Strat-O-Matic Baseball: Basic Closer Rule

One of the nice things about playing a sport simulation on the tabletop instead of a computer is the ability to “mod” things to your liking.

And while I like the Advanced and Super Advanced versions of Strat-O-Matic Baseball and completely understand people who don’t see why anybody would play otherwise, I tend to stick to Basic.

My reasons, really, are to expedite things.

I get the richer experience and additional levels of play – the lefty/right splits, the individual WP/PB/BK ratings, the N/W power ratings, the ballpark/weather effects, the clutch ratings, the separation of one generic fielding rating into separate range and error ratings, use of fielder arms, better managing of the stolen base game…

I could go on, but the fact is that I’d rather just be able to quickly put out a lineup without thinking of the lefty/righty matchup and ballpark effects. That takes one minute instead of three or four to think things over.

And I can roll out a game in 20 minutes instead of 30.

It’s enough for me to stick with Basic.

Although… there are a couple of things in the Advanced world of play that I really wish were a part of the Basic game.

And after years of playing, I’ve got a few easy tweaks that you might want to consider using in your next Basic replay.

The first of these is a basic version of the Closer Rule.

My simple method goes like this…

Basic Closer Rule
At the start of the game, I find which available pitcher (i.e. a pitcher who is not currently resting or injured) has the most Saves on the carded team. That pitcher, as well as any other available pitcher who has at least half as many Saves is designated as a potential closer for the team in this game. If any other non-closer is used in a save situation in the 9th inning, all X Chart readings come from the 5 column. In addition, change all error readings to hits. (Example: 1-base error is a single, single + 1-base error becomes a double, etc.)

For example, I’ve got the 2016 Chicago Cubs cards over here, so I’m going to go through their cards. Here are the carded Saves totals:

32 – Wade Davis
3 – Mike Montgomery
2 – Koji Uehara
1 – Justin Grimm

On most game days, Davis will be the only pitcher who is designated as a closer for the team. If any other reliever is on the mound in a save situation in the 9th inning, it’s as if Kyle Schwarber is playing every position on the diamond. (No offense, Kyle.)

Let’s say Davis is currently resting or injured, but every other pitcher in that list is available for the game. At this point, either Montgomery or Uehara is eligible to be used as closer. Montgomery because he’s the top Saves guy, with 3. Uehara because he has 2, which is at least half as many as Montgomery’s 3. Grimm is left out because he has 1 save, which is less than half of 3.

Grimm could sneak in there as an eligible closer, but only if Davis and Montgomery are both out. This is because he’d still have at least half as many saves (1) as Uehara (2).

I’m over-explaining it, but it’s a simple idea in that above paragraph.

I’ve enjoyed using this rule in my own replays as it’s both simple to implement and also helps keep you honest with how you use the players.

To reference Davis again, it would be tempting to play Basic and plan on using Adam Ottavino (2.43 ERA, 6 SV) or Scott Oberg (2.45 ERA, 0 SV) as the closer for the 2018 Rockies instead of Davis (4.13, 43 SV).

This method is going to force your hand a bit and use Ottavino and Oberg more as the setup-type pitchers they actually were.

Of course, it’s a game. So you can always feel free to throw this out the window and say “I’d like to see how the 2018 Rockies season would have played out if Ottavino was the closer” and just go with it. Have fun.

But for those looking to find a way to implement the Closer Rules in Basic play, I think you’ll find this approach works very well.

I have a couple of other Basic Add-Ons I’ll try to post on the page throughout the winter: Pitcher Fatigue; Weak Home Runs; and Pitcher Rest.


Strat-O-Matic Baseball: Basic Outfield Assists

I have my own game I developed and have been selling on the side. This is definitely cribbed from a chart I use in that game, but here’s one suggestion for crediting outfielder assists when a base-runner is thrown out on the bases in a Basic game of Strat-O-Matic Baseball.

If (like me) you’re a score-keeping fanatic, you may be dismayed to roll a SINGLE, try to score a runner from 2nd base, roll the d20 that results in the runner being thrown out at the plate and then have to decide who gets credit for the outfield assist.


Here’s a quick and dirty chart I use for my replays played with Basic Strat-O.

