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.

Plate Appearance Outcomes Over the Years

We know that the three true outcomes have been increasing in recent years, but I’ve never seen a good graphical representation of it. I’ve been wanting to examine this data for a while—a conversation with a friend last night spurred me on to do it.

The goal was to track the outcomes of plate appearances over the years, categorized into plays that involve ball-bat contact and those that don’t. The greenish areas in the chart are the “contact” plays, and the reddish areas are the non-contact outcomes. The major takeaway for me is that, over the last 75 years or so, strikeouts have increased by about the same amount that in-play outs have decreased. (In-play outs are balls in play that are not hits, or, in other words, outs that are not strikeouts.)

I was surprised that the decrease in contact plays overall has not caused a proportionate decrease in the percentage of hits. The percentage of hits (singles, doubles, triples, and home runs) has stayed remarkably constant from 1940-2019, never going outside the range of 22-24%!

Likewise, the percentage of walks has been more consistent than I expected. It has been within the 7-10% range since 1936. Also, there’s no clear recent trend in walk percentage, unlike the case for strikeouts.

Although recent home-run percentages (2.7% for 2010-2019) are higher compared to the 1980s (1.9%), they aren’t that different from the “steroid era” (2.5% for 1990-2009) or the 1950s (2.4%).

One way to look at it is to say that the contact plays (green) are “exciting,” while the non-contact plays (red) are “boring.” By that measure, in 1973 (when I started following baseball) 76.7% of plate appearances were “exciting.” In 2019 that figure had dropped to 67.3%, so one could say that the game is only 88% as exciting now compared to when I starting following it.

By the way, this is just a presentation of the data. I’m not getting into the reasons for why the percentages have changed.

Miscellaneous notes:

  • The raw data is from the excellent Baseball Reference site.
  • I chose the National League because it’s the longest continuous league. Excluding the American League avoids effects of the Designated Hitter.
  • I excluded the 2020 season because of the relatively small number of games and because of the DH in the NL.
  • The “other” category collects outcomes like catcher’s interference.
  • Reaching base on an error is included in the “in-play outs” category, because such a play is officially scored as an out for the batter (but for the error).
  • The home-run statistics include inside-the-park home runs. They are very rare today, but they accounted for about 35% of home runs in 1901.
  • Statistics for sacrifice hits were not recorded prior to 1894, and sacrifice flies were not always in the scoring rules. No matter—they should all be counted in the “in-play outs” category.
  • Prior to 1889, more than four balls constituted a walk.

Hitter/Pitcher-Friendly Leagues

I had a random thought about the differences between minor leagues in terms of being hitter-friendly or pitcher-friendly. I’ve often read qualifications of individual performances, for example, “he’s hitting well, especially since that’s a pitchers’ league,” or “his ERA is not bad, considering that he’s in a hitter-friendly league.” So I decided to go to the stats. I chose to compute the averages of the last five complete regular seasons, 2013-2017. But which stats to use? Runs per game? ERA? Batting average? I decided to compile OPS and ERA as the measurements for hitting and pitching, respectively. I knew that the two would be highly correlated, and that was indeed the case. I really didn’t see anything interesting by considering both stats together, so I simply sorted the leagues by OPS. The data appears in the table below.

I was surprised to see the huge difference between the top and the bottom: 126 points of OPS, 1.59 earned runs! The next surprise was that the leagues don’t cluster much by level. The Rookie leagues are all over the map.

I had a few ideas to explain the differences, then the Commish suggested a few others. Here’s a list of possible explanations.

  • Elevation. The Pioneer and Pacific Coast Leagues parks are generally at higher elevations, which helps the hitters.
  • Big Spring Training Parks. The Florida State League teams play in the Spring Training parks, which are big. The same probably goes for the Gulf Coast League, even though those are back fields.
  • Wood Bats. Hitters in the Short-Season A leagues may be at a disadvantage, because some of the hitters are using wood bats regularly for the first time.
  • Windy Florida. Maybe windy conditions are tough on the hitters in the Florida State League and GCL.

