# Fielding Independent Bowling Average

Written by Shlok Goyal

Since his return to international cricket, Mohammad Amir has found his Test bowling average balloon above 30.1 Is he a worse bowler than before? Perhaps. Undoubtedly, however, that figure would be lower if his fielding side had dropped fewer catches off his bowling. Amir is not alone in this, of course. To varying degrees, bowlers have often been lucky or unlucky with the fielding around them, which doesn’t just affect the wickets bowlers take, but also the runs they concede. Thus, both misfields and missed catches affect bowling average far more than we desire, distorting the assessment of a bowler’s skill.

It becomes obvious, then, that a measure of bowling average is needed that decouples luck from bowling ability. We want to judge a bowler’s wicket-taking ability based on events resulting solely from the bowler’s skill. To do this, I propose a new statistic, Fielding Independent Bowling Average (FIBA)—inspired from baseball’s similarly-named Fielding Independent Pitching statistic—that considers only sixes, extras, bowled, and leg-before-wicket.2

The formula is fairly simple:

Wides and no-balls are at most one even if they lead to a boundary, since those extra runs are fielding-dependent. Only bowled and leg-before-wickets are dismissals that do not depend on the fielding side, while the same can be said of sixes, wides, and no-balls when it comes to runs.

One may squirm at the statistic’s selectivity in considering deliveries. Even in the IPL3, which is full of sixes and wickets, this formula eliminates 90% of deliveries. This, though, should serve to emphasize the importance of fielding and field placements. What FIBA does is hone in on the deliveries that are almost entirely the result of the bowler’s performance. With a sufficiently large sample, the deliveries we didn’t consider won’t matter and in fact would bias the results by factoring in the effects of fielding.

I tested the idea that bowling average doesn’t offer a good account of a bowler’s skill by seeing how much bowling average varies each year in the IPL for each bowler, excluding sixes, bowled, and lbw. Call this non-FIBA bowling average, so non-FIBA = $\frac{\text{Batted Runs Conceded - Runs Conceded in Sixes}}{\text{Wickets Taken - Bowled - LBW}}$

If non-FIBA bowling average tends to remain relatively constant for a bowler each season, it must be a good measure. If not, then it doesn’t properly explain a bowler’s skill. I conducted a chi-squared test on the six bowlers with at least four wickets in each of the last five seasons and compared it to their average non-FIBA bowling average over that period. Assuming non-FIBA bowling average is a static product of bowlers’ skill, the probability of observing the non-FIBA averages we do was found to be less than 0.001%. Thus, it’s clear that the components of bowling average that don’t make up FIBA are largely random and thus a poor explanation of the bowler’s skill.

I ran the same test for FIBA, looking at bowlers with at least three wickets in bowled or leg-before-wicket each season, and found the probability of observing the FIBA we do as being 3.1%. Certainly, it’s not great, but it offers a better look at skill than bowling average. And considering that bowlers change—they have lean runs and purple patches, develop new deliveries, adjust to batsmen who have adjusted to them—we could never reasonably expect any statistic to remain perfectly constant since bowlers’ skill is inconstant.

This is not to say that FIBA is foolproof. Bowlers often aim for a caught-behind or caught in the slips. It’s also the bowlers’ job to bowl to the field around them. Hence, it can be argued that they should be responsible for conceding those runs. Moreover, since FIBA eliminates so many deliveries from consideration, it takes many matches for it to stabilize for a given bowler. But even bowlers aiming for caught-behind will change their lines and bowl batsmen out, while giving up fewer sixes with their original lines. And while bowlers should bowl to their field, they cannot will chances to go to their strongest fielders.

Furthermore, we can now compare fielding sides’ quality by looking at the difference between $\frac{\text{Runs Conceded}}{\text{Wickets Taken}}$ (this includes run-outs and extras conceded since we are judging fielding quality) and the bowler’s FIBA. For the last IPL season, I compared each team’s FIBA with their bowling average and ranked fielding sides based on this:

 Team Runs/Wicket FIBA Average FIBA - Runs/Wicket Gujarat Lions 37.06 44.07 7.01 Rising Pune Supergiants 21.56 24.92 3.37 Kings XI Punjab 30.07 32.67 2.60 Royal Challengers Bangalore 26.06 25.27 -0.79 Delhi Daredevils 28.54 27.55 -0.99 Average 26.51 25.91 -1.32 Mumbai Indians 25.13 21.48 -3.65 Kolkata Knight Riders 26.45 22.11 -4.34 Sunrisers Hyderabad 22.56 17.10 -5.47 Source for Data: cricsheet.org

The results here largely pass the smell test. Rising Pune Supergiants and Gujarat Lions were first and third, respectively, in run-outs. The second-best team, Delhi Daredevils, dropped far too many catches to rank higher. Near the bottom of the table, Kolkata Knight Riders became well-known this season for dropped catches. The below-average ranks for Mumbai and Hyderabad, however, are worrisome. The reason is that Hyderabad was unusually led by Bhuvneshwar Kumar and Rashid Khan and Mumbai had Jasprit Bumrah and Lasith Malinga, all bowlers who don’t surrender many sixes and pick up a significant number of bowled and leg-before-wicket dismissals. While this skill is highly desirable, especially in the death overs, FIBA is susceptible to rewarding such bowlers too greatly.4 This doesn’t destroy its power over bowling average, but indicates that considering other components of bowling average might be useful for FIBA, albeit at a lower weight.

Of course, this is only one application of FIBA. FIBA can also help teams trying to pick the best bowlers and fans the best fantasy teams. Using a simple equation and data found on every modern cricket scorecard, FIBA offers an easy and more effective way to assess bowlers’ wicket-taking ability than bowling average.

1 Test cricket is the longest of the three formats in cricket. Each match takes place over five days with each team batting twice. The Test bowling average, then, is the average number of runs a bowler concedes in Test cricket for each wicket taken.

2 A six is when a batsman hits the ball out of the ground without it touching the ground (like a home run in baseball). Extras have many components, but the ones used in the FIBA formula are those that are dependent on the bowler: wides (when the ball is thrown too far for the batsman’s reach) and no-balls (when the bowlers oversteps while throwing the ball and so delivers the ball from too close). Bowled and leg-before-wicket are two types of ways batsmen can be out.

3 The IPL is the Indian Premier League, an annual tournament in which Indian franchises compete with one another in the shortest format of the game, Twenty20.

4 The death overs refer to the end of a batting team’s innings, in which it tends to score runs faster than before through boundaries such as sixes.