Sports Simulation Board Games

Plugging in Delta and Sigma Ratings for HMB

One of the features of the new HMB 4.0 game book is the optional “sigma rating.” It works just like the “delta” rating, except that it’s associated with doubles rather than singles. What this means is that you can reduce a player’s likelihood of hitting a double by giving him an alternate result when the sigma symbol occurs. But, exactly how would you incorporate this into your tabletop baseball adventures? Or, for that matter, the delta rating? Let’s “discuss amongst ourselves”…

First, let me mention here that I recently updated to the How-To Guide to include a little more information on batting power. Based on the number of e-mail queries I got on this topic, I felt like I had been remiss in the how-to explanation and some additional illumination was necessary! So I added a couple paragraphs about how the delta and sigma ratings work. I also added an "expected production" table to give you an idea of how each combination of qualities might be expected to perform over a typical season, about 600 at-bats. (NOTE that we use "at-bats" instead of plate appearances, because that's what's typically on the back of a baseball trading card.)

For discussion purposes, here’s the approximate production you can expect from each of the above combinations of batting power qualities, over approximately 600 at-bats. You can use these distributions to help you make decisions in rating players who are on the fringes of one category or another…

HR 2B power qualities
40 18 HR KING
10 24 no designation

At the end of this section of the "How-To", is this sentence: “You can adjust any player's statistics by using a “delta rating” or “sigma rating," explained later.” So, here’s the “later” explanation…

“To help account for player batting performances that are outside the normal distribution of results and hence aren't captured entirely accurately by the standard HMB qualities, we've incorporated a couple of special ratings symbols, “delta” and “sigma.”

“Both ratings are activated by certain results from the game’s main and mini-charts, and are indicated by a delta ( Δ ) or sigma ( Σ )symbol after the reading. When they occur, you substitute a player's delta or sigma rating result for the printed result. Delta ratings are associated with singles, sigma ratings with doubles. A full-time starter can expect to have an opportunity to use a delta and/or sigma rating approximately ten times each per season.

“Thus, any statistic that you'd like to increase by ten more occurrences, you can call for with a delta or sigma rating. The delta rating result will replace singles, the sigma rating result will replace doubles. The new result can be most anything—doubles (delta rating only; a sigma result is already a double!), triples, home runs, stolen bases, hit by pitch, walk, strikeout, or whatever. For example, a light-hitting infielder might get a single for a sigma rating; a long ball hitter might be given a sigma rating of a home run. Similarly, a “doubles hitter” can have his doubles production increased with a delta rating that calls for a double.

“You can use the POWER section of this guide to help you make these decisions. For example, a SLUGGER is projected to hit around 30 home runs and 36 doubles over 600 at-bats. If you give a SLUGGER a sigma rating for home runs, ten of those doubles would be converted to home runs—he would be now be projected to hit around 40 home runs and 26 doubles. However, If you gave him a delta rating for home runs, he would convert singles to home runs, and would be projected to hit 36 doubles and 40 home runs.

“Similarly, a SCRAPPER is projected to hit 3 home runs and 24 doubles in 600 at bats. By giving a SCRAPPER a sigma rating for singles, his doubles production will be reduced to around 14. By giving him a delta rating for triples instead, his doubles production will remain around 24, but he’ll now hit around a dozen triples, converted from singles. His home run production will be unaffected.

“There are other possibilities, too. For example, an injury-prone player might be given an injury result as a delta rating. A player who is frequently hit by pitches—say, more than fifteen times per season—could be given a delta rating for HBP. A notably poor baserunner could be given a sigma rating that calls for him to be thrown out trying for third on a decider die “bullet.” We designed these ratings to be open-ended and flexible for many potential uses. Feel free to use your imagination!”

OK, so that’s what’s now in the “How-To” guide. Let me emphasize that both the delta and sigma ratings were created in such a way that they can be used extensively, minimally, anywhere in between, or not at all. Using them or failing to use them is not going to make or break anybody’s game experience. It’s just an added bit of “chrome” that you can use as desired. I foresee many gamers choosing to treat the sigma the same way as they’ve been treating the delta rating, as something they could use but don’t. And that’s perfectly fine: it’s how I want it to be. But if you’re a gamer who wants to sharpen your player definition a bit more, especially that of the star players who strongly outperform the rest in certain statistical categories, the delta and sigma ratings can help you do that.