The Designated Hitter

This analysis didn’t turn up much interesting. Although I’m not a fan of the DH rule, I had some ideas that the use of the DH had probably changed from its MLB inception in 1973 to the present day. I figured that the early DHs were the ageing sluggers like Cepeda & Oliva, and that the modern game uses a more mix-and-match approach to the DH. Nope.

I looked at regular-season starting lineups from the Retrosheet Event Files. I limited the analysis to American League lineups, because I wanted to focus on teams that used the DH most/all of the time. I included AL lineups in inter-league games when the DH was used.

I looked at the lineup slot occupied by the DH to see how that changed over the years. The table below shows the slots used for each season, 1973 through 2017. Cells are colored like a heat map, with red for the maximum and blue for the minimum.

I’m surprised how variable the data is from season to season. For example, in 1992 the DH led off 209 times (9.2%), and the following season the number was down to 32 (1.4%). Undoubtedly there were a couple of DHs in ’92 that led off regularly and did not do so in ’93. Still, the variation at all batting-order slots is more variable that I had expected. Maybe there’s a bit more consistency in the last ten years or so, but I didn’t do a numerical analysis of this.

Note that the only starting-lineup slot that was not filled by a DH for the entire season was the 9 spot, which had no DH in 1975 and 1997.

Of course, it’s clear that the DH is usually slotted in the heart of the lineup, and that hasn’t changed through history. The totals for all seasons are shown in the chart below. It’s no surprise to me that cleanup is the most common DH slot.

The other thing I looked at is how often a team used a single player as DH through the season. I looked at the number of games started by the most used DH on a team. The team with the most starts by one DH is plotted for each season, as is the team with the least starts by one DH. The mean plotted is the average of the DH leader of all teams. For example, in 1973 Orlando Cepeda started 142 games at DH for Boston (the max), while Kansas City had seven players with ten or more starts at DH, of whom Hal McRae had the most (33, the min).

The 1981 and 1994 seasons were shortened by strikes, so keep that in mind when looking at the data for those seasons.

There’s not much variation over history. I expected to see a decline in the max, but I don’t see it.

The coolest tidbit from this otherwise dull analysis was noticing that the maxima during 1978 & 1979 were 162, meaning that at least two players started every regular-season game at DH. That turned out to be Rusty Staub for the 1978 Tigers, and Willie Horton for the 1979 Mariners. Because of inter-league play, this record will likely never be broken!

Errors at Different Levels of OB

Commish & I were discussing the standards for official scorers giving errors. Should the same standard be applied regardless of the level, or should the standards be higher at the higher levels?

Commish made the excellent point that throwing errors (especially to first) are going to be automatic and are not really subject to any subjective standard. Since these types of errors are obviously made more frequently at the lower levels, we expect the number of errors to go up as the level goes down.

So, I can’t answer my original question with stats, but I still thought it would be interesting to look at the fielding percentages at the different levels of OB. I used 2013 stats and excluded leagues south of the border.

Screen Shot 2014-06-18 at 9.36.42 PM

The trend is clear. Actually, it’s clearer than I expected! When you get down to A ball, errors are twice as likely compared to the Bigs.

The Worst Hitting Pitchers in MLB History

Baseball Reference has a free trial for their Play Index, so I’m giving it a whirl.

Who are the worst hitting pitchers of all time? I’ve got no magic criteria, but it’s easy find some guys who were epic fails at the plate.

Rob Herbel pitched in 332 games in the 60s and early 70s, mostly for the Giants. He managed only six hits in 227 plate appearances for an anemic .029 batting average. He struck out 125 times (55% of PAs) and walked only eight times. Actually, one third of his hits were doubles, which raised his OPS to .104. I bet a few of those doubles were hit to sleeping outfielders.

