Strat-O-Matic Basic Average e Ratings

I broke out some Basic Strat last night. I don’t like the basic fielding charts, so I’d rather use the simplified “card charts” I use for the Advanced game. Trouble is, the Old Timer cards don’t have e Ratings. If I had some average e Ratings for each position, I could use that.

I found an old article in Strat Fan that gives a formula for e Ratings:

SOM e = 1458 * Errors / Innings_Played

I can find this data for specific positions and seasons on Baseball Reference. I scraped the data for the National and American Leagues from 1901 through 2021 and calculated the average e Ratings. (I treat all outfielders together.) The whole mess can be seen in the busy chart below.

I broke the seasons into six somewhat arbitrary periods. (The longer periods have less variation.) Then I averaged the seasons in each period. This gave me the numbers for the new chart:

Now, if a card doesn’t have an e Rating, I can look up the average value here and use it. Of course, every player at a particular position will have the same rating, but at least it will be representative of the era.

The updated card charts can be downloaded here.

2021 Power Rankings

Pre-Draft value sums the positive values of all signed and presumptive players. 

Post-Draft values are for the eight best position players at all positions, plus the next two best position players, plus five starters, plus four relievers, including one closer. Negative values are used as well as positive values. Replacement levels are recalculated after the draft.

XR Prediction

The initial goal was to predict XR values for pitchers prior to the cards coming out. So I used MLB 2019 stats and ABL 2020 XR values (all parks). Got ERA, xFIP, & SIERA from Fangraphs. Correlations were fair, around 0.7. Best was xFIP at 0.71 for starters.

Finally found some linear weights at Baseball Savant, namely wOBA. This provided a much better correlation. (Also tried xwOBA, but it was worse.) Used a list of exclusive starters and exclusive shorts. They were fairly different, with shorts having worse correlation. I’m guessing that’s a combination of smaller sample size and deviation from average platoon rates. Did not try longs, closers, or combos. The pitcher estimate equations:

STARTER:  XR = 824 * wOBA - 103     R=0.88
  SHORT:  XR = 601 * wOBA -  33     R=0.80

If I ever had to choose keeps without cards, I would get data for all qualified pitchers, then sort them into categories, when appropriate.

Did batters too. Unsurprisingly, correlation to wOBA was even better. (xwOBA was again worse.) For batters:

      XR =  736 * wOBA - 138    R=0.86


  • TPB pitcher ratings correlate with linear weights, as opposed to, say, ERA.
  • I could get reasonable XR estimates for both batters and pitchers if I didn’t have access to the cards.

The spreadsheet with the data is named ABL Predictions.

2020 ABL Post-Draft Power Ranking

The power ranking is based on player value for an average of all ABL parks. Batter value is the sum of the greatest combination of the eight fielding positions, plus the highest values of two remaining position players. Pitching values are from the top five starters and top four relievers (includes one closer or short rated at closer). All 30 players on each team immediately after the draft are considered. The Titusville value is adjusted for system bias.

The scale is somewhat different from that of the pre-season ranking, which counted the maximum value of all players, without regard to position.

Power ranking is an estimate of team strength for entertainment purposes only and does not take into account management skill, trading savvy, or the luck of the dice.

2019 Post-Draft Power Ranking

Long Beach Island has the most valuable hitting, and Crown Heights has the most valuable pitching (both starting rotation and bullpen).

The power ranking is based on player value for an average of all ABL parks. Batter value is the sum of the greatest combination of the eight fielding positions, plus the highest values of two remaining position players. Pitching values are from the top five starters and top four relievers (max one closer). Only the active roster is considered, apart from some assumptions about early-season starter taxi moves. The Titusville value is adjusted for system bias.

The scale is somewhat different from that of the pre-season ranking, which counted the maximum value of all players, without regard to position.

Power ranking is an estimate of team strength for entertainment purposes only and does not take into account management skill, trading savvy, or the luck of the dice.

Player Value

This is a description of the player values that I compute for the ABL. I have bits and pieces of the explanation in various places, but thought it would be good to have everything in one place.

The basis of my calculations is linear weights, which is a method for estimating the number of runs produced by a player using the number of each play outcome for the batter. The particular variety of linear weights I use is called Extrapolated Runs. (See note below.) Each outcome is associated with a run value. A home run is 1.44 runs, a single is 0.5 runs, a strikeout is -0.098 runs. Note that the calculation can be done for both batters and pitchers. Of course, good batters will produce more runs, and good pitchers will allow fewer runs.

Now let’s consider a particular batter’s Triple Play Baseball card. If I can estimate the outcomes of each possible roll (000-999), then I can add up the run values (Extrapolated Runs) for each of those outcomes. If I divide that by 1000, then I have an average run estimate for one plate appearance by that batter. Note that I can do the same thing for a particular pitcher’s card.

To get all those outcomes requires a lot of data and a lot of estimates. The data part involves all the numbers in the main area of the card: this much of a home-run range, this much of an easy-fly range, etc. Then we need to create an average pitcher to face each batter, and vice versa. Then we need to estimate the number of times a batter will face righty and lefty arms, then weight those two values appropriately. We need to calculate the average outcomes of range plays and Deeps! But in the end we can get an estimated runs per plate appearance for every player.

Run values do not take into account the following ratings: injury, jump, steal, speed, hold, catcher throw, outfield throw, and double-play turn.

What’s missing at this point is defense. The Range and Error charts can be used to determine the runs saved by a defender using the same linear weights concept. These adjustments can be applied to a particular player, but if that player is carded at multiple positions, then the combined offensive-defensive run estimate is different for each position.

The goal is to calculate a player “value” that is something like WAR (Wins Above Replacement). Replacement players at different positions have different run-producing capacities. That holds true for both MLB and the ABL. For the ABL I set replacement levels close to the estimated run levels of the best available free agents at each position during the regular season. That level of runs at each position becomes the zero point of my calculated player value. The zero-adjusted run values are then scaled such that only the best players have a player value above 100. Players can have negative player values when free agents with higher run estimates are available at a position.

Defensive ability and position value can lead to very different player values for the same player. For example, an average-hitting catcher may have a significant value behind the plate, but a very low value playing first base, especially if his defense at first is FR/8.

Values are adjusted according to the average number of appearances as a full-time pitcher or position player. For example, on average closers will face fewer batters than a starter, so a closer’s value is adjusted down relative to a starter.

When I total the value of all players on a team, I do not count players with negative player value, because such players are unlikely to get lots of playing time. If a player plays multiple positions, I use the position with the highest value.

Since all free agents are rated, I can use historical ABL draft data to estimate the player value for various points in the draft.

TL;DR: The numbers and ratings on the cards are used to estimate the frequency of outcomes (single, home run, walk, strikeout, etc.). The outcomes are converted into runs using linear weights. The run estimate is adjusted for defense, then adjusted to a scale with zero indicating that an equivalent free-agent player is available, and 100 indicating an arbitrary superstar level.

A note on Extrapolated Runs
Extrapolated Runs (XR) appealed to me, because it is an estimate of absolute runs, unlike Palmer’s Batting Runs, which is measured relative to an average player. XR also includes double plays, which can be estimated from TPB cards.

The big weakness of XR is that it’s formulated to apply over a large span of seasons, specifically 1955-1997. I don’t find any XR coefficients for single, recent seasons.

Jim Furtado wrote an article about the development of XR in 1999.

56-Value Dice System

Thought about this ordered dice system for some reason. The idea is to use multiple, uniformly colored, six-sided dice to produce a number of values, not all of which have the same probability. For example, with three dice, one can order the die values in ascending order, like 123, 256, 255, 224, 333, etc. This yields 56 possible values with the following probabilities.

20 values of probability 6/216 = 2.78% (no dice identical)
30 values of probability 3/216 = 1.39% (two dice identical)
 6 values of probability 1/216 = 0.46% (three dice identical)

This system is actually used in an old tabletop baseball game, “Be A Manager.” My Brother found a group of guys playing in a bar several years ago.

Sports Illustrated / Avalon Hill / 10-39 Dice

The family have a couple of tabletop games from the 70s that use funky, six-sided, wooden dice. (Superstar Baseball has a selection of all-time MLB greats, while Bowl Bound has college football teams from the 60’s & 70’s.) There are three dice: one black and two white. There are no pips on the dice—instead numerals are printed on the sides. It’s a bit like Strat-o-Matic. The black-die value is multiplied by ten, and the two white die are added to the total. So, for example, a black 2 and white 3 & 4 represent a value of 27. The faces of the dice are marked as follows:

 BLACK: 1, 2, 2, 3, 3, 3
WHITE1: 0, 1, 2, 3, 4, 5
WHITE2: 0, 0, 1, 2, 3, 4

Continue reading Sports Illustrated / Avalon Hill / 10-39 Dice

Post-Draft Power Rankings

The rating system is based on the run value of a player at a particular position, relative to a replacement player. Replacement-player values are based on post-draft free agents at each position. The scale is set to zero for replacement players and 100 for an arbitrary “superstar” level. Run values are adjusted to expected game participation of regular position players, starters, and relievers. Run values do not take into account the following ratings: injury, jump, steal, speed, hold, catcher throw, outfield throw, and double-play turn. Run values are based on an average of all current ABL parks.

Team power rankings are calculated by adding the run values of 19 players on each team:

  • 8 position players chosen for maximum value as a group (Platoons are not considered.)
  • 2 additional position players, which represent DH and bench strength
  • 5 most valuable starters
  • 4 most valuable relievers

The post-draft power rankings are depicted in the chart below.

Syracuse has the strongest position players, Orlando has the weakest. La Jolla has the strongest starting rotation, Ocracoke has the weakest. Chesapeake Bay has the strongest bullpen, Mudville has the weakest.

The power rankings are a simple measurement of team strength and may not accurately predict win/loss records.

2017 ABL Draft: Titusville Picks

The most significant feature of this year’s draft was the lack of starting pitching. Relief pitching was good at the top, but poor in the middle. Batters in the draft pool were stronger than normal. Titusville’s picks went very much according to plan for the first five rounds or so, before the normal confusion set in.

    1/  6        Steven Wright       starter
    2/ 16        Kevin Kiermaier     CF
    3/ 26        Tyler Thornburg     reliever
    4/ 36        Evan Longoria       3B
    5/ 46        Ervin Santana       starter
    6/ 56        Miguel Gonzalez     starter
    7/ 65        Adam Rosales        IF
    8/ 74        Michael Lorenzen    reliever
    9/ 84        George Kontos       reliever
   10/ 93        Jett Bandy          C
   11/102        Curtis Granderson   OF
   12/111        Matt Holliday       1B/LF
   13/120        Fernando Abad       LH reliever
   14/129        Domingo Santana     OF
   15/138        Jackie Bradley      CF
   16/146        Jake Barrett        reliever

2015 ABL Draft: Titusville Picks

I expect to go from first to worst this season, as there wasn’t a good return from last year’s championship squad. In fact, I kept only 13, so had two extra picks, including the last of the entire draft. The strategy was to invest in young position players that might take major strides in 2015. Pitching was relegated to the later rounds. I was hoping to snag Starlin Castro and Mookie Betts, but LBI was clever enough to pounce before me.

    1/ 10        Carlos Gomez       CF
    2/ 21        Marcell Ozuna      OF
    3/ 32        Ian Desmond        SS
    4/ 41        Travis d’Arnaud    C
    6/ 61        Tyson Ross           SP
    7/ 71        Rougned Odor       2B
    8/ 81        Eduardo Escobar    IF
    9/ 91        Oswaldo Arcia      RF
   10/101        Casey Fien           RP
   11/111        Danny Salazar        SP
   12/121        Scott Atchison       RP
   13/131        Dustin Ackley      LF
   14/141        Yovani Gallardo      SP
   15/151        Jonathan Broxton     RP
   16/161        Jared Hughes         RP
   17/171        David Buchanan       SP
   18/181        Justin Wilson        RP

Goodbye R, Hello L

During the 2014 ABL season everyone noticed the increase in pitcher cards with the R symbol. I wrote about it in
the 2014 ABL Yearbook. Now that my 2015 card data is in the computer, it’s a good opportunity to see if the Rs are still as numerous. I did a simple count of the pitchers in recent seasons that have each symbol. Starters and relievers are all grouped together. The data is from only the pitchers with ABL eligibility; not all Triple Play cards are represented. I don’t think I’ve missed too many eligible players over the last few seasons, but the first couple of seasons considered here are probably missing a few, especially for the 2008 season. The years listed refer to the ABL season, so the 2015 data is from the 2014 Triple Play cards that we’ll be using in the upcoming 2015 ABL season. OK, enough of the fine-print bullshit, let’s go to the graphs.


Well, it looks like 2014 was a blip for the R symbol. The frequency has dropped down to the previous level.

