Glossary: Archaic

Clay Davenport includes a brief explanation of this concept in this article on third-order wins.

Clay Davenport includes a brief explanation of this concept in this article on third-order wins.

A method introduced by Pete Palmer in the book "Total Baseball" to calculate a pitcher's value in runs above average. It is calculated differently here than in "Total Baseball."

Formula:

APR = L * IP - R / pf(P)

• L: Average number of runs per inning pitched in the league
• IP: Innings Pitched
• R: Runs Allowed
• pf(P): park factor for the player's home park P.

This measure was introduced by Michael Wolverton here.

Adjusted Pitching Wins. Thorn and Palmer's method for calculating a starter's value in wins. Included for comparison with SNVA. APW values are calculated using total runs allowed instead of earned runs allowed.

Michael Wolverton talks about adjusted pitching wins here.

Measures a reliever's contribution using the Run Expectancy Matrix. For each base-out situation, the Run Expectancy Matrix tells us how many runs are expected to score in that inning.

Formula:

ARP = (ER(sS,P) - ER(sF,P) + IF*ER(s0,P) - R) / pe(P)

• ER(s,P): The expected number of runs that will score in the remainder of an inning starting in base-out state "s" in park "P"
• sS: The base-out state when the reliever entered the game
• sF: The base-out state when the reliever left the game
• IF: The number of innings the reliever finished
• s0: A special state for the beginning of an inning which is distinct from the state for no outs, none on.
• R: The number of runs that scored while the reliever was in the game
• pe(P): The park effect for park "P"

This method was introduced by Michael Wolverton and further explained by Derek Jacques.

Average Pitcher Abuse Points per game started

Adjusted Games: The estimated number of real, nine-inning games played at this position.

Statistics that have been adjusted for all-time have all of the adjustments for a single season, plus two more. One adjustment normalizes the average fielding numbers over time. Historically, the fielding share of total defense has been diminishing with time - more walks, more strikeouts, and more home runs means less work for fielders. In the single-season adjustments, fielders from before WWII have a lot more value than fielders today; the all-time adjustments have attempted to remove that temporal trend. The second adjustment is for league difficulty. League quality has generally increased with time. Each league has been rated for difficulty and compared to a trend line defined by the post-integration National League. In addition to the adjustments for season, an adjustment is made for league difficulty.

Statistics that have been adjusted for a single season are the best stats to use when you are only interested in that one season. In these, adjustments have been made to account for the home park and for the offensive level of the league as a whole. Hitters have an adjustment for not having to face their own team's pitchers; pitchers have a similar adjustment for not having to face their own hitters. Hitters in the AL since 1973 have a disadvantage in these statistics, since the league average is artificially inflated by the use of the DH and no adjustment is made for that.

Batting Runs Above Average. The number of runs better than a hitter with a .260 EQA (i.e., an average hitter) and the same number of outs; EQR - 5 * OUT * .260^2.5.

Batting runs above average (BRAA), adjusted for league difficulty.

Batting Runs Above Replacement. The number of runs better than a hitter with a .230 EQA and the same number of outs; EQR - 5 * OUT * .230^2.5.

Batting runs above replacement (BRAR), adjusted for league difficulty.

Batting runs above a replacement at the same position. A replacement position player is one with an EQA equal to (230/260) times the average EqA for that position.

Batting Runs above Replacement for the Position. This is, essentially, the equivalent average version of VORP. It is the number of equivalent runs this player had above what a replacement level player with the same mix of positions.

The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a player's forecast. The Baseline developed based on the player's previous three seasons of performance. Both major league and (translated) minor league performances are considered.

The Baseline forecast is also significant in that it attempts to remove luck from a forecast line. For example, a player who hit .310, but with a poor batting eye and unimpressive speed indicators, is probably not really a .310 hitter. It's more likely that he's a .290 hitter who had a few balls bounce his way, and the Baseline attempts to correct for this.

A measure of the relative volatility of a player's EqA or EqERA forecast, as determined from his comparables. The Beta for an average major league player is 1.00; players with Beta's higher than 1.00 have more volatile forecasts than others ("riskier"), while Betas lower than 1.00 represent less volatile forecasts ("less risky").

Betas are adjusted for the amount of playing time that a player is expected to receive. Thus, a player's Beta will not be higher simply because he's expected to receive less playing time (as a relief pitcher might as compared with a starter, for example), which naturally produces more variance because of higher sample sizes. Betas may be unreliable for players with few appropriate comparables.

A category 1 start is a start in which the pitcher throws 100 pitches or less.

A category 2 start is a start in which the pitcher throws 101-109 pitches.

A category 3 start is a start in which the pitcher throws 110-121 pitches.

A category 4 start is a start in which the pitcher throws 122-132 pitches.

A category 5 start is a start in which the pitcher throws 133 or more pitches.

Career Path Analysis is the name for a chart on a player's PECOTA card. The solid, curved lines represent a player's VORP at his 90th, 75th, 60th, 50th (Median), 40th, 25th and 10th percentile levels of performance over the course of his next five seasons. All of these lines appear in BLUE, except for a player's Median/50th percentile forecast, which appears in RED.

Comparable Year represents the season analogous to the current projected year for a comparable player. For example, if Dick Allen is listed as a comparable, and the year listed next to his name is 1974, Allen's 1974 is used as a component of the player's forecast. It also indicates that Allen's Baseline performance entering into the 1974 season was similar to the Baseline performance of the player in question.