Dean Chance won the AL Cy Young in 1964 and accumulated 759 plate appearances in 406 games. He recorded 44 hits (.066 BA), all but two of which were singles. He struck out 420 times (55%) and walked only 30 times. With 128 wins and a 2.92 career ERA, he’s probably the best pitcher ever who was useless with a bat in his hands.

Of the active guys, Tommy Hanson & Ben Sheets are notable. Hanson is 11 for 187 (.059) with 92 strikeouts, 5 walks, and zero extra-base hits. Sheets is 34 for 449 (.076) with 212 Ks and 19 walks.

hanson           sheets

Although Randy Tate was in the bigs for only one year, he holds the distinction of having the most career plate appearances (47) without a hit. He did manage to draw one walk, though! In six minor league seasons he hit .113, so I guess ’75 was just a down year for him. Tate had an unusually symmetric career: three years in the minors, followed by one full season with the Mets (He pitched in every month of the ’75 season.), followed by three more years in the minors. He was never called up during his minor league seasons, and wasn’t sent down during his only major league season!

And, finally, of the pitchers with the dubious distinction of never having reached base safely ever, the guy with the most plate appearances (33) is none other than Justin Verlander. I think I’ve heard that he’s a decent pitcher, though. Verlander did not reach base during his three post-season PAs, and he never went to the plate during his 20-game minor league career. Let’s hope that the increase in interleague play will give Justin the chance to get off the schneid in 2013.

2013-09-30 UPDATE Verlander got only two plate appearances during the 2013 regular season, and they both came in the 162nd game. He went hitless, but so did the rest of the Tigers, as this was Henderson Alvarez’ no-hitter!

2014-06-18 UPDATE On April 12, 2014 in San Diego, California, in the top of the second with two outs, Justin Verlander reached base safely for the first time in his professional career when he grounded a single up the middle against Ian Kennedy. When he next came to the plate in the fourth… he hit another single!!! He would later score his first run. As of today Verlander has a .069 batting average. He is still looking for that first walk.

2012 ABL Playoff Odds

I was curious about the chances playoff teams have of getting to the Bambino Cup Finals and their chances of being crowned ABL champions. The playoff structure itself has a big impact, for example, the division champions have shorter roads to the cup. Of course, the relative strength of each team is very important, but how can that be measured?

First, let’s consider the playoff structure in isolation. Assume that all playoff teams have equal strength. If that’s the case, then the chance of winning a game or a series is 50%, a coin flip. A division champ (C-Bay or Orlando) has to win two series, so they have to flip a coin twice and have it come up heads both times. That’s one chance in four, 25%. A team with a one-game showdown to get into the lower bracket (LBI or Manahawkin) has win four series. The chance of having heads come up four times in a row is only one in 16, 6.25%. The probabilities of the 2012 playoff teams winning the ABL Championship under these conditions are shown in the table below.

Now let’s look at team strength: how to measure it, and how to use it to determine the probability of winning a game and a series. Bill James applied some statistics to the question of how to measure the probability of one team beating another in one game. He called it log5, and it uses winning percentage to measure team strength. I’ll use the ABL regular-season winning percentages for this exercise.

The log5 method works for one game, but what about a best-of-five or best-of-seven series? Well, there are formulas for that too. So now we can use these formulas to calculate the probabilities of teams reaching the finals. Three pages of scratch paper later…

Quite a spread, isn’t it?

One more series of calculations (and three more sheets of paper) gives the ultimate probabilities of teams getting their name on the hardware in 2012.

A superior winning percentage sure indicates a big advantage in the playoffs. Of course, this is simply a cold calculation based on only the playoff structure and the teams’ winning percentages. Among the factors this calculation does not take into account are:

  • Home-field advantage
  • Changes in team strength due to trades & injuries
  • Runs scored & runs allowed
  • Picther/batter match-ups
  • Strength of three-man rotations
  • Sticks
  • BFHes
  • Loaded dice
  • PEDs

All-HR & no-HR games

I was watching a Cardinals game the other day—can’t remember exactly which one—and after a few innings the only runs were off solo homers. I hate games like that. I don’t mind a few taters, but small ball is more fun. It got me wondering: How many games have all their runs knocked in by homers? And how many games have no home runs? I took a guess at both numbers. You have a guess. I’ll wait.