Roll Outfield Assist Chart
1 Runner thrown out by left fielder.
2 Runner thrown out by center fielder.
3 Runner thrown out by right fielder.
4 If left fielder’s fielding rating is better then center fielder, runner thrown out by left fielder; otherwise, center fielder.
5 If left fielder’s fielding rating is better then right fielder, runner thrown out by left fielder; otherwise, right fielder.
6 If center fielder’s fielding rating is better then right fielder, runner thrown out by center fielder; otherwise, right fielder.

If a runner is thrown out at home on a single, score it directly from the outfielder to the catcher. (Examples: 7-2, 8-2, or 9-2.)
If a runner is thrown out at 3rd on a single, score it directly from the outfielder to the third baseman. (Examples: 7-5, 8-5, or 9-5.)
If a runner is thrown out at home on a double, left fielders go 7-6-2 and right fielders go 9-4-2. If you credited the center fielder and your d6 roll was a 2, score it 8-3-2; if your d6 roll was a 4, score it 8-6-2; if your d6 roll was a 6, score it 8-4-2.

That’s all, folks!

APBA – Simple Fatigue Rules

I’m soon going to be embarking on a project full of all-time great teams, played out between my older brother and myself.

(He’s the one who first introduced me to APBA when I was a tyke, so this obsession is sort of his fault.)

We’ve been trying to lay down some simple, home-brewed rules for the tournament.

One of those governs pitcher fatigue.

Let’s face it, there’s no reason why a team with an A starting pitcher should ever remove them from a game, especially if nobody in their bullpen is better than an A.

Sure, there are Grade Advancement and Grade Reduction rules you could play with, but they don’t kick in all that often, especially for an A pitcher.

So here’s the rule we’ll be using.

Each pitcher is rated for throwing a certain number of innings before fatigue sets in.

For starting pitchers, you calculate this number by finding their statistics (in their starts only – use BaseballReference, Fangraphs or whatever…) and use the following formula:

Fatigue = Ceiling(.25 + (IP / GS))

If you are using players from an era before game logs are available, use the following formula instead:

Fatigue = Ceiling(.25 + (IP / (GS + (GR / 2))))

The .25 is sort of a “fudge factor” that accounts for things like pitching in games on the road where you may never get a chance to pitch the bottom of the 9th if your team loses. And the Ceiling (which basically means “always round up”) accounts for some other factors, like helping to ensure your pitcher could go the distance, even if he may not bother because he’s pitching in a blow-out, or gets pinch-hit for, or injured, or whatever…

Let’s use a few guys with December 15th birthdays for examples.

First, a guy from the modern era – Rick Helling.

In 1999, Helling had 35 starts and pitched 219.1 innings.

His fatigue would be a 7.

And then an older player – Mike Prendergast.

In 1915, he made 30 starts and pitched 228.2 innings in those starts.

His fatigue would be an 8.

(Say, by the way, that we didn’t have split stats available for Prendergast, who also made 12 relief appearances that season and totalled 253.2 innings. Using our alternate formula, he’d actually still end up as an 8.)

Now that you have that fatigue number, how do you use it?

Essentially, you just say that following that inning, they automatically go down a grade for each inning after that.

I have no idea what 1999 Helling’s grade is, but looking at his stats, let’s assume he was a C. He could pitch as a C for innings 1-7. But if he comes out for the 8th inning – even if he’s throwing a no-hitter – he’s down to a D.

An A pitcher who has a 6 fatigue is downgraded to a B to start the 7th, a C to start the 8th and a D to start the 9th.

This rule helps keep your starting pitchers in line, especially when playing with teams who come from modern eras where specialized relief pitchers are brought in and starting pitchers have their workloads shrunk in order to keep them firing massive strikeout rates in each game out.

Relief pitchers are a bit trickier to do, particularly since they often enter games mid-inning or are lifted for pinch-hitters as soon as their spot in a lineup comes up.

I don’t have a hard and fast calculation here, but in general you can do something similar to what I believe Strat-O-Matic does and sort all their relief appearances by innings pitched, go down 10% and use that number, rounded up.

It’s been a few years since I looked at that, but I think that’s how they do it. I’m in the ballpark, anyhow.

For example, Prendergast made 12 relief appearances in 1915.

We sort those 12 by innings pitched, and go down to the 2nd record – he pitched 3.2 innings in that game. I’d give him a 4* fatigue rating in relief, which means he would start getting downgraded after 4 innings.

For relievers, I’d also consider stiffer penalties – perhaps downgrading them one grade immediately after they’ve pitched their maximum number of innings and making them a D after the conclusion of an inning.

