Replacement Level

Source: There are tons of sources on replacement level in baseball, but of course, I’ll only cite the good ones. Here’s The Book Wiki’s article. There’s the Keith Woolner piece that’s involved in defining VORP (we don’t and won’t talk about VORP here). Here’s a good one by Sean “Rally” Smith showing some examples based on his CHONE projections. Also, there’s Dave Cameron’s excellent series on replacement level examples (this was the last position player one, but it has all the previous links).

I won’t go into a terribly large amount of detail, but Woolner’s piece and the later WAR pieces go over the economic reasons why replacement level is a convenient baseline for establishing a player’s value. Replacement value is best defined as the value provided by freely available talent, either in the minor leagues or on the free agent market. The major league minimum is around $400K, and all teams must pay at least that much for talent. Since that is the floor for salaries, there’s no way to optimize economic value any further; whether players are at below that level of talent, teams still have to pay the league minimum salary.

As a result, the league minimum can be seen as a baseline at which a certain amount of production can be attained, whether it is through the farm system (the classic Quad-A player) or as free agent journeyman. It’s “free” to teams because they have to fill a roster and have to at least pay each player the minimum. Anything teams pay over the minimum is supposed to produce above this level of talent. For position players, the classic example is Willie Bloomquist.

Currently, most of the research has a team of replacement level players theoretically winning around 48 games (you’ll hear figures between 47 and 50), a .300 win% team. That’s one bad team, but that’s what you’d expect for 25 players paid at the league minimum AND performing at that level of talent. This is contrary to what Woolner’s article mentions, and at a later time I may do a compilation of articles regarding this.

Wins Above Replacement (WAR)

Source: The awesome FanGraphs Win Value series by Dave Cameron, the WAR Lords of the Diamond two-part series (position players and pitchers) by Jabberwocky over at Purple Row and reposted on Beyond the Box Score, and originator Tom Tango’s explanation.

Wins Above Replacement (WAR) is the result of a lot of different runs-based numbers being plugged in to a big algorithm to achieve a number in familiar terms (wins) compared to a baseline (replacement level). Actually, it’s not all that complicated and it is mentioned in all of the pieces shown above. Among the ones most commonly quoted are FanGraphs’ values and values from Rally’s historical WAR database. Both use similar processes but work on slightly different inputs. WAR for position players and pitchers is calculated differently, and particularly WAR for pitchers is of some interest due to the variety of inputs used.

How I Do It

The FanGraphs series by Dave Cameron does a wonderful job explaining all of the intricacies of the WAR calculation, most of which are actually fairly easy to explain. I do the same basic process and use different inputs, so mine versions are always a bit different. Keep in mind that when I quote WAR here, as when I quote any other stat, I will mention the source, whether it be my homebrewed version, the FanGraphs version, or Rally’s version.

It’s important here to make sure your terminology is correct. WAR refers to a specific process as outlined in the above links and below (generally). Do not confuse this with Baseball Prospectus’ WARP1/2/3, and definitely do not confuse this with VORP. There are supposedly numerous issues with BP’s wins statistics, particularly with their low replacement level.

For position players:

1) Offense: I will use wOBA as the primary entrant on offense, mostly because it is the most easily accessible set of linear weights and it is so darn convenient. For this, I’ll use custom linear weights derived using the methods shown here. These values will not include pitchers hitting. For baserunning, I’ll use BP’s Equivalent Baserunning Runs (EqBRR), as it seems like the best baserunning metric in the business.

2) Defense: For defense, I’ll use three different inputs, bUZR (FanGraphs), TotalZone (B-R and Rally’s site), and Fan Scouting Report data (Tango’s site). I’ll weigh the two zone-based metrics at .375 each and weight FSR data converted to runs at .25.

3) Positional Adjustment: I’ll use the same positional adjustments found on FanGraphs. Here’s the research done by Tango using 2002-2005 UZR data provided by MGL. After much work, here’s the scale in its entirety posted as part of the Win Values series over at FG. The initial study focusing on this was done by comparing players who played multiple positions in that time period. The results now being used for this era (and this is somewhat era-sensitive, as Tango mentions in this post) make intuitive baseball sense. Catchers receive the most help, as they play the most difficult and scarce position. First basemen receive the most penalty, as they play the easiest position to replace on the field. The other positions are in between; shortstops receive 7.5 runs more for their work while corner outfielders receiving that much of a penalty for theirs. DH’s receive a -17.5 run penalty for being eminently replaceable.

4) Replacement adjustment: With all the research done on replacement level, the general consensus is a value of 20 runs below average per 600 plate appearances. The reason for the importance of the replacement adjustment is the value of playing time; any time that is spent on the field derives value over a replacement player who provides far less worth, so elite players who do not accrue playing time are docked value. To account for difference in league talent level, we can use 18 runs per 600 PA in the National League and 22 runs per 600 PA in the American League (Tango accounts for this slightly differently, using a rate per 162 games).

For pitchers:

1) Pitching runs: There are a lot of different defense independent metrics that attempt to use component stats to determine run values per nine innings. For the purposes of my calculation of WAR, I’ll be using two inputs, FanGraphs’ FIP/.92 (FIP scaled to runs allowed instead of ERA) and StatCorner’s tRA. Both do similar things, but tRA accounts for batted balls, while FIP uses the traditional home runs, strikeouts, and walks.

2) Pythagenpat: In order to determine wins, we’ll use Pythagenpat directly. For runs allowed, we use the pitcher’s runs per nine innings. For runs scored, we use the league average. We can then determine the run environment exponent and derive a win%, which of course is in terms of win/9 innings.

3) Replacement level: As discussed in the Tango post initially linked, the replacement level for pitchers are different depending on their role. I don’t use a separate level for closers, but I do use one for starters and relievers. For the National League, the replacement level for starters is .390 win% for starters and .480 for relievers, while those values are at .370 and .460 respectively for the American League. To use these adjustments, we use the simple formula:

Win% (pitcher) – Win% (replacement level)

to determine the wins above replacement. For relievers, there is an additional leverage index calculation that is used to give half of the credit for the leverage situations a reliever faces. Starters do not get such an adjustment because they will pitch on average around a 1.00 LI. The equation for reliever wins is:

Win% (reliever) – Win% (replacement level)*(1+average LI/2)

You can multiply this difference by Innings Pitched/9 to determine WAR. Voila!

More on leverage and other topics a little it later.

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