Ready? OK, continue reading.
Continue reading All-HR & no-HR games

ABL at the All Star Break: Pythagorean winning percentage

The Pythagorean winning percentage is a measure developed by Bill James to estimate a team’s winning percentage based on runs scored and runs against. (It was named after Pythagoras, the famed Greek Sabermatrician.)

At the half-way point of the ABL regular season, the Pythagorean winning percentages are listed below. (I used the 1.83 exponent used by Baseball Reference.) The results are sorted by Pythagorean wins, the number of wins expected based on the runs scored and runs against.


The difference between the actual wins and the Pythagorean wins is a measure of how “lucky” a team was. It indicates the teams that scored their runs in the situations that won games. And the teams that didn’t. Sorted by Pythagorean win difference, the table below shows the lucky teams at the top and the unlucky ones at the bottom.


Consecutive steals of second & third

This has come up twice this season. A runner steals second, then, with the same batter at the plate, the runner wants to steal third. The Commish sent out a clarificaiton on 2/13/2008:

Can you steal 2nd base and before the batter swings, steal 3rd base?

ANSWER: No. If the offense attempts a jump for a steal and fails or is successful, the offense must then swing away. The offense isn’t allowed to call a hit and run, bunt, pinch hit, pinch run, steal another base, or make any other moves until the next batter. The defense is also not allowed to make a move until the next batter.

And, yet, consecutive steals of second & third do occur with the same batter at the plate. Questions: 1) How often does it happen in MLB, and 2) could that sequence of events be incorporated into ABL/TPB?

Here’s the definition of the situation. A runner steals second, then, with the same batter at the plate, steals third or is caught stealing third. (I didn’t count straight pick-offs from second.) Per the Retrosheet event files, in 2007 that situation occured 40 times. There were a total of 2,542 steals of second, so the attempt for third occurred 1.6% of the time following a steal of second. The stat for the last five seasons taken together is also 1.6% (185/11,657). So, that answers question 1. Only about one time in every 60 does a runner who has stolen second attempt to steal third with the same batter at the plate.

Does this occur often enough to incorporate into the ABL? I’d say… maybe. It could be added by requiring an extra roll in trying to get the jump to steal third. For example, after the defense is given a chance to set, the offense states that he wants to steal third immediately. If the extra roll allows it, he can try for the jump in the normal way.

So, what should that extra roll be? Let’s assume that the runner would get a normal jump one-third of the time. If the runner always tried to steal third immediately, that would indicate that a 1-in-20 extra roll would produce an attempt once every 60 opportunities, which would reproduce the MLB stats. However, managers will not always try this risky sequence. How often would they try if it were allowed? Stealing seems very lopsided in the ABL (a few players steal all the time, everyone else never steals), so I’ll say 50%. So, if the extra roll requires a zero be rolled with a ten-sided die in order to try for the jump, the percentage of attempts will be: 1/2 manager choice * 1/10 extra roll * 1/3 gets the jump = 1/60, which would reproduce the MLB stat.

Average Errors per Game

The SOM basic fielding chart seems to produce a lot of errors, at least compared to TPB. Reality check: what’s the average number of errors per game in MLB? A quick Retrosheet hack gives the average over the years. It’s not a perfect count—multiple errors during one play are all counted as one.


Is the drop due to a change in fielding prowess or a change in official scoring? I reckon it’s the latter.

Deep Engine 2

More data from the Deep Engine. All results are based on ten million trials.

Here’s the results for all 30 parks from the TPB 2007 data:

     power:     5        4        3        2        1

   homerun:   48.55%   32.38%   19.18%    9.26%    3.11%
    caught:   47.55%   63.72%   76.92%   86.84%   92.99%
      foul:    3.90%    3.90%    3.90%    3.89%    3.90%

As expected, no significant changes from 2006.