For example, Prendergast enters with 1 out in the 3rd inning. With 1 out in the 7th inning, he is downgraded one letter grade. But at the conclusion of the 7th inning, he’s an automatic D.

1901 APBA: New Board Strikeout Ratings

As an addendum to an earlier post, I understand that some folks wouldn’t be terribly keen on changing pitcher grades.

This is particularly true for those who think that pitchers can “pitch to the score” (despite evidence to the contrary) and therefore the pitcher win statistic is somehow meaningful.

Those folks believe a 20-10, 4.50 ERA pitcher who throws for a team that scores 5 runs per game deserves an A while a 15-10, 2.50 pitcher who throws for a team that scores 2 runs per game doesn’t.

Obviously you can figure out where I stand on that.

But I digress.

At the simplest, I’d recommend making the following changes to strikeout ratings for the 1901 APBA cards when bringing them over to the newest board version:

  • National League
    • Chesbro – add (Y)
    • Dinneen – add (Y)
    • T. Hughes – replace (Y) with (X)
    • Leever – add (Y)
    • Pittinger – add (Y)
    • Tannehill – add (Y)
    • Townsend – add (Y)
    • Waddell – replace (Y) with (X)
    • Willis – add (Y)
  • American League
    • Garvin – add (Y)
    • Patten – add (Y)
    • Young – add (Y)

This is to account for the fact that when the 1901 cards were issued, A pitchers earned about 1 strikeout per game because of PRN 9 rolls with the Bases Empty.

That’s no longer the case with the new boards and we need to find those strikeouts somewhere.

An A is roughly equivalent to a (Y) and an A(Y) is roughly equivalent to an (X).

Among pitchers who saw significant playing time, the cards as issued had 2 A(Y), 6 A without a (Y), and 4 non-A (Y) pitchers in the NL. That boiled down to needing to find a place to assign 2 (X) and 10 (Y) ratings.

Keeping their (Y) were W. Donovan, Hahn, Mathewson and White.

You may notice one additional (Y) in there and that’s Townsend, who had decent strikeout rates but is the #5 starter for the Phillies. He’s not likely to get a whole lot of appearances and throwing him a (Y) seems acceptable here.

Over in the AL, there was 1 A&C and 2 A pitchers with no (Y) ratings. So we basically needed to find place for 3 (Y) ratings.

That was easy enough as we distributed them out to the 3 pitchers with the best strikeout rates – Garvin, Young and Patten.

1901 APBA Baseball: Re-Grade

I’ve dove back into a replay of the 1901 season using APBA Baseball.

I have a long, horrible history with this project.

I tried to do it once and quickly found something was amiss with the cards.

For example, of the 32 pitchers who are members of the 4-man rotations in the National League, 29 have a (Z) and 1 has a (W).

How can 29 of them have a (Z)?

Only 6 of the 32 NL starting pitchers have a (Y), while none of the 32 American League pitchers have a strikeout rating.

I entered every result of every card into a spreadsheet, weighting them by their plate appearances that season and I couldn’t find any way that strikeout totals would come anywhere close to historically accurate.

So I set off on an adventure of re-grading and re-rating every card from that set based on an elaborate set of equations using the card data.

However, it was only recently that a thought occurred to me.

I’d been trying to play these cards with the latest set of boards.

The 1901 set was issued in 1988, before things like (ZZ), (K) or (R) ratings had been issued.

And, more to the point, when this set was published, the board included Strikeout readings for some pitchers on those hits that get taken away due to being an A or B pitcher.

Oh dear…

So, for example, my concern about a guy like Christy Mathewson not being able to come anywhere near his real-life strikeout rates with only a (Y) on his card were somewhat unfounded. After all, by my math, that’s good for maybe one extra strikeout per game.

But giving him a Strikeout with the Bases Empty when a batter rolls up a Play Result Number of 9? That’s good for another additional strikeout per game.

So now I realize that him being an A with a (Y) was actually good for about 2 extra strikeouts per game over a pitcher who was neither an A nor a (Y).

Given the National League average that year was 3.8 strikeouts per 9 innings and Matty whiffed 5.9 per 9 innings – a difference of 2.1 – that suddenly seemed pretty valid.

In short, I started replaying the season by “retro-fitting” my current boards so that they more closely resemble the boards at the time that the 1901 card set was first released.

(You can find PDF files online that document the history of APBA board changes to accomplish this.)