PECOTA constructs a 182-day interval on either side of a player's birthdate in order to match ages; this method is more precise than the Bill James similarity scores, which use a player's age as of July 1.

Delta-hits. The number of hits above or below what would be expected for this pitcher.

Defense-adjusted ERA. Not to be confused with Voros McCracken's Defense-Neutral ERA. Based on the PRAA, DERA is intended to be a defense-independent version of the NRA. As with that statistic, 4.50 is average. Note that if DERA is higher than NRA, you can safely assume he pitched in front of an above-average defense.

How much a pitcher is underrated by Adjusted Pitching Runs (DIFF = ARP - APR).

A player's defensive wins above replacement, as listed on his PECOTA card, and accounting for the value of his position and the quality of his defense. Analagous to FRAR.

Days eXpected Lost -- used as an estimate of how many days a player is expected to miss due to an injury or illness. For starters, five days equals one start.

Defense, as listed in a player's PECOTA card, provides the player's number of defensive games played, primary position, and fielding runs above average (FRAA) with a given team in a given season.

The number of hits above or below average for this pitcher, based on his own number of balls in play and his team's rate of hits (minus home runs) per ball in play; (H-HR) - BIP * (team (H-HR)/BIP). Essentially, the Voros McCracken number. For a team, Delta-H should be zero. Positive numbers signify more hits allowed than expected ("bad luck," if you believe pitchers have nothing to do with the outcome of a BIP), negative numbers mean fewer hits than expected ("good luck").

The number of runs, more or less, that a pitcher allowed, compared to his statistics. The pitcher's statistics (such as hits, walks, home runs) are run through a modified version of the equivalent runs formula to get estimated runs. Again, positive is "bad luck," negative is "good luck."

The number of wins, more or less, that a pitcher won, compared to estimated wins. Estimated wins are derived from the pitcher's actual runs allowed and team average run scoring. Here, a positive number is "good luck," negative is "bad luck."

Each league has been given a difficulty level, based on the performance of players in that league compared to the same players' performance in other seasons. The reference difficulty level was defined by the trend line of the National League from 1947 to 2002, and extended backwards to 1871. The difficulty adjustment is the ratio between the actual difficulty level and the reference level.

Drop Rate is the percent chance that a player will not receive any major league plate appearances in a given season, based on comparables who disappear from the dataset entirely. Because of the conventions PECOTA uses in selecting comparables, the Drop Rate is always assumed to be zero for the current year, but it is an important consideration in a hitter's Five-Year Forecast.

Expected loss record for the pitcher, based on how often pitchers with the same innings pitched and runs allowed earned a win or loss historically (this differs from how it was computed, which was a more complicated, theoretical calculation).

Expected win record for the pitcher, based on how often pitchers with the same innings pitched and runs allowed earned a win or loss historically (this differs from how it was computed, which was a more complicated, theoretical calculation).

Expected winning percentage for the pitcher, based on how often a pitcher with the same innings pitched and runs allowed in each individual game earned a win or loss historically in the modern era (1972-present).

Also known as a BSP chart, an acronym for bloodstain spatter pattern, which these graphs seem to bear an eerie resemblance toward. The BSP charts plot a rate performance statistic (EqA or EqERA) on the one axis and playing time on the other (PA or IP). Each of the diamonds you see represents the performance implied by one of a player's comparables; the higher the similarity score for that comparable, the larger the size of the diamond. There is also an area of the chart shaded in a yellow color; this is the ‘golden zone' of performance in which a player both performs well (an EqA of .300 or higher) and remains in the lineup frequently (at least 500 plate appearances). Pitchers actually have two golden zones, one each for roles as starting pitchers and relievers.

In PECOTA projections, the ERA Distribution chart displays a pitcher's ERA forecast at various levels of probability. It progresses in sequential intervals of five percentage points, ranging from a pitcher's 95th percentile forecast on the left, to his 5th percentile forecast on the right.

In addition to the probability distribution for a given pitcher, which appears in blue, the chart also includes a normal distribution on ERA for all pitchers in the league, as adjusted to the player's current park and league context ("Norm"), and a dashed line representing the performance of a replacement level pitcher ("Replace").

Expected Return Date: An estimate of the date a player is expected to return to the lineup/rotation based on the current information. A player listed as "10/4" is done for the season; October 4th is the final day of the regular season.

Equivalent Average. A measure of total offensive value per out, with corrections for league offensive level, home park, and team pitching. EQA considers batting as well as baserunning, but not the value of a position player's defense. The EqA adjusted for all-time also has a correction for league difficulty. The scale is deliberately set to approximate that of batting average. League average EqA is always equal to .260.

EqA is derived from Raw EqA, which is

RawEqA =(H+TB+1.5*(BB+HBP+SB)+SH+SF-IBB/2)/(AB+BB+HBP+SH+SF+CS+SB)

Any variables which are either missing or which you don't want to use can simply be ignored (be sure you ignore it for both the individual and league, though). You'll also need to calculate the RawEqa for the entire league (LgEqA).

Convert RawEqA into EqR, taking into account the league EqA LgEqA, league runs per plate appearance, the park factor PF, an adjustment pitadj for not having to face your own team's pitchers, and the difficulty rating. Again, you can ignore some of these as the situation requires. xmul can simply be called "2", while the PF, diffic, and pitadj can be set to "1".

xmul=2*(.125/PF/Lg(R/PA)/pitadj)

EQAADJ=xmul*(RawEqa/LgEqa)* ((1+1/diffic)/2) + (1-xmul)

UEQR=EQAADJ*PA*Lg(R/PA)

To get the final, fully adjusted EqA, we need to place this into a team environment.