I re-ran with the 12 2008 ABL parks, using the TPB 2007 data.

     power:     5        4        3        2        1

   homerun:   40.45%   24.74%   12.86%    5.28%    1.54%
    caught:   55.65%   71.36%   83.24%   90.82%   94.56%
      foul:    3.90%    3.90%    3.90%    3.89%    3.90%

Wow, there are some big parks in the 2008 ABL! It’s much harder to homer, especially for the light hitters who will find it almost twice as hard to hit them out in the ABL compared to the 30-park circuit.

Now let’s see how the numbers look for the different hitting types. Again, this is ten million trials in the 2008 ABL parks.

     power:     5        4        3        2        1
   homerun:   39.79%   24.05%   12.36%    5.01%    1.44%
    caught:   57.61%   73.34%   85.03%   92.38%   95.95%
      foul:    2.60%    2.61%    2.61%    2.60%    2.60%

     power:     5        4        3        2        1
   homerun:   39.96%   24.20%   12.48%    5.02%    1.46%
    caught:   57.44%   73.19%   84.91%   92.38%   95.94%
      foul:    2.60%    2.60%    2.61%    2.59%    2.60%

     power:     5        4        3        2        1
   homerun:   40.83%   25.34%   13.35%    5.72%    1.68%
    caught:   53.98%   69.47%   81.46%   89.09%   93.11%
      foul:    5.19%    5.19%    5.19%    5.19%    5.21%

     power:     5        4        3        2        1
   homerun:   41.23%   25.34%   13.21%    5.37%    1.58%
    caught:   53.55%   69.47%   81.58%   89.43%   93.23%
      foul:    5.21%    5.19%    5.21%    5.20%    5.19%

Not surprisingly, the pull hitters end up with more foul balls. In spite of that, they still end up with a greater probability of homering.

This data can be combined with the batter’s power & the average deeps to estimate the number of home runs a batter will get with Deep! rolls against an average pitcher. Actually, the difference in home-run potential is so similar among the hitting types, that it’s not worth making a distinction. So, for example, a power-5 hitter will homer on about 40% of his 18.7 deep rolls against the average pitcher, effectively giving him an additional 7.5 home-run range.

Combine this with the power distribution, and the probability of a home run on a Deep roll works out to 20.4%. That’s an important number for rating individual pitchers against the average batter.

average power

To assess deep ranges I need stats on the power ratings. The breakdown for the 212 franchise players:

power  #   pct
-----  --  ---
  5    60  28%
  4    50  24%
  3    33  16%
  2    33  16%
  1    36  17%

The average is 3.31 (3.29 vs L, 3.32 vs R). These numbers are likely inflated, as the franchise hitters surely have more power compared to the entire field, but the franchise players will get most of the PAs.

L/R averages

Another vital parameter: How often does a batter face a righty/lefty pitcher? From the 2007 ABL stats: 78.3% of innings pitched were by right-handers, 21.7% of the IPs were from lefties. I had guessed it would have been about a third lefties.

Another way to figure this is to figure the total splits for 2007 PAs at Baseball Reference. (NL, AL) Can figure the batting sides while we’re at it.

       TOTAL     NL       AL
       -----    -----    -----
RHP    72.6%    71.8%    73.4%
LHP    27.4%    28.2%    26.6%

RHB    58.9%    60.6%    56.9%
LHB    41.1%    39.4%    43.1%

Range Factor and range ratings

The Bill James Handbook lists Range Factor, which is the number of Successful Chances (Putouts plus Assists) times nine divided by the number of Defensive Innings Played. Does this statistic correlate with the TPB range ratings? I picked a couple of the more important defensive positions and compared the 2007 Range Factors for starters with the TPB range ratings from the 2007 TPB Statistics Book. Graphs for shortstops and center fielders are below.