And, as low-fidelity as APBA can be, I’ve been enjoying it so far. I’ve rolled about 35 games and it’s been fun.

However, there are a few things that have still been bothering me.

Guys like Rube Waddell (6.2 SO/9) and Tom Hughes (6.6 SO/9) had higher strikeout ratings than Mathewson that season, but they are both B(Y)(Z) pitchers.

As B pitchers, they don’t get the benefit of strikeouts on a PRN of 9 with the Bases Empty, so even though their strikeout rates were noticeably higher that that of Mathewson, they will actually strikeout fewer batters than him.

My obsessive compulsive tendencies over these games started to kick in.

As I have been rolling these games and comparing my sim rates to historical rates, they’re really not all that far off.

So I know that as a whole there are probably a fairly correct number of (Y), (Z) and (W) ratings out there.

But where I’d still find a point of contention is how they are distributed.

So I got to work.

I plugged every carded pitcher into a spreadsheet, calculating how many total batters faced are given to each grade and each rating.

For the purpose of bringing these ratings over to the modern board, an A pitcher was the equivalent of a (Y). An A(Y) was the equivalent of an (X).

Doing this, I came up with the National League having 2,851 Batters Faced allocated to an (X) – this was contributed by Mathewson and “Wild Bill” Donovan, each of whom are A(Y) pitchers in the original set. 11,784 Batters Faced belong to (Y) pitchers.

Then I re-distributed everything.

By a point of example, I sorted all carded pitchers by strikeout rate (strikeouts per batters faced). I started giving out (X) ratings until I had given them out to 2,851 totals Batters Faced. Then I gave out (Y) ratings until I had given out some type of rating to a total of 14,635 Batters Faced – this is 2,851 plus 11,784 from above.

So what I did was just try and ensure that the chances of a plate appearance being affected by a pitcher grade, strikeout rating or control rating were no different than before.

All I did was move things around.

One other note about this – the re-distribution didn’t penalize pitchers with small sample sizes. Much like the newly issued sets of cards from the APBA Game Company, these formulas are assuming that you will use pitchers close to their historical usage. So a pitcher could get an A even if he only made one appearance. It’s expected that the re-player won’t cheat the system and use this guy as a regular member of the rotation.

Okay, that’s the backdrop. What changed?

Well, surprisingly little. I’ll call some things out alphabetically as I go through the list.

Name Old New Notes
Jack Chesbro A(Z) A(Y)(Z) A touch above league average in K/9
Roger Denzer D(Z) B(Z) Close to league average ERA in 62 IP
Bill Dinneen B(Z) B(Y)(Z) A touch above league average in K/9
Ed Doheny C(Z) B(Z) Close to league average ERA in 150 IP
Jack Harper B(Z) C(Z) ERA was 29th out of 34 qualifying pitchers
Tom Hughes B(Y)(Z) B(X)(Z) Led league with 6.6 SO/9
Brickyard Kennedy D(Z) B(Z) Nice 110 ERA+ in 85 IP
Bob Lawson D(W) B(W) 110 ERA+ in 46 IP
Sam Leever C(Z) B(Y)(Z) Finished 10th in ERA and 9th in SO/9 but had just 20 GS
Gene McCann D B Right around league average ERA but just 34 IP
Mike O’Neill D(Z) A(Z) 1.32 ERA in 41 IP
Togie Pittinger B(Z) B(Y)(Z) A touch above league average in K/9
Ed Poole D C Only 80 IP, but really only slightly below average in ERA
Jack Powell B(Z) D(Z) ERA was 26th out of 34 qualifying pitchers
Jesse Tannehill A(Z) A(Y)(Z) A touch above league average in K/9
Happy Townsend C C(Y) A touch above league average in K/9
George Van Haltren D(W) A(W) 3.00 ERA in 6 IP
Rube Waddell B(Y)(Z) B(X)(Z) 6.2 SO/9 was 2nd best in NL
Vic Willis A(Z) A(Y)(Z) Above league-average strikeout rate

Now, how about the AL, where we originally had 1 A&C, 2 A and no strikeout ratings?

Remember from above that I am converting this to the equivalent of 3 full-time (Y) pitchers.