SO, if you’d like to get your feet wet with these ratings, how/where do you start? Here are a few ideas…

• LOW SLUGGING PERCENTAGE BATTERS: In virtually every case batters with slugging percentages below .250 can confidently be given sigma ratings for singles. Many batters with slugging percentages hovering around .300 are also usually good candidates. That is to say, when these batters get a result from the 4-4-5 PITCHER or 5-5-6 FIELDER column, the double result is changed to a single. This would include most batting pitchers. As a general rule, you could say that any batting pitcher who has the SCRAPPER quality also has a sigma rating for a single. A pitcher who is SAD SACK, UTILITY, SCRAPPER and WHIFFER could be given a sigma rating for a strikeout.

• LEAGUE LEADERS IN DOUBLES, TRIPLES, HIT BY PITCH: You can go online to any of a number of resources and get “leaderboards” for doubles, triples and many other stats. Usually, a delta rating is going to be used for these extra extra base hits. Generally speaking, if a normal batter accumulated more than 40 doubles, or a SLUGGER batter more than 50, he could be given a delta rating for doubles. You don’t have to examine every batter from every team, just look at the leaders—it can provide a nice splash of additional depth to your results without taking much time at all.

Regarding triples and HPB results, the base HMB game treats all batters equally in these areas. (As a point of reference, both triples and HBP results typically account for less than 1% of a batter’s overall production, which is why we chose not to rate players in these categories.) But the delta and sigma ratings can add some distinction/definition if you want it. In HMB, the average batter will hit a few triples per season. Some will hit 1 or 2, others will hit 4 or 5, most will hit 2 or 3. If you want a batter to generate more than 10 triples in a season, he can be given a delta for triples. For HBP, the game is set up so that any given batter will get hit by a pitch about 4 or 5 times in 600 at bats. If you want a player to be HBP more than that, say, a dozen times in a season, he can be given a delta rating for HBP.

NOTE that you can be creative in assigning these ratings. For example, when creating the 2015 “trading cards,” I noticed that Pittsburgh’s Josh Harrison had somewhat elevated totals for BOTH doubles (38) and triples (7), while really not high enough in either category to warrant a delta rating. So, I gave him a delta rating for double/triple, meaning that when the delta result happens for Harrison, I roll the decider die: “bullet,” triple; “blank” double.

• VERY FAST, LIGHT-HITTING BATTERS: In a few cases, a sigma rating for triples is appropriate. Consider Jerry Remy of the ’77 Angels, for example. In 575 at bats, Remy had 19 doubles and 10 triples (along with 41 stolen bases). The SCRAPPER profile (in which Remy is classified) can be expected to produce a couple dozen doubles and a couple of triples. By giving him a sigma rating for triples, 9 or 10 of Remy’s doubles would be extended to triples, changing his rough projections to around a dozen of each. Again, these are the “bulls eye” of the targets—remember, the game is designed so that not everyone will hit the bulls eye, with or without the delta/sigma ratings.

• INJURY PRONE PLAYERS: Both the delta and sigma ratings will come up about every 15th game for each batter. That is to say, in fifteen games you can expect that a batter will see one delta and one sigma symbol attached to an at-bat. If you want to re-create a player’s propensity to get hurt, you could associate an injury with one of these symbols, and have the player roll on the Game Day Extras injury table when it comes up. If an injury possibility every fifteen games seems like too much, you could make it hinge on a decider die roll: then the player would be injured every 30 games. A “double decider die roll” (i.e., needing to roll two consecutive bullets instead of just one) would reduce the injury chance to about every 60 games.

• EXTREME HOME RUN KINGS: In 1964, Harmon Killebrew hit 49 home runs, and just 11 doubles—on our card, we give him the HR KING and SLUGGER• qualities, which would project to about 50 home runs and 24 doubles. From a “big picture” standpoint, I’m perfectly OK with that because for virtually every season before and after that, Killebrew fit that profile very neatly and who’s to say he wouldn’t have performed similarly in a second ’64 go-round. However, if you want to re-create Killebrew’s specific ’64 performance, the sigma rating will allow you to aim more closely for it. Just give him a sigma rating for singles, and his projected doubles total will be reduced from 24 to 14. Pretty slick, huh?!

Incidentally, this last example touches on the reason why we DON’T include the delta and sigma ratings on the cards themselves or make them a fixed part of the game. The “vision” of HMB is to offer a “blue sky” perspective of a given season—real or fictional—emphasizing possibilities rather than percentages. At the same time, I recognize that the paradigm of our hobby is precise statistical re-creations of historical seasons. The delta and sigma ratings are offered as a “bridge” between the “vision” and the paradigm.

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