Shortstops show a bit of correlation. It’s no surprise to me that Furcal & Vizquel are highly rated by both measurements. I’m surprised to see that Reyes has such a low Range Factor.

Center fielders are all over the place. Vernon Wells has a Superior TPB rating and the lowest Range Factor!

The red lines are the linear fits to the data. The graphs assume that the TPB ratings are linear, that is, that the difference between VG & SP is the same as between PR & WK. Whether or not that’s the intent, it’s clear that there’s no strong correlation between the Range Factor and the TPB range rating. That could mean that either 1) the two measurements are meant for different purposes, or 2) one or both of the measurements are inaccurate.

I don’t think #1 is likely. Surely each is trying to quantify the ability of a fielder to field balls that are hit in his general direction. Of course, measuring any kind of defensive ability is difficult. (See this discussion of various methods.) Whatever the case, it’s clear that the TPB ratings are not based on Range Factor.

Team selection for 2008 ABL expansion

At the ABL Winter Meetings on the 16th I needed to select a team to bring into the league. Going in, I figured it would be between Boston & Philly. Here’s how I decided.

Fifteen players can be selected, so I made up lists of nine position players (eight from each non-pitching position plus a “DH”), three starters, and three relievers. Minimum requirements for the ABL are 175 ABs (125 for catchers), 70 IPs for starters, and 30 IP for relievers.

I used OPS+ to rate the hitters. For pitchers I started with WHIP, then added some arbitrary factors to get something that roughly mirrors OPS+, that is, higher is better and average is 100. I came up with (2.25-WHIP)*110. (It’s listed as “WHIP+” in the tables below.) I weighted starters twice as much as relievers, based on innings pitched (six-inning starts). I then averaged the position players and pitchers separately to get team hitting and pitching ratings. The lists for Philly & Boston are shown below.


Of course, you choose the wrong guys here, and the method suffers. Notably absent are Beckett & Schilling, who are already in the ABL. Philly has no one in the ABL.

I did not consider fielding.

In addition to Boston & Philly, I ran the numbers for a few other teams to see how they compared. The graph below shows the results.


So Philly & Boston come out equal. That was no help at all!

So the decision was down to hitting vs. pitching. I chose hitting. Also, Philly looks to have a very balanced lineup, and Utley & Rollins are a superior middle infield. The biggest temtations of Boston were Papelbon & Okajima, both of whom have sick numbers. Big Papi & Ramirez are pretty good too!

Go Phillies! Go Perfectos!

Krazy striKeout Krap

From a Newsweek article about an upcoming jounal article by a couple of psychologists:

If the preference for people, places and things that share one of your initials is conscious, then it shouldn’t work if the thing you’re choosing is basically undesirable. Strikeouts are undesirable. Yet based on data from 1913 through 2006, for the 6,397 players with at least 100 plate appearances, “batters whose names began with K struck out at a higher rate (in 18.8% of their plate appearances) than the remaining batters (17.2%),” the researchers find. The reason, they suggest, is that players whose first or last name starts with K like their initial so much that “even Karl ‘Koley’ Kolseth would find a strikeout aversive, but he might find it a little less aversive than players who do not share his initials, and therefore he might avoid striking out less enthusiastically.” Granted, 18.8% vs. 17.2% is not a huge difference, but it was statistically significant—that is, not likely to be due to chance.


This comment on the Newsweek site sums up my feelings:

If you survey enough sets of numbers you get random patterns that don’t always come out even. For example, the information about batters is really incomplete. It isn’t sufficient to just compare K against everybody else. Look at the entire alphabet and you will probably see variations of one or two percent between the letters. They won’t all come out the same. Does Q do better than F? Does C do better than M? If so, what does that really mean? Why aren’t they comparing S for strikeout? And what about the name of the pitcher? If it counts for the batter, why doesn’t it also count for the pitcher? This is not a question that can even be really addressed in isolation from everything else.