# Roto Fantasy Baseball Part 2: A Mathematical Approach to Starting Pitchers

March 7, 2012In Part 1 of this three-part series, we discussed the mathematical evaluation of hitters for fantasy baseball using a formula we called Dominance Factor (DF). If you missed that article you can catch up on the series here:

But as we all know, filling a team with stud hitters is only half of the equation for developing an all-world fantasy baseball team. Pitching statistics are going to account for half of your team’s total score.

With pitchers, much like hitters, fantasy owners go into a draft with a high degree of bias towards certain players and often times overvalue or undervalue players and are not able to objectively compare similar players. Much like with the leagues hitters, a mathematical approach to evaluating these pitchers is in order.

In the pitching realm, there are two distinct sets of pitchers. With starting pitchers, the owner is primarily concerned with four of the five standard scoring categories: wins, ERA, strikeouts, and WHIP.

Due to the amount of innings starting pitchers log, ratio stats like ERA and WHIP will be heavily determined by these players. In terms of relief pitchers, the player is primarily concerned with saves. Despite the fact that these pitchers will often times have very low ERA and WHIP stats, their limited amount of innings greatly reduces the effect to your overall stat line.

To some degree, the same thing can be said about strikeouts for relievers, although a high strikeout rate for a reliever can give a team the needed boost to get over the hump if the team’s starters are primarily of the “pitch to contact” variety.

Because of these differences, we need to split these two sets of players into two different groupings to effectively evaluate them. Today, we will be discussing starting pitchers. Part 3 of this series will be focused on relievers.

Much like with hitters, throughout the draft or auction you’ll face many tough decisions regarding player selection for your pitching staff. Just like we did with the hitters, we’ll be using a DF formula to compare players based on projected stats.

The one main difference you’ll see with starting pitchers, compared to hitters, is that they are only useful in four of five standard scoring categories as they likely will not produce saves. Theoretically, each of the four stats would be worth 25 points for a total of 100 total points for DF.

However since wins are extremely dependent on luck, I decided to use five points from the win total for K/9, a very useful category for evaluating starting pitching.

Even though K/9 isn’t typically a scoring category, it gives a strong indication of a pitcher's ability to work out of trouble and indirectly keeps ERA and WHIP down—and obviously it has a direct correlation to the number of strikeouts. The total DF points are broken down in our formula as follows:

Wins-20 points, ERA-25 points, K-25 points, WHIP-25 points, K/9-5 points

To understand DF, you need to once again be familiar with two imaginary players. The first player is the fantasy stud. He projects to lead the league in just about everything. For this player, think Jake Peavy in his prime years with the Padres. His stat line was:

18 W/2.20 ERA/210 K/1.00 WHIP/13 K/9

The second player is the fantasy bum. This player has a stat line similar to what happens when a guy who should be in Triple-A starts all season in the big leagues. Basically, we are talking about Jake Peavy lately (sorry Jake, I still pull for a fellow Mobile, Alabama boy but you ain’t what you used to be). His stat line is:

8 W/4.50 ERA/110 K/1.40 WHIP/6 K/9

Again, we need to use our *reliable* projections for pitchers. Without question, pitching projections are much more volatile than hitting projections for a number or reasons, including injury, more frequent down years and just plain dumb luck. However, at the end of the day, solid projections are really the best you’re going to do.

Once you have exported the projections to a spreadsheet, it’s time for your shiny, new formula. Just like with the hitters, we are going to evaluate on the percentage of the way from the bum level to the stud level.

For stats where more is better (wins, strikeouts, K/9), we’ll subtract the bum’s stat from each player’s stat and divide by the stud’s stat minus the bum’s stat. This number is then multiplied by the points for that category. If lower numbers are better (ERA, WHIP), we’ll do the opposite and subtract each player’s stat from the bum’s stat and divide by the bum’s stat minus the stud’s stat.

As with last time, stay with me.

A good example to use here is Felix Hernandez. Assume King Felix to project to a stat line of:

15 W/3.00 ERA/213 K/1.19 WHIP/8.4 K/9

As with most players, he falls some where between the stud and the bum. Using Felix’s wins, where more is better, as an example you would have:

(15-8)/(18-8)x20 = 14 out of 20 Points

If we look at WHIP, where less is better, the calculation would be:

(1.4-1.19)/(1.4-1.0)*25 = 13.13 Points

For the other stats you would do the same thing, giving Felix:

Wins: 14 out of 20 points

ERA: 16.3 out of 25 points

K: 25.75 out of 25 points (notice, actually better than stud level)

Whip: 13.13 out of 25 Points

K/9: 1.71 out of five Points

Adding all of these together, King Felix ends up with a DF of 70.89, good for seventh overall for starting pitchers behind Clayton Kershaw (88.30), Roy Halladay (84.76), Justin Verlander (83.71), Cliff Lee (82.73), C.C. Sabathia (72.59), and Stephen Strasburg (71.06). He also projects to be twice as valuable as Derek Holland (35.83) and Ervin Santana (34.63.

While it may seem complicated, if you use Excel and place wins, ERA, saves, strikeouts, WHIP and K/9 in the "C" through "H" columns and paste the following formula in column "I" you will have the DF for every single player in seconds.

Excel formula for DF for Column G:

=((C2-8)/10)*20+((4.5-D2)/2.3)*25+((F2-110)/100)*25+((1.4-G2)/0.4)*25+((H2-6)/7)*5

Now, in addition to having a solid foundation for evaluating the hitters in the draft, you are also prepared to compare any starting pitcher in the game. Now we just have to get a grasp on those tricky closers and you’ll be draft ready. Stay tuned for Part 3 of our series. And of course, enjoy the game and have a great season.

UPDATE: The Hitter and Closer articles can be found at: