(Key above for Men on Base - each of the three numbers
This matrix specifies the average run production in 2015 associated for each of the 24 possible situations that you can encounter in an inning. Zero out and no man on base is one such situation. Zero out and a man on first is another situation. Teams on average produced 0.48 runs per inning in the first situation, and teams on average have produced 0.84 runs per inning in the second situation. Thus, a lead-off walk or single is worth the difference, 0.36 runs (0.84-0.48). Still with no one on base, but with one out, a walk is worth (0.50-0.26) = 0.24 runs. And with bases loaded, a walk is worth one run: the run expectancy has not changed, since the situation is still the same (bases are still loaded, still two outs), but a run has scored. So you can calculate the value of a walk for all 24 situations. If you cross this matrix with another matrix that yields the frequency for each situation, you can calculate the value of each Strat event. So assuming that 25% of all plate appearances (PA) are with no out and no one on base, 16% of all PA with no one on base and one out, and barely 1% of all PA with bases loaded and two outs, you can calculate the average value of a walk by summing all cross-multiplications: (0.36 X 25% + 0.24 X 16% + (…) + 1.00 X 1%), which will give you the value of a walk: 0.33 runs. By playing with the run expectancy matrix, you can for example estimate the additional value of hitting a single** compared to a single* with, for example, a man on first and no out (it’s worth 0.23 run=1.67-1.44).
A word of caution:calculating outs using this method will yield very different values compared to outs as estimated in traditional linear weights formulas. In fact outs can have different values depending on whether you are calculating runs per se, runs above replacement level or runs above league average, so that's why their value change so much. Explaining why would take too long, so I’ll just say that what I did is to calculate the value of a strikeout (or of a lineout), adjust its value to make it equal to the value of strikeout as provided in the linear weights formulas that has a specific value for K, and adjust all the other outs accordingly by preserving the differences obtained in using the run expectancy matrix. Final note: there are ways to adjust the matrix for higher or lower scoring environment, so you could batch a set of matrix depending on the type of scoring environment you are interested. Also, I prefer to use a run expectancy matrix based on a 3-year period to insure more stability in the weight system.
So by using the run expectancy matrix and the frequency matrix, I could calculate the weights for each Strat event, in a typical 2012-2014 neutral environment from the latest version I have (2015 has not been incorporated). Here are the results:
Calculating the weights of gbB and gbC are kinda tricky, since the rules governing when the player scores from third base vary on a number of parameters, including whether defense plays in or not. But for the sake of this exercise, I assume that a runner on third never scores on a gbB and always score on a gbC.
As for clutch, a clutch single is worth 1.42 runs (on the positive or negative side, depending on whether an out or a hit is inverted), quite higher than the value of a “normal” single. But be careful to not multiply this value with the clutch chances: the horseshoe (Ω) (or $ for the on-line version) comes into play by inverting the result only in clutch situation, which happen roughly 12% of all at-bats. So the net of value of having a positive chance of clutch is 0.17. The same is true of pb/wp/bk---a pitcher having a pb-7 does not mean that he will allow 7*0.29 runs= 2 runs per 216 chances—it depends on the frequency of the event. But after you completed a season, if you know that Mr. X has allowed 7 passed balls, and then you could assume that this has roughly cost 2 runs to your team.
Of course, these weights are useful if you know, for any individual card, the chances for each event. If you are playing historic seasons, or the online version called ATG8, a rating file with over 4000 players can be downloaded on the diamonddope website which contains most of these ratings. I also believe that a script called “Grease monkey” provide some of these ratings online. Unfortunately, if you play 2015, these numbers are not easily accessible, since the SOM rating file doesn’t give them straight-forwardly. Of course, you can read the cards individually. There are also ways to tweak formulas to roughly estimate and sometimes deduce the chances of singles, doubles, even sometimes the combined chances of gbC and flyB on individual cards (to give an example, Soler vs rhp does have more than 3.7 chances of gbC/flyA/flyB combined). But the following formula is more general and can be used as a general sketch:
Offensive runs (based on 108 chances)=
0.17*H + 0.30*TB + 0.05*HR + BB/HBP*0.33 – 0.18*gbA – 0.11*K –0.04*gbC/flyA [if available] – 0.10* (all other outs) + 0.17*clutch + stadium adjustment for ballpark single + stadium adjustment for homeruns + “weak” adjustment + lefty/switch/righty adjustment
This formula is fairly close to the NERP formula, but it’s more precise and it handles clutch and gbA better. But whenever I have the chance, I use the weights for each event, particularly when it comes to evaluate defence, where you know by looking at the charts, the probability of getting gbA/gbB and gbC (or what SOM calls G1/G2/G3 in the super-advanced charts). Well the weights provided here stand for a typical 20XX season, it’s obvious that the same run expectancy matrix can be used in different environment (Coors Field, or at Forbes against all-time great pitchers).
As you probably all know, there are 108 chances on a Strat card, and these chances are usually responsible for 50% of the results from 216 plate appearances (PA)- or 216 rolls (pitchers’ cards and defensive-X chart make up for the rest). At this stage, it’s very tempting to just multiply by 3 (or some factor close to it), and assume that what you get is the offensive contribution a player for a full season or so.
Intuitively, this strategy makes perfect sense, but it’s wrong. Doing this is possible only if you take for granted that the number of rolls a full-time player will have over the course of a season is constant for everyone, other things like injuries being equal. In truth, the number of rolls will vary by two factors that are not equal among players: what on-base a player has, and what position slot this hitter holds in a line-up.
Let’s first discuss about the variation caused by on-base. Every team disposes of 162 games X 27 outs to win ball games. So what is constant is that every team will have 4374 outs or so at its disposal in a full season (give or take some for extra outs for overtime games and unnecessary 9th innings when you win at home). If team A has a .400 team on-base, and team B has a .300 on-base, both team will nevertheless finish the year with 4374 outs. However, team A will have many more PA than team B, which means owner A will roll the dices many more times than owner B until both teams reach 4374 outs. And since teams are made up of players, players with higher on-base are the one responsible for the extra value generated by rolling more dices.
Consider two players with the same run production as estimated by computing the 108 chances that are present on their cards—let’s say a slugger, Mr. Cespedes and an on-base machine, Mr. Vitto. So we are assuming that both Cespedes and Vitto are worth 30 runs (based on 108 chances, or 50% of 216 rolls). Even though they have the same offensive value after 216 rolls, we know that Vitto will generate fewer outs than Cespedes, since Vitto on-base is better by, say, 20 chances. If Vitto has 20 lesser outs per 216 chances, the team that employs Vitto will not reach 4374 outs at the same pace than the team that has Cespedes. In fact, if the Vitto team has an on-base of 0.350, it will take slightly more than 90 PA to reach 4374 outs compared to the very same team that has Cespedes instead. By plugging in league average value (assuming here a 80M league on the online game), the extra on-base that Vitto generates will give to his team almost 10 extra runs. If you don’t adjust for Vitto’s on-base, your seasonal run prediction will be underestimated by 1 full win. Of course, the full impact of this adjustment will depend on the type of league you are playing in, but you get the idea.
The other issue is lineup positioning. Players at the top of a lineup will always have more PAs than players at the bottom, simply because their chances to getting an extra at-bat is higher. Assuming that a full season represents 688 PA per player, we can expect the following PAs per batting order:
1 ... 752 (almost 10% more than the 5th slot)
2 ... 736
3 ... 720
4 ... 704
5 ... 688
6 ... 672
7 ... 656
8 ... 640
9 ... 624 (10% less than the 5th slot)
That being said, the number of PAs (or of rolls) is not the whole story with regards to lineup positioning. Common sense tells us that your most important hitters should hit in the 3rd or 4th holes because these positions have more important at-bats than any other positions, and this observation has been backed-up by sabermetrics. In other words, even though the 4th hitter has 50-60 fewer at-bats compared to a lead-off hitter, the importance of these at-bats make up for the fewer at-bats. In turn, a lead-off hitter has more at-bats than any other hitter with bases empty, and hitting with bases empty has less impact than hitting with men on base, which cause the weights to reduce a little bit. So even though lead-off hitters do have 10% more PA than someone hitting 5th, their true impact in turn of offensive run production is not as high, it’s more in the 5% range.
I should add that sabermetrics studies also showed that the 2nd role is as important as the 4th slot and might be even more important than 3rd. The lesson here is that, when evaluating offense, a premium of roughly 5-7% should be applied to any hitter that is likely to hit between the first and fourth holes of a lineup: without that adjustment, the run value based on a Strat card will not reflect the overall run production over the course of a season. A player whose card is estimated at 6.0 offensive WAR and likely to hit in the first four slots will really contribute to 6.4 WAR over the course of a season. Conversely, players expected to hit down in the lineup should have a lowering of their offensive contribution by up to 10% (up to 8% in non-dh leagues). Of course, the logic has to be applied separately vs. lefty and righty pitching.
I’ll admit, it’s a small adjustment, and some readers might not like the idea that a coaching decision impacts how we assess a player’s overall contribution. But even though the difference between 6.3 WAR and 6.0 WAR may look small, I believe it does have some impact when you evaluate which player to choose. Imagine for example that you are hesitating between a gold glove shortstop who is likely to hit down in the line-up and a silver bat ss who has an average glove. You do your homework, calculate the offensive, running, and defense run contribution of both strat cards, and you find out that it’s a wash, both are valued 6.0 WAR. In fact, the offensive player is the better choice---his usage in the top four slots of a lineup will drive his contribution over the gold glove.
The same logic applies the other way round when it comes to evaluate between two weaker players. For example, if you are hesitating between a gold glove ss with such a weak bat that his offensive contribution is negative (below replacement level) and a 3-rated ss who is likely to hit 6th or 7th, and if both have the same WAR based on the card evaluation, than the gold glove is likely to be the better choice because his usage at the bottom of a line-up will limit Between you and me, both decisions described here are commonsensical, and I think it’s a positive aspect of my rating system to reflect that common sense.
There are some limitations to my rating system with regards to calculating the offensive contribution: the weight I calculated assume that no outs are made on the basepaths (no out on base), which of course is not the case. With the "add baserunning decision" set on, this limitation affects all events except homeruns, so there is a case to provide more weight to homeruns, but I resisted to do it. Furthermore, I didn’t assign any value for bunting and hit-and-run. It’s obvious that players with weaker bats can upgrade their offensive contribution, especially with a hit-and-run rated B.
So the final yearly estimation for offensive run production will look like this:
Season offensive run estimation=
Offensive runs (based on 108 chances) * 3.1 + on-base adjustment + lineup positioning adjustment – league adjustment (to adjust for pitcher’s quality)
I won’t get into the details of how I calculate the value of running and defense, but I do integrate the most important statistics: I consider not only stolen bases and caught stealings, but also catcher’s arm, pitcher’s hold, catcher’s overall defense, the probability for a runner to be held at first and the ensuing consequences (turning double-plays into singles), runner’s speed combined with outfielder arms and of course both range and errors from defensive players. To calculate these values, I use the weights above when I can, but many of the formulas are derived from simulating seasons on the Window games.
I shall perhaps conclude with a few words on the concept of “replacement level”. In sabermetrics, the replacement level player is defined by the contribution of a typical player in a .350 team or so. In no-cap leagues (and most face-to-face leagues have no cap, you just go with your best players), I find that this definition roughly reflect the value of a team that has to pick after every other team has made their draft picks. For this reason, I consider that a player is a replacement player is typically the Xth+20% best ranked player of any position, X being the number of teams in your league. So in a 12-team league, I usually take the 15th best player at any position against each lhp and rhp (for more stability, I might average the value of 5-6 players, for example, the average value of the 12th to 17th best player combined). In 80M cap league, for the online game, I consider a player at 2.5M to be at the level of replacement.
The replacement level has two more functions. First, it serves
as the basis to determine whether a player will be considered by
my ratings as a platoon or an everyday player. If the value of a
player goes below the replacement level vs either lhp or rhp,
that replacement level is given to that player on his weaker
side, which is then added up to the value on his strong side.
Doing so neatly allows platoons to fit appropriately in a system
ranking and to have an appropriate estimated price tag in the
on-line version. Second, similarly to platoon players, the value
of missed games due to injuries is also replaced by the value of
the replacement level rather than by zero. This allows the
rating system to correctly attribute the value of injury-prone
players in no-cap league, where the quality level is much higher
than in leagues with money cap, and of players used in platoons.
Stay tuned to Part II of my article discussing my system to evaluate each pitcher who is available in the draft to prepare for your 20XX league in the next issue of this newsletter as I begin to prepare the Wolfman for his foray into the land of Baseball 365 and the 20XX leagues.Marc Pelletier
(NOTES from the Wolfman: As Marc wrote in the introduction, we will provide full examples and even player rankings based on WAR on the next edition of this article, next month, see you there!
We want to thank Marc for his willingness to explain in this article his system and strategies ....
Finally, if any members of our newsletter
would like to speak to Marc directly, you can reach him at his
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