This is an average team:

AVGTM=Lg(R/Out)*Lg(Outs/game)*PF*Games*(DH adjustment)

The DH adjustment is for playing in a league with a DH. "Games" is the number of games played by this player.

Replacing one player on the average team with our test subject:

TMPLUS=AVGTM+UEQR-OUT*Lg(R/Out)*DH*PF

Get pythagorean exponent

pyexp=((TMPLUS+AVGTM)/Games)**.285

Calculate win percentage

WINPCT=((TMPLUS/AVGTM)**pyexp)/(1+(TMPLUS/AVGTM)**pyexp)

Convert into adjusted space, where the Pythagorean exponent is set to 2.

NEWTM=(WINPCT/(1-WINPCT))**(1/2)

Fully adjusted EqR:

EQR=.17235*((NEWTM-1)*27.*Games + Outs)

Fully adjusted EqA

EQA= (EQR/5/Outs)** 0.4

Equivalent Average, as taken from the Davenport Translation (DT) Player Cards. EqA1 is EqA adjusted for the season in which the performance occurred, as opposed to EqA2, which is adjusted for comparisons across multiple seasons or eras. For example, if you wanted to compare Albert Pujols's 2008 performance against those of other players in the 2008 season, you would reference his EqA1; if you wanted to compare Pujols's 2008 against Lou Gehrig's seasons in the 1920s and 30s, you would reference Pujols's and Gehrig's respective EqA2s.

Equivalent Batting Average, sometimes also referred to as Translated or Normalized Batting Average. This is a player's batting average, adjusted for ballpark, league difficulty, and era, and calibrated to an ideal major league where the overall EqBA is .260. While a major league hitter's equivalent stats should not differ substantially from his actual numbers, a minor league hitter's equivalent stats undergo translation and may differ significantly.

EqBA, or Equivalent Batting Average, is calibrated to an ideal major league with an overall EqBA of .270. While a major league hitter's equivalent stats should not differ substantially from his actual numbers, a minor league hitter's equivalent stats undergo translation and may differ significantly. Equivalent stats also account for park effects.

EqBB9 is calibrated to an ideal major league where EqBB9 = 3.0. While a major league pitcher's equivalent stats should not differ substantially from his actual numbers, a minor league pitcher's equivalent stats undergo translation and may differ significantly. Equivalent stats also adjust for park effects.

EqERA is calibrated to an ideal major league where EqERA = 4.50. While a major league pitcher's equivalent stats should not differ substantially from his actual numbers, a minor league pitcher's equivalent stats undergo translation and may differ significantly. Equivalent stats also adjust for park effects, and the quality of a pitcher's defense. EqERA is conceptually identical to NRA, as used in the DT cards.

EqH9 is calibrated to an ideal major league where EqH9 = 9.0. While a major league pitcher's equivalent stats should not differ substantially from his actual numbers, a minor league pitcher's equivalent stats undergo translation and may differ significantly. Equivalent stats also adjust for park effects.

EqHR9 is calibrated to an ideal major league where EqHR9 = 1.0. While a major league pitcher's equivalent stats should not differ substantially from his actual numbers, a minor league pitcher's equivalent stats undergo translation and may differ significantly. Equivalent stats also adjust for park effects.

EqK9 is calibrated to an ideal major league where EqK9 = 6.0. While a major league pitcher's equivalent stats should not differ substantially from his actual numbers, a minor league pitcher's equivalent stats undergo translation and may differ significantly. Equivalent stats also adjust for park effects.

EqMLVr, or Equivalent rate-based Marginal Lineup Value, is calibrated to an ideal major league with an overall EqMLVr of .000. While a major league hitter's equivalent stats should not differ substantially from his actual numbers, a minor league hitter's equivalent stats undergo translation and may differ significantly. Equivalent stats also account for park effects.

EqOBP, or Equivalent On Base Percentage, is calibrated to an ideal major league with an overall EqOBP of .340. While a major league hitter's equivalent stats should not differ substantially from his actual numbers, a minor league hitter's equivalent stats undergo translation and may differ significantly. Equivalent stats also account for park effects.

The formula:
Batting Runs Above Average + Plate Appearances * Average Runs Per Plate Appearance

Equivalent Runs allowed by a team.

EqSLG, or Equivalent Slugging Percentage, is calibrated to an ideal major league with an overall EqSLG of .440. While a major league hitter's equivalent stats should not differ substantially from his actual numbers, a minor league hitter's equivalent stats undergo translation and may differ significantly. Equivalent stats also account for park effects.

Standard deviation of per-start SNVA for each pitcher. This was previously shown as the variance, and was used to compute the "flakiest" pitchers. Standard deviation is just the square root of the variance, so these are equivalent.

Fielding runs above average.

Fielding runs above average (FRAA), adjusted for league difficulty.

Fielding Runs Above Replacement. The difference between an average player and a replacement player is determined by the number of plays that position is called on to make. That makes the value at each position variable over time. In the all-time adjustments, an average catcher is set to 39 runs above replacement per 162 games, first base to 10, second to 29, third to 22, short to 33, center field to 24, left and right to 14.

Fielding runs above replacement. A fielding statistic, where a replacement player is meant to be approximately equal to the lowest-ranking player at that position, fielding wise, in the majors. Average players at different positions have different FRAR values, which depend on the defensive value of the position; an average shortstop has more FRAR than an average left fielder.

