09 wins above average

Cantu: 3.12 wins above average

Each of the three stats I listed are perfectly viable options for you to include in a WAR calculation, based on what you feel is the right way to measure offense. There are a few more stats that you could use such as WPA/LI, but I won’t get into those here. The key is to make your choice on what you want to evaluate and go with it. My personal choice will always be to use linear weights, because I do not believe in giving a hitter credit for the baserunners (or lack thereof) he inherits at the plate. Whenever I mention position player WAR, I’ll be mentioning it in terms of context-neutral offense. But, to each his own; make WAR calculations using whichever appropriate stat you feel is right.

**Park Adjustments**

I won’t go into detail about park adjustment here, but you should know some of the drill. Clearly, a ball hit in Sun Life Stadium (ugh) is not the same as one hit in Coors Field or in Petco Park. Adjustments need to be made for players playing half of their games at their home park. The way to make these adjustments is to calculate park factors and use as appropriate. I already pointed out how to approximate a park-adjusted wOBA (see the wOBA article linked above), and I’ll talk a little bit more about adjustment when we get to pitchers.

**Baserunning**

A quick note on baserunning. On FanGraphs, wOBA already includes stolen bases and caught stealing in its calculations. However, there is obviously more to baserunning than that, and there is a place we can find those kind of numbers. Baseball Prospectus has Dan Fox’ Equivalent Baserunning Runs available and constantly updated. EqBRR not only takes into account stolen bases/caught stealing, but also baserunning advances on hits, ground balls, and fly balls. It is the best baserunning metric to date, and is a very useful tool to evaluate the best baserunners in the game. If you want to use FanGraphs’ batting runs and include baserunning, an easy way to do this is to add all of the EqBRR components that do not go into stolen bases/caught stealing.

**Offensive Conclusion**

This is just the start of how we find the value of a player. I wanted to emphasize here that you can choose whatever offensive evaluative method you want to find a player’s production, but make sure that you define this accordingly and tell others what you mean by “offense.” From here, you have one half of a player’s contribution. Of course, defense is a big thing, and that’s what’s coming next on Saber-Terms.

**Topics:** Dan Uggla, Hanley Ramirez, Jorge Cantu, Miami Marlins