The H symbol continues to occur infrequently. (To the relief of all ABL managers!) It’s interesting that the level of the H symbol seems to follow that of the R from year to year. I didn’t notice that before, probably because the yearbook study weighted the symbols by how many innings were pitched in the ABL, and nobody likes to give an H pitcher a lot of innings. In 2014, when the R frequency doubled, the H frequency doubled too, from 4.5% to 9.5%! In 2015 it’s back down to 4.5%.


The L symbol is back with a vengeance! Lots of shorts have the L this year, and it looks like every single qualified closer has one. In the yearbook I speculated that the combination of B & L might be constant. It sure doesn’t look like that in 2015. This season should see more walks than ever before erased from batter cards, because the frequency of Bs is up too.


And finally, the F symbol (found on relievers’ cards only) has not fluctuated much over the years.

In summary, compared to last season, expect fewer homers & deeps to be re-rolled, and expect to lose more walks off the batters card.

R & H Symbols

A few guys have mentioned that there are a lot more R symbols out there this season. Commish & I were talking about it and speculated about how the symbols are calculated. I guessed that the R & H symbols depend solely on how many home runs a pitcher gave up with runners on base relative to the total number of homers he surrendered.

I collected some stats from Baseball Reference to see how they compared to the symbols. I initially selected the 43 starters currently on the ABL active rosters. I later added some H-symbol starters from Taxi Teams and the free-agent pool, because the H symbols were underrepresented. I didn’t look at any relievers, but I don’t expect they would have rules different from the starters. I looked at the 2013 MLB stats and the TPB cards we’re using for the 2014 ABL season. In B-R you can find the relevant stats under the “Splits” menu in the “Standard Pitching” section on the particular pitcher’s page. Scroll down to the “Bases Occupied” table. Strasburg’s stats are shown below: 7 homers with the bases empty, 9 with runners on.


I noticed some patterns and figured out an easy rule that predicted all the actual symbols. It’s best understood by looking at the grid shown below. There are two measurements that figure in. The first is the number of homers hit with runners on base divided by the total number of homers. Call this HRonbase. My initial thought was that the symbols would depend on this number only. The average value of this measurement in my sample is 40%. The second measurement is the overall home-run rate: the total number of homers surrendered divided by the batters faced. Call this one HRt. The average value in my sample is 2.2%. So here’s the table showing how the combination of these measurements determines the symbol:


When the overall home-run rate is greater than 2%, the symbols act like I expected them to. If the percentage of home runs with runners on is large, the guy gets an H. If that percentage is small, he gets an R. But it’s a different story when the overall home-run rate is less than 2%. In that case, it doesn’t matter what the stats are for on-base and bases empty; the guy gets an R, period. The clearest example is Henderson Alvarez, who had guys on base every time a home run was hit against him. But that was only two homers in 418 plate appearances, a very low rate of 0.48%. That low rate earned him an R, despite the fact that he gave up zero solo shots.

So it’s obvious that the R symbol is used to reduce the number of homers from the batter’s card when the pitcher gives up fewer than average home runs in general. With power becoming scarcer recently, it’s not surprising that more Rs are required. On the other hand, although there were 273 fewer home runs in 2013 compared to 2012 (as Commish pointed out), there were even fewer in 2011.

I wondered why the overall homer rate couldn’t instead be handled via the Deep ranges. I think the answer is that if you lose the Deeps, then you lose the park variation that forms such an important part of the game. If a guy has no Deep ranges (and there are some, of course), then it doesn’t matter what park he’s pitching in or what Power the batter has (except for the Deeps from Park Effects, of course).

So, my conclusion is that the R & H symbols are based more on the overall home-run rate of the pitcher, and not so much on the state of the bases when the home runs were hit.

Outfielder Errors

In Strat-O-Matic, outfielder errors result in the batter reaching second or third. What kind of errors do outfielders really make?

I looked at the 2,386 errors made in MLB 2005-2009. (From Retrosheet, natch.) That’s about one every five games. I divided them into the five categories shown in the chart below.


Only a quarter involve the batter reaching base on the error. The majority involve advancement of other baserunners, most after a hit.

A little more detail in the table below, which shows how many bases the batter advanced on the error.


An error that allows the batter to go to second on a single is, by far, the most common occurrence. The table hides a lot of detail, though, like the base situation and the advancement of those other runners.