Fielding Runs Above Replacement. The difference between an average player and a replacement player is determined by the number of plays that position is called on to make. That makes the value at each position variable over time. In the all-time adjustments, an average catcher is set to 39 runs above replacement per 162 games, first base to 10, second to 29, third to 22, short to 33, center field to 24, left and right to 14.

See FRAR, FRAR2. FRAR2 incorporates adjustments for league difficulty and normalizes defensive statistics over time.

The Five-Year Attrition forecast measures a player's Attrition Rate and Drop Rate over the forthcoming five seasons. These forecasts consider only players who have completed the comparable year in question.

The Five-Year Forecast is a player's weighted mean PECOTA forecast, taken over his next five seasons.

The Five-Year Performance forecast measures a hitter's forecast EqA or a pitcher's EqERA at various percentiles (90th, 75th, 60th, 50th, 40th, 25th and 10th) over the course of the next five seasons. The percentile forecasts are indicated by solid lines, usually in BLUE, except for his median/50th percentile forecast which is indicated in RED. Also listed is the player's weighted mean forecast in that category, indicated with a dashed YELLOW line.

The Five-Year WARP forecast measures a player's projected wins above replacement. For position players, this value is subdivided into batting wins, and defensive wins.

Historical Stats are the player's previous three seasons of performance as they appear in the BP book (with the addition of a player's WARP scores).

A "quick and dirty" measure of the lost value due to injuries. The formula used is MORP divided by 180 multiplied by days expected lost.

Luck, as measured by the number of extra wins, and short losses the pitcher actually got, versus his expected record. LUCK = (W-E(W))+(E(L)-L)

The highest number of pitches thrown by a pitcher in one outing.

The maximum amount of Pitcher Abuse Points a pitcher has accumulated in a single start.

Maximum number of pitches in a start

Maximum Pitcher Abuse Points (PAP) in a single start

Marginal Lineup Value, a measure of offensive production created by David Tate and further developed by Keith Woolner. MLV is an estimate of the additional number of runs a given player will contribute to a lineup that otherwise consists of average offensive performers. Additional information on MLV can be found here.

MLVr is a rate-based version of Marginal Lineup Value (MLV), a measure of offensive production created by David Tate and further developed by Keith Woolner. MLV is an estimate of the additional number of runs a given player will contribute to a lineup that otherwise consists of average offensive performers. MLVr is approximately equal to MLV per game. The league average MLVr is zero (0.000). Additional information on MLV and MLVr can be found here.

Marginal Value Above Replacement Player was as introduced in this article. It was updated in this article and this article.

It is set to MORP = $5.0*WARP3 for 2010. Subsequent years can be estimated at about 8% inflation. The benefit of our new MORP formula is that it adjusts for the facts that (1) Draft Picks are part of the cost of Free Agents, (2) Free Agents typically under-perform their projections, and (3) Deals signed before the off-season are part of the labor market.

Normalized ERA

Normalized Runs Allowed. "Normalized runs" have the same win value, against a league average of 4.5 and a pythagorean exponent of 2, as the player's actual runs allowed did when measured against his league average.

Equivalent Outs.

A player's offensive wins above replacement, as listed on his PECOTA card. Analagous to BRAR.

'Out of Baseball' is the tag assigned to a player's five-year forecast when his Drop Rate in that season exceeds 66.7%. That is, we do not list a player's forecast line when it is substantially more likely than not that he will not be playing professional baseball.

Pitcher Abuse Points. When used in the Pitcher Abuse Point report, PAP refers to PAP^3, which assigns 0 PAP to a start in which the pitcher throws 100 or fewer pitches and (PC-100)^3 PAP for all other starts.

Pitcher Base-Run Average. The PBRA is a newer, slightly more accurate replacement for the PERA. As the name indicates, it is a modification of the BaseRuns concept of run estimators.

Set B = 1.36 (H-HR) + BB + HBP - .06 K

This is your baserunner term.

PBR = HR + X * B * (B+HR) / TBF ,

where X is a constant set for the league, typically around .67.

PBRA is simply PBR/IP *9.

You can also use expected hits allowed instead of actual hits allowed; I call that the PBRA2, and also adjust the innings for the difference between actual and expected hits. If you are working with translated statistics, then you can use the per nine inning stats, with X=.695 and TBF=27 + H/9 + BB/9. You may see small differences between this calculation and what is displayed; HBP, which are included in the DTs even though they are not displayed, are the biggest reason for that.

PEAK refers to a series of metrics designed to evaluate a player's value in some statistic - most often WARP or non-negative WARP (used by UPSIDE calculations) - over a series of consecutive seasons. It has had two variations. The one currently in use for UPSIDE on the player cards is the five-year variant referenced by Nate Silver:

The version of Upside that we’re using here is the peak-adjusted variant, which measures a player’s most valuable five-year window up through and including his age 28 season (or simply his next five years of performance if he’s already age 25 or older). -- Nate Silver, 2007

Also used in some writings simply uses the next six seasons of a player's career.

In both cases, seasons which have yet to be played are projected using PECOTA instead of ignored, so young players will have the full complement of five (or six) seasons of data. See also: UPSIDE.

Payroll Efficiency Rating, measure developed by Shawn Hoffman expressing the ratio of a team's estimated marginal revenue (derived from third-order win totals and market size factors) to its expected marginal revenue (derived from payroll). Draft pick value is also factored in to account for the increased value of a high first-round pick. The concept behind PER was introduced here though the name came later. PER' is a variant of this which substitutes actual win totals for third-order win totals in the estimated marginal revenue calculation.

