What to root for

by BaseballHQ.com on May 20, 2010 @ 09:00:00 PDT

 


Note: This article has been edited with a more current player example.

Let's say San Diego Padres first baseman Adrian Gonzalez went 3-for-5 at the plate with two HR and five RBI.

If you have Gonzalez on your Rotisserie team, you had to be pleased with his performance that day. But just how pleased should you be? How much will his stats in that game actually help your team at the end of the season? Would you rather have had Gonzalez's big game, or a starter's outing on the same day, in which he earned the win, pitching nine innings while allowing just six hits, two walks, and one earned run?

While it is almost always obvious whether a player has helped or hurt your team on a given day, you may not be aware of just how much he has helped or hurt. Being able to relate a player's performance in a single game, or even a single at bat, to its impact on your league's final standings is beneficial for at least two reasons.

First, if you can accurately assess the ultimate impact of short-term player performance, you can make better roster management decisions. For example, if you are trying to decide whether to replace a catcher who has gone on the 15-day DL or whether to reserve a pitcher for his upcoming start in Colorado, it may help to understand just how much the anticipated incremental stats will help or hurt your team. If your league charges transactions fees, you may want to establish a threshold return on each dollar you spend to ensure that you are getting enough value for your money.

Second, knowing just how your players' individual at bats and innings pitched are affecting your Roto team can enhance the fun, or at least the appreciation, of watching your players come up to bat and pitch every day during the season.

Fortunately, the SGP equations used by BaseballHQ.com to produce player dollar values can also be employed to calculate the marginal impact of each Rotisserie-relevant statistic that a player generates. For instance, we can apply the 2003 NL SGP equations to compute the standings gain points generated by each of Gonzalez's stats:

HR SGP = HR / 9.3 = 2 / 9.3 = 0.215

RBI SGP = RBI / 30.5 = 5 / 30.5 = 0.164

SB SGP = SB / 8.1 = 0 / 8.1 = 0

BA SGP = (((1614 + Hits) / (6000 + AB)) - 0.269) / 0.0021

 = ((1617 / 6005) - 0.269) / 0.0021 = 0.000276 / 0.0021 = 0.131

In other words, since teams in standard NL Roto leagues are separated on average by 9.3 HR in the HR category at year's end, Gonzalez's two HR would be worth 0.215 points in the typical league standings. Likewise, his five RBI would gain his Roto team 0.164 points in that category in a typical league. Since he did not steal a base, he had no effect on the SB category.

For computing the impact of Gonzalez's 3-for-5 performance on team BA, the concept is similar, but the formula is more complicated. Essentially, this formula says that Gonzalez's three hits in five at bats would raise the BA of a typical team from .269000 to .269276. Since teams are separated on average by .0021 in BA, Gonzalez's performance would add 0.131 points in the BA category.

In total then, Gonzalez's performance was worth 0.215 + 0.164 + 0.131 = 0.510 SGP.

(Those interested in the details of the equations will notice that the formula for BA presented here differs slightly from the standard one used. The standard formula measures the marginal effect of a player's entire season and is therefore based on a team's AB before it acquires its last hitter. The formula here measures the marginal effect of only a few AB and is hence based on a team's AB including all hitters.)

We can perform a similar calculation to assess the impact of the pitching performance:

 W SGP = W / 3.5 = 1 / 3.5 = 0.286

 Sv SGP = Sv / 5.8 = 0 / 5.8 = 0

 ERA SGP = (3.95 - ((585.04 + ER) / ((1333 + IP) / 9))) / 0.090

 = (3.95 - (586.04 / (1342 / 9))) / 0.090

 = (3.95 - 3.9302) / 0.090 = 0.220

 WHIP SGP = (1.34 - ((1786.22 + H + BB) / (1333 + IP))) / 0.016

 = (1.34 - (1794.22 / 1342)) / 0.016

 = (1.34 - 1.33698) / 0.016 = 0.189

The pitcher's performance produced 0.286 + 0.220 + 0.189 = 0.695 SGP, so his day was somewhat more valuable to the typical Roto team than Gonzalez's.

For cumulative categories, like HR and W, the translation from statistics to SGP is straightforward. Since 3.5 wins typically equate to one point in the standings, one win equates to 1/3.5 or 0.286 SGP.

For rate-of-performance categories, like BA and ERA, the relationship is less straightforward but not too difficult to unravel. For example, the average NL Rotisserie team compiles 6,000 AB over the course of a season, generating 1,614 hits and a BA of .269.

Teams are typically separated in the BA category by .0021. Over 6,000 AB, this .0021 difference in BA equates to 12.6 hits. So, a player who outperforms the average of .269 by 12.6 hits moves his team up one point in the standings; a player who outperforms by one hit moves his team up by 1/12.6 = 0.079 SGP.

At the level of a single AB, if a hitter could get 0.269 hits, his AB would have no effect on his team. Of course, 0.269 hits is not a possible outcome; the only possible outcomes for a single AB, as far as BA is concerned, are zero hits or one hit.

If a hitter goes hitless in an AB, he has underperformed by 0.269 hits. At the end of the season, this shortfall of 0.269 hits can be expected to cost his team 0.269/12.6 = 0.021 SGP. Conversely, if the hitter gets a hit, he has outperformed by 1 - 0.269 = 0.731 hits. That additional fractional hit can be expected to boost his team by 0.731/12.6 = 0.058 SGP.

Following similar reasoning for ERA and WHIP, we can deduce that one additional earned run loses 0.075 SGP, while one-third IP without an earned run gains 0.011 SGP. One additional hit or walk costs 0.047 SGP, while one-third IP without a hit or walk adds 0.021 SGP.

These equations can be applied to any time period from a single play to a few weeks to evaluate ultimate standings impact. One interesting application is to answer that old Rotisserie quandary: when your pitcher is facing your hitter, what outcome should you root for? The answer is surprisingly complicated, and it depends on the specific situation and the eventual consequences of the plate appearance.

An out (without an RBI) is a positive event for your team. It costs you 0.021 SGP in BA, but the one-third IP without an earned run or baserunner is worth a total of 0.032 SGP.

On the other hand, a single (without a run scored) is initially an equally positive event, producing 0.058 SGP in BA, while costing 0.047 SGP in WHIP. The single, however, carries risk of further negative consequences for your pitcher in the form of earned runs or missing a win or save. Therefore, except in unusual circumstances, you should prefer an out to a base hit.

If the batter's single drives in an earned run for your pitcher, that only makes matters worse. An earned run costs your team more than twice as much as an RBI benefits it (0.075 vs. 0.033 SGP). Of course, if the run is unearned, the RBI becomes a net positive for your team, although you would still have to weigh that benefit against any risk that the run costs your pitcher a win or save.

A solo HR becomes a net positive for your team, even if the run is earned. The combined gain in HR, RBI, and BA is 0.198 SGP, while the loss in ERA and WHIP is 0.122 points. Again, though, if the run jeopardizes a win or save for your pitcher, then you may still want to root against the HR.

Keep the following caveat in mind when applying these formulas to calculate SGP: The formulas are based on the typical team in the typical league. They provide a useful measure, especially early in the season. But as your season unfolds, they may become less accurate for your team's situation. To take an extreme example, on the last day of the season, your team may be "locked in" to a certain number of points in some categories, while very small changes in stats may affect your standing in other categories. At that point, it clearly would not make sense to apply these formulas.

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About BaseballHQ.com

Ron Shandler began publishing statistical reports for baseball analysts and fantasy leaguers in 1986. Since then, his enterprise has grown into one of the largest information providers in the industry, producing quality products continuously and over a longer period than any other fantasy baseball company.

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