Name Old New Notes
Bill Bernhard C(Z) D(Z) 17 Wins but ERA was 32nd out of 34 qualifying pitchers
Pete Dowling C D ERA was 28th out of 34 qualifying pitchers. On the cusp here.
Jack Dunn D B ERA was just better league average but only 60 IP
Chick Fraser B C Another downgrade for Philly. ERA worse than league average.
Ned Garvin B B(Y) League-best strikeout rate deserves one of the (Y) ratings
Clark Griffith A(Z) B(Z) 4th-best ERA in the league, but if we’re only giving out 3 As or better…
Bill Hart D C 3.77 ERA was only 0.08 worse than league average.
Zaza Harvey D B ERA was a little better than league average in 92 IP
Ed High D(Z) B(Z) 3.50 ERA is better than average. 18 IP.
Watty Lee C(Z) D(Z) ERA was 31st out of 34 qualifying pitchers
Ted Lewis B(Z) C(Z) ERA a touch better than league average, but no world-beater
Jack McAleese D D(Z) Walked 1 of 17 batters he faced.
Harry McNeal D D(Z) BB rate in line with other full-time pitchers who have a Z
Fred Mitchell D C In 109 IP, his ERA was barely worse than league average
Jerry Nops D(Z) C(Z) ERA was 26th out of 34 qualifying pitchers
Frank Owen D C ERA not great, but not bad enough for a D
Casey Patten C C(Y)(Z) 3rd best strikeout rate in the AL deserves one of the Y ratings
Wiley Piatt D C ERA was 27th out of 34 qualifying pitchers
George Prentiss D A(W) 1.80 ERA and 5.4 BB/9 in just 10 IP
Bill Reidy C(Z) D(Z) ERA was 29th out of 34 qualifying pitchers
Crazy Schmit D(W) A(W) 1.99 ERA in just 23 IP
John Skopec D(W) B(W) 111 ERA+ in 68 IP
Tully Sparks C B ERA was 13th out of 34 qualifying pitchers
Snake Wiltse C(Z) B(Z) ERA just a touch better than league average
Joe Yeager B(Z) A(Z) 3rd best ERA in the league makes him deserving of one of the 2 A grades
Cy Young A&C(Z) A&C(Y)(Z) Led league in ERA and was a very close 2nd in strikeout rate

So I hope some folks find that interesting.

Honestly, I’m this far into my replay already that I will probably just stick with things as they are.

But as I get into this a little further, I’ll be interested to see a few things in particular from the top 4 pitchers on each staff:

  • Tom Hughes and Rube Waddell should easily simulate to be the top 2 strikeout rates in the National League. But with B(Y) readings as-carded, will they even make the top 5?
  • How badly will Jack Harper and Jack Powell over-perform? Because they sure don’t seem to warrant B grades.
  • How badly will Sam Leever under-perform?
  • Will the top 3 strikeout leaders in the American League resemble real life or will the 3 A pitchers dominate it despite two of them ranking 14th and 16th that season?

Been a While

Just checking in with an update.

Been laying a bit lower as of late, though I have been plenty busy in the hobby.

Here are all the projects I am currently logging time on…

  • 1984 MLB
    • A 64-game replay using all 26 teams, played with Strat-O-Matic Cards & Dice. I started this towards the beginning of 2016 and it is nearing completion. I’ve rolled 774 of the 832 games in the regular season schedule, which is good for 93% of the project. Hoped to get it done by year’s end and that won’t happen, but it’s still good progress.
  • 1901 MLB
    • A full season replay using APBA Cards & Dice. This is early going, but I still re-visit it from time to time.
  • 2004 NFL
    • A full season replay using Strat-O-Matic Cards & Dice. Just started this this fall and, gotta’ say, pleasantly surprised. Thought it would take too long to roll games and I’d lose interest, but the opposite has happened. I’m half-way through Week 2 of the season and sometimes would rather roll these games than the 1984 MLB project, but I don’t want to flake on that thing. It’s so close to wrapping up, that I just have to hammer away.
  • 1966 NFL
    • A team replay of the Green Bay Packers using Strat-O-Matic PC. I’m off to a 3-0 start with one amazing come-from-behind victory in there. Enjoying it.
  • 1997-98 NBA
    • A replay of the postseason using Strat-O-Matic Cards & Dice. Haven’t played this since last winter and need to get back into it. So far I had played 2 games for each team in the postseason.
  • 2012-13 NHL
    • A full season replay using Strat-O-Matic Cards & Dice. This is going way too slow. Again, other projects seem to get in the way, but I really enjoy Strat Hockey.

And this doesn’t include other projects I intend to be running right now…  I’d like to get another team replay using Diamond Mind Baseball going. I’d like to get a team replay using Strat-O-Matic Basketball for PC going. I’ve got some other things that I’ve been play-testing that I’d like to dive into more.

There’s just not enough time to get to it all.

I may be stretching myself a bit thin with all of these projects!

Hope everybody is finding time for everything.

Strat-O-Matic Baseball: Basic Hit By Pitch

This came up on the Strat Fan Forums recently, so I thought I’d dive into it.

The question came from a forum user (and I’m paraphrasing here) – How do I incorporate Hit By Pitch into the Basic version of the game?

For those who don’t know, Strat-O-Matic Baseball cards have two sides – one for use if playing the Basic version of the game, and a flip side if playing either the Advanced or Super Advanced versions.

One quirk about the Basic side is that it gives no chances for a batter to be hit by a pitch.

I’ve never quite understood why that was left out. My hunch was that, when the game was first being created, HBP stats were not readily available and so they were simply left out of the game. When the Advanced version of the game was created, however, that HBP data was available and so it was added at that point. However, re-doing the formulas to “retrofit” the Basic sides of cards wasn’t worth the effort, so it continued to be left out.

Again, that is all just a hunch. I don’t work for the game company and that’s pure conjecture. I still maintain it would be really easy to start adding it to the Basic side of the batter cards and really wish they would, but given that it really only affects a handful of batters in a typical season, I can see where it wouldn’t be high on the company’s priority list. Particularly when fewer and fewer folks play the cards and dice version of the game.

In short, there’s no really easy way to convert the Basic side over to allow for chances of being hit by a pitch.

All the formulas to calculate chances on the Basic side of the card discount Plate Appearances in which the batter was hit by a pitch.

When you calculate how many chances at a Walk the Basic side of the card will have, for example, you are going to use unintentional walks as the numerator of your Walk rate, and the denominator will factor things in like total plate appearances but it will not include intentional walks and it will also not include times hit by a pitch.

That right there is the crucial point to make. Because if you now want to include chances for being hit by a pitch, you’d need to re-calculate everything else on the Basic side of the card – WALK, STRIKEOUT, SINGLE, DOUBLE, TRIPLE, HOMERUN, GB() A.

If you convert some WALK readings to HIT BY PITCH, that’s not really accomplishing anything. You’re not correcting the high-HBP guy who’s getting short-changed on his OBP as it is. You’re only changing how he got to first, not improving his chances.

And if you add some new HIT BY PITCH chances to the Basic side of his card, you’re throwing off how accurate the player’s Batting Average will be.

The only way that you can really pull it off, then, is to do a roll before the plate appearance.  In other words, roll first to see if the batter is hit by a pitch and, if he isn’t, resolve the plate appearance as you normally would.

If you ask me, it’s freaking tedious. Believe me. I tried it. Then I came to realize “What am I doing? The whole point of playing Basic was to try to speed games along? This isn’t doing that!!!”

If you’re interested, however, the trick I used was basically this…  (And you could use a spreadsheet to really speed this along and get all the numbers for any particular season in less than a minute.)

Take the player’s Plate Appearances (PA) and their times Hit By Pitch (HBP).  Use 400 * HBP / PA to get their “HBP Chance”.

Before each plate appearance, roll d20. If the roll is a 1, that means the batter might have gotten hit by the pitch. Roll d20 again and if the roll is less than or equal to that number you got above, they were hit by a pitch.

You might recognize this as being pretty similar to the way Wild Pitches, Balks and Passed Balls are implemented in the Advanced versions of the game.  So if rolling a 1 to advance to the check seems confusing, then change it to a 20. Whatever makes sense for you.

So let’s take 1966 Orlando Cepeda, for example. He had 563 PA and had 14 HBP. Using 400 * 14 / 563 gets you 9.95, so he would draw a HBP on a roll of 1-10.

1966 Carl Yastrzemski, however, had 1 HBP in 680 PA, so 400 * 1 / 680 is 0.59, meaning he gets hit only on a roll of 1.

If you’re into marking your cards, you could always pencil this in on the Basic side of the card.

Anyhow, it will give you the accuracy you’re looking for. It’s a lot more accurate than looking at the HBP chances from the Advanced side of the card and then converting over some of the Basic readings to add in HBP.

Happy New Year.