PERA is a pitcher's ERA as estimated from his peripheral statistics (EqH9, EqHR9, EqBB9, EqK9). Because it is not sensitive to the timing of batting events, PERA is less subject to luck than ERA, and is a better predictor of ERA going-forward than ERA itself. Like the rest of a pitcher's equivalent stats, his PERA is calibrated to an ideal league with an average PERA of 4.50.

Player Injury Projection Probabilities. This is the name for the rating system that underlies the Team Health Reports. The name was submitted by reader braden23 in honor of Wally Pipp, who may have the most famous injury in all of baseball history.

A pitcher's park-adjusted RA, expressed on a scale like ERA or RA. RA+ -- Park and league normalized Run Average. Similar to ERA+ found in Total Baseball, but based on RA rather than ERA.

Positional MLV. Runs contributed by a batter beyond what an average player at the same position would produce in a team of otherwise league-average hitters.

Positional MLV rate. Runs/game contributed by a batter beyond what an average player at the same position would hit in a team of otherwise league-average hitters. Like MLVr, it is a rate stat. The comparable season total is PMLV.

Pitcher-only runs above average. The difference between this and RAA is that RAA is really a total defense statistic, and PRAA tries to isolate the pitching component from the fielding portion. It relies on the pitching/fielding breakdown being run for the team, league, and individual. The individual pitching + defense total is compared to a league average pitcher + team average defense, and the difference is win-adjusted.

Pitcher runs above average, adjusted for league difficulty.

Pitcher-only runs above replacement. Similar to PRAA, except that the comparison is made to a replacement level player instead of average. The nominal RA for a replacement pitcher is 6.11 (the same ratio, compared to a 4.50 average, as a .230 EQA is to .260). This assumes that there is a 50/50 split between pitching and fielding. If the pitch/field split is less than that, as it was in the 1800s, the replacement ERA is reduced.

Pitcher-only runs above replacement. Similar to PRAA, except that the comparison is made to a replacement level player instead of average. The nominal RA for a replacement pitcher is 6.11 (the same ratio, compared to a 4.50 average, as a .230 EQA is to .260). This assumes that there is a 50/50 split between pitching and fielding. If the pitch/field split is less than that, as it was in the 1800s, the replacement ERA is reduced.

Pitching runs above replacement (PRAR), adjusted for league difficulty.

An adjustment made to account for the fact that some parks are easier to hit in than average, giving an advantage (in raw statistical terms) to hitters who play for that team. Park factors are always made relative to a league average of 1.00. The park adjustments in the BP are made only on the park factor for runs, averaged over five years; they can be found here. The first column is a one-year park factor, the second column is the five-year average centered on that year (assuming the team did not change or massively renovate their park).

The number of additional runs charged to the starting pitcher that his bullpen allowed to score after he left the game, compared to an average bullpen. Negative Pen Support means the bullpen prevented more runs from scoring than an average pen (i.e. the pitcher's ERA looks better than it should because of good bullpen support).

Described more completely in the 2002 Prospectus, the breakdown is a sequence of calculations designed to separate the pitching and fielding components of defense from each other. Certain events (walks, strikeouts, home runs) are considered to be entirely the responsibility of the pitcher. Errors and double plays are assumed to be entirely the domain of the fielders. Other hits and outs are assumed to be 75% fielding, 25% pitching.

For Hitters:

The Player Profile is a chart that evaluates a given hitter's primary production metrics (batting average, isolated power, unintentional walk rate, strikeout rate, and speed score) as a percentile compared to all major league hitters. For example, a player with an isolated power rating of 75% is superior in this category to three-quarters of all major leaguers. The player profile is based on the player's three previous seasons of performance, rather than his projection.

For Pitchers:

The Player Profile is a chart that evaluates a pitcher's performance in five categories: strikeout rate, walk rate, opponents' isolated power (e.g. home run rate), hit rate on balls in play, and groundball-to-flyball ratio. The rates are presented as a percentile compared to all major league pitchers; for example, a player with a strikeout rating of 75% is superior in this category to three-quarters of all major leaguers. The player profile is based on the player's three previous seasons of performance, rather than his projection.

Pythagenport was the first such formula to use the team's run environment to modify what in the original formula had been a fixed exponent (2 or 1.83), deriving the exponent as X = .45 + 1.5 * log10 ((rs + ra)/g). The winning percentage is then calculated as (rs^x)/(rs^x + ra^x). The formula has been tested for run environments between 4 and 40 runs per game, but breaks down below 4 rpg. The original article is here.

These three components--K rate, BB rate, GB/FB--stabilize very quickly, and they have the strongest predictive relationship with a pitcher's ERA going forward. What's more, they are not very dependent on park effects, allowing us to make reasonable comparisons of pitchers across different teams.

Formula:
QERA(unscaled) =(2.69+K%*(-3.4)+BB%*3.88+GB%*(-0.66))^2

Then, QERA is scaled to league average.
QERA(scaled) = QERA(unscaled) / League ERA * League QERA

Note that everything ends up expressed in terms of percentages: strikeouts per opponent plate appearance, walks per opponent plate appearance, and groundballs as a percentage of all balls hit into play. If, for example, Andy Pettitte has a 19.6% K rate, a 7.9% BB rate, and a 62.7% GB rate, he would have a QERA of 3.68. Note further that QERA is exponential, which is appropriate since run scoring is not linear.

Learn more in this article by Nate Silver.

For Pitchers:

Runs above average. At its simplest, this would be the league runs per inning, times individual innings, minus individual runs allowed. However, we have gone one step beyond that, because being 50 runs above average in 1930, in the Baker Bowl, doesn't have the same win impact as being +50 in the 1968 Astrodome. The league runs per inning need to be adjusted for park and team hitting (and difficulty, for the alltime RAA), and then you can multiply by individual innings and subtract individual runs. Finally, that quantity needs to be win-adjusted. See win-adjustment.

For Fielders:

Runs above average at this position, similar to Palmer's Fielding Runs as far as interpretation is concerned.

Rank by Equivalent Average

Rank by equivalent strikeouts per 9 innings

Rank by Fielding Runs Above Replacement

Rank by Wins Expected Above Replacement Player

Runs Above Position: The number of Equivalent Runs this player produced, above what an average player at the same postion would have produced in the same number of outs.

Runs Above Replacement. For a fielder, it is simply Runs Above Replacement for the position, where a replacement-level fielder is determined to be about 20 runs below average for the position; the number varies slightly depending on the number of balls in play.

Runs Above Replacement, Position-adjusted. A statistic that compares a hitter's Equivalent Run total to that of a replacement-level player who makes the same number of outs and plays the same position. A "replacement level" player is one who has 22.1 fewer EqR per 486 outs than the average for that position. For the overall league average (.260), that corresponds to a .230 EqA and a .351 winning percentage.

Essentially, this is the Equivalent Average analog of VORP.

Raw equivalent average, the first step towards building the EqA. In its fullest form, REQA = (H + TB + 1.5*(BB + HBP + SB) + SH + SF) divided by (AB + BB + HBP + SH + SF + CS + SB). REQA gets converted into unadjusted equivalent runs, UEQR.

Runs Prevented. The extra number of runs an average pitcher would have allowed in the same number of innings pitched (adjusted for park and league). RP greater than zero indicates that the pitcher allowed fewer runs than an average pitcher (i.e. he's better than average). Negative RP indicates the pitcher allowed more runs than an average pitcher (i.e. he's worse than average).

Replacement level MLV rate. Runs/game contributed by a batter beyond what a replacement level player at the same position would hit in a team of otherwise league-average hitters. The comparable season total is RPMLV. It differs from VORPr and VORP only in that it is solely based on batting performance whereas VORP includes basestealing.

A way to look at the fielder's rate of production, equal to 100 plus the number of runs above or below average this fielder is per 100 games. A player with a rate of 110 is 10 runs above average per 100 games, a player with an 87 is 13 runs below average per 100 games, etc.

See Rate. Rate2 incorporates adjustments for league difficulty and normalizes defensive statistics over time.

The first step in putting together equivalent average.

In its fullest form,

RawEQA = (H+TB+1.5*(BB+HBP+SB)+SH+SF-IBB/2) / (PA+SB+CS),

where PA=AB+BB+HBP+SH+SF. Feel free to drop any variable that isn't readily available.

Simple Fielding Runs -- The runs above average contributed by a defender. SFR is a defensive metric currently in a "beta" form based on Retrosheet-style play by play data. SFR for infielders is calculated differently than that for outfielders and for outfielders the metric is park-adjusted.

SIERA accounts for how run prevention improves as ground ball rate increases and declines as more whiffs are accrued, while grounders are of more materiality for those who allow a surplus of runners. The formula for SIERA is:

SIERA = 6.145 - 16.986*(SO/PA) + 11.434*(BB/PA) - 1.858*((GB-FB-PU)/PA) + 7.653*((SO/PA)^2) +/- 6.664*(((GB-FB-PU)/PA)^2) + 10.130*(SO/PA)*((GB-FB-PU)/PA) - 5.195*(BB/PA)*((GB-FB-PU)/PA)

where the +/- term is a negative sign when (GB-FB-PU)/PA is positive and vice versa.

This was explained in more detail in the following series: part one, part two, part three, part four, and part five.

Support-Neutral Losses. the pitcher's expected number of losses assuming he had league-average support.

Support-Neutral Lineup-adjusted Value Added - like SNVA, but also adjusted for the MLVr of each batter the pitcher faced.

Support-Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.

like SNLVA, but comparing to replacement level, rather than average. Replacement level is now being computed the same way in SNVA and in VORP (using the formulas from Keith Woolner's BP 2002 article).

Rate of Support-Neutral Lineup-adjusted Value Added above replacement level

Rate of Support-Neutral Lineup-adjusted Value Added

SNW / (SNW+SNL)

Support-Neutral Value Added - wins above average added by the pitcher's performance.

Support-Neutral Value Added (wins above average added by the pitcher's performance) per game pitched.

like SNVA, but comparing to replacement level, rather than average. Replacement level is now being computed the same way in SNVA and in VORP (using the formulas from Keith Woolner's BP 2002 article).

Rate of Support-Neutral Value Added

Support-Neutral Wins. the pitcher's expected number of wins assuming he had league-average support.

Support-Neutral Wins Above Replacement-level. the number of SNWs a pitcher has above what a .425 pitcher would get in the same number of (Support-Neutral) decisions.

A pitcher's calculated winning percentage given his pitching performances, assuming he had a league average offense and bullpen behind him.

Michael Wolverton gives an explanation of support-neutral stats here.

Formula:

Read about the underlying mathematical method in this article.

Abbreviation for Speed Score as used in PECOTA cards.

Stuff. A statistic developed by Clay Davenport that measures a pitcher's likelihood of success in the majors by analyzing his component rates.

Similarity Index is a composite of the similarity scores of all of a player's comparables. Similarity index is a gauge of the player's historical uniqueness; a player with a score of 50 or higher has a very common typology, while a player with a score of 20 or lower is historically unusual. For players with a very low similarity index, PECOTA expands its tolerance for dissimilar comparables until a meaningful sample size is established (see Comparable Players).

Similarity Score is a relative measure of a player's comparability. Its scale is very different from the Bill James similarity scores; a score of 100 is assigned to a perfect comparable, while a score of 0 represents a player who is meaningfully similar. Players can and frequently do receive negative similarity scores, and they are dropped from the analysis. A score above 50 indicates that a player is substantially comparable, and scores in excess of 70 are very unusual. The comparable player observations are weighted based on their similarity score in constructing a forecast.

The "standard league" is a mythical construction, in which all statistics have been adjusted for easy comparison. Its primary features are that runs scored is 4.5 runs per game; equivalent average is .260; and the pythagorean exponent is exactly 2.00.

The Stars & Scrubs Chart represents the probability that a player will demonstrate a given level of performance over the course of his next five seasons.

In PECOTA, stolen base attempts as a percentage of times on first base.

A rough indicator of the pitcher's overall dominance, based on normalized strikeout rates, walk rates, home run rates, runs allowed, and innings per game. "10" is league average, while "0" is roughly replacement level. The formula is as follows: Stuff = EqK9 * 6 - 1.333 * (EqERA + PERA) - 3 * EqBB9 - 5 * EqHR9 -3 * MAX{6-IP/G),0}

As listed on a player's PECOTA card, SuperVORP is VORP with additional adjustments for the following: 1) League difficulty. Players in a more difficult league (e.g. the American League) receive a boost in their SuperVORP to reflect their work against tougher competition. 2) Defensive support (for pitchers). A pitcher's BABIP, and therefore his VORP, are affected by his defense. SuperVORP adjusts the pitcher's VORP by assuming he has a league average defense behind him. 3) Fielding runs above average (FRAA) (for position players). The number of runs a player saves or subtracts with his glove, relative to league average, is added to his SuperVORP score. SuperVORP can be thought of as analogous to WARP, but with a higher threshold for replacement level.

Total number of pitches thrown as a starter.

Total Pitcher Abuse Points (PAP) accumulated

Translated at-bats: number of at-bats adjusted for park and season.

Translated batting average: batting average adjusted for park and season. Equal to T_H / T_AB.

Translated doubles: number of doubles adjusted for park and season.

Translated triples: number of triples adjusted for park and season.

Translated walks: number of walks adjusted for park and season.

Translated caught stealing: number of times caught stealing adjusted for park and season.

Translated hits: number of hits adjusted for park and season.

Translated hit by pitch: number of times hit by pitch adjusted for park and season.

Translated home runs: number of home runs adjusted for park and season.

Translated OBP: on-base percentage adjusted for park and season.

Translated outs: number of outs made (AB-H+CS+SH+SF) adjusted for park and season.

Translated runs: number of runs scored adjusted for park and season.

Translated RBI: number of runs batted in adjusted for park and season.

Translated stolen bases: number of stolen bases adjusted for park and season.

Translated SLG: slugging percentage adjusted for park and season.

Translated strikeouts: number of strikeouts adjusted for park and season.

Team's expected winning percentage in games started by a pitcher

Team's expected losses in the games started by the pitcher. This will always add (with TmW) up to the pitcher's total games started.

Team's expected wins in the games started by the pitcher. This will always add (with TmL) up to the pitcher's total games started.

Team's expected winning percentage in the games started by the pitcher.

Total WARP (Wins Above Replacement) as listed on his PECOTA card, considering both a player's offensive and defensive contributions. See WARP1.

Converts the player's batting statistics into a context that is the same for everybody. The major characteristics of the translation are: 1) that the translated EQA should equal the original, all-time adjusted EQA (within some margin for error); 2) that all seasons are expanded to a 162 game schedule; 3) that the statistics are adjusted to a season where an average hitter would have, per 650 PA: 589 AB, 153 H, 31 DB, 3 TP, 19 HR, 56 BB, 5 HBP, 113 SO, 10 SB, 5 CS, 79 R and 75 RBI. His rates would be a .260 batting average, .330 onbase average, .420 slugging average, and a .260 EQA with 76 EQR.

Converts all pitching statistics into a standard context. Pitchers are translated to a league where the top five pitchers (in innings) pitch an average of 275 innings. An average pitcher will have rates, per nine innings, of 9.00 hits, 1.00 home run, 3.00 walks, 6.00 strikeouts, and 4.50 earned runs. In the standard context, a replacement level pitcher has a 6.00; the translation is set up to conserve runs above replacement (alltime PRAR). Wins and losses are set using the pythagorean formula with average run support, with the pitcher's actual deviation from his real expected win percentage added back in.

Trend identifies players who demonstrate dramatic changes from their Baseline during their comparable year.

For Hitters:

Hitters who improve their EqR/PA by at least 20% are identified by a green, upward-pointing arrow and contribute to a hitter's Breakout score; hitters whose EqR/PA decreases by at least 20% are identified by a red, downward-pointing arrow and contribute to a hitter's Collapse score.

For Pitchers:

Pitchers who improve their EqERA by at least 20% are identified by a green, upward-pointing arrow and contribute to a pitcher's Breakout score; pitchers whose EqERA increases by at least 25% are identified by a red, downward-pointing arrow and contribute to a pitcher's Collapse score.

Unadjusted Equivalent Runs; (2 * REQA/LgREQA - 1) * PA * LgR/LgPA. Analogous to runs created.

UPSIDE is determined by evaluating the performance of a player's top-20 PECOTA comparables. If a comparable player turned in a performance better than league average, including both his batting and fielding performance, then his wins above average (WARP minus replacement value) are counted toward his UPSIDE. A base of two times wins above average is used for position players, and an adjustment is made to pitcher values such that they are comparable. If the player was worse than average in a given season, or he dropped out of the database, the performance is counted as zero.

VORP rate. Runs/game contributed beyond what a replacement level player would produce. Also a rate stat.

As listed in a player's PECOTA card, a series of metrics designed to evaluate a player's value to his team going forward. See individual entries for detail.

"First order wins." Pythagenport expected wins, based on RS and RA.

"Second order wins." Pythagenport wins, based on RPA and RPA Against.

"Third order wins." Pythagenport wins, based on AEQR and AEQRA.

Wins Above Replacement Player, level 1. The number of wins this player contributed, above what a replacement level hitter, fielder, and pitcher would have done, with adjustments only for within the season. It should be noted that a team which is at replacement level in all three of batting, pitching, and fielding will be an extraordinarily bad team, on the order of 20-25 wins in a 162-game season. WARP is also listed on a player's PECOTA card. The PECOTA WARP listing is designed to correspond to WARP-1, not WARP-2 or WARP-3.

Wins Above Replacement Player, with difficulty added into the mix. One of the factors that goes into league difficulty is whether or not the league uses a DH, which is why recent AL players tend to get a larger boost than their NL counterparts.

WARP2, expanded to 162 games to compensate for shortened seasons. Initially, I was just going to use (162/season length) as the multiplier, but this seemed to overexpand the very short seasons of the 19th century. I settled on using (162/scheduled games) ** (2/3). So Ross Barnes' 6.2 wins in 1873, a 55 game season, only gets extended to 12.8 WARP, instead of a straight-line adjustment of 18.3.

For most hitters, at least, it is just that simple. Pitchers are treated differently, as we not only look at season length, but the typical number of innings thrown by a top starting pitcher that year (defined by the average IP of the top five in IP). We find it hard to argue that pitchers throwing 300 or more innings a year are suffering some sort of discrimination in the standings due to having shortened seasons. This why Walter Johnson has almost no adjustment between WARP2 and WARP3, while his contemporaries Cobb, Speaker, and Collins all gain around 7 or 8 wins.

Expected wins added over an average pitcher. WX uses win expectancy calculations to assess how relievers have changed the outcome of games. Win expectancy looks at the inning, score, and runners on base when the reliever entered the game, and determines the probability of the team winning the game from that point with an average pitcher. Then it looks at how the reliever actually did, and how that changes the probability of winning. The difference between how the reliever improved the chances of winning and how an average pitcher would is his WX.

Expected wins added over an average pitcher, adjusted for level of opposing hitters faced. WXL factors in the MLVr of the actual batters faced by the relievers. Then, like WX, WXL uses win expectancy calculations to assess how relievers have changed the outcome of games.

Expected wins added over a replacement level pitcher. WXR uses win expectancy calculations to assess how relievers have changed the outcome of games, similar to WX. However, instead of comparing the pitcher's performance to an average pitcher, he is compared to a replacement level pitcher to determine WXR.

Expected wins added over a replacement level pitcher, adjusted for level of opposing hitters. WXRL combines the individual adjustments for replacement level (WXR) and quality of the opposing lineup (WXL) to the basic WX calculation.

A correction made to raw runs when converting them to a standard league to preserve their win value. Define an average team from season games played, league runs per game (9 innings or 27 outs, depending on whether you are using pitcher or batter data), and appropriate adjustments (park, team hitting/pitching, difficulty). "Team" is the effect of replacing one player on the average team with the player we are analyzing. Calculate the pythagorean exponent from (average + team) / games as your RPG entry; calculate winning percentage using the modified pythagorean formula. Now, go backwards, solve for "team" runs, given the winning percentage, an average team that scores 4.5 per game, and a pythagorean exponent of 2.00.

Adjusted Innings Pitched; used for the PRAA and PRAR statistics. There are two separate adjustments:

1) Decisions. Innings are redistributed among the members of the team to favor those who took part in more decisions (wins, losses, and saves) than their innings alone would lead you to expect. The main incentive was to do a better job recognizing the value of closers than a simple runs above average approach would permit. XIPA for the team, after this adjustment, will equal team innings. First, adjust the wins and saves; let X = (team wins) / (team wins + saves). Multiply that by individual (wins + saves) to get an adjusted win total. Add losses. Multiply by team innings divided by team wins and losses.

2) Pitcher/fielder share. When I do the pitch/field breakdown for individuals, one of the stats that gets separated is innings. If an individual pitcher has more pitcher-specific innings than an average pitcher with the same total innings would have, than the difference is added to his XIPA. If a pitcher has fewer than average, the difference is subtracted. This creates a deliberate bias in favor of pitchers who are more independent of their fielders (the strikeout pitchers, basically), and against those who are highly dependent on their defenses (the Tommy John types).