A New Statistic: Hammer Factor

Welcome to the new stat of 2018. To be fair, this is a simple calculation using two existing statistics: Hammer Efficiency (or HE) and Steal Defense, otherwise known as SD, though in the early days it was SDE.  These are the two primary stats that Gerry Geurts and Dallas Bittle created over a decade ago to measure a team's performance with hammer.  They also created Force Efficiency (FE) and Steal Efficiency (SE) which measured a teams play without hammer.  Here's a quick refresher on what these actually are:

• Hammer Efficiency (HE) - the percentage of time a team takes 2 or more points with hammer, in ends which are scored. Includes all non-blank ends in which a team has hammer.
• Force Efficiency (FE) - measures the ability of a team to force their opponent to one point. Calculated by number of ends in which the opponent took 1 point divided by all ends against without hammer where the opponent scores. Stolen and blank ends are not included in the calculation.
• Steal Efficiency (SE) - the percentage of ends a team is able to steal. It's calculated by dividing ends stolen without hammer by the total ends played without hammer, Blank ends are included.

Steal Defence (SD) - ability to limit the number of stolen ends. Calculated by number of ends stolen against divided by ends with hammer. Blank ends are included

Over the years, HE and SD have provided some indication on whether a team was average, good or great.  Generally, stats without hammer are less of an indicator of success.  

Looking at last season, I grouped teams into several categories, based on World Ranking.  Top 5, Next 5, Top 11 through 20, 21 through 30 and 31 to 50.  Let's first look at without hammer numbers. For men, FE ranged between .48 and .63 with average for each grouping .55, .56 or .57.  The .63 was Gushue, an anomaly at the top, however Tanner Horgan (Rank 23) was .62 and Karsten Sturmay (Rank 48) was .61.  For comparison, Reid Carruthers, Ranked 6th, had an FE of .49.  For all groups SE averaged .25 with only two teams below .22 and two above .28.  Often these non-hammer stats are an indicator of the level of competition.  A top 5 team (like Carruthers) can have a much lower FE than a 35th ranked team who plays against weaker opponents.  In the womens game, FE last year may have been a subtle indicator, with the Top 10 teams averaging .6 while 11 through 50 averaged .55.  SE was similar to the mens, with an average between .25 to .28 for each grouping, with top teams actually being the lower number.  Now on to our new stat...

When digging into these CurlingZone stats, over the years it's become apparent that strength of a team was related to how much they avoided stolen ends.  A low Steal Defence (say, below .20) meant a good team.  When combined with a high Hammer Efficiency (above .45) , indicated likely a great team.  Some teams have differing styles and you could see one team with higher HE but higher SD, and vise versa.

Oddly enough, it was staring at us all along and we only just recently thought to combine these numbers into a formula...  

Hammer Factor = (Hammer Efficiency) - (Steal Defence)

Going back to my team groupings from earlier, when I took this formula and averaged it for each grouping, it jumped off the spreadsheet.  Have a look:

Team World Ranking (2017-18 Season)	Men Hammer Factor	Women Hammer Factor
Top 5	0.30	0.28
6 to 10	0.23	0.20
11 to 20	0.21	0.19
21 to 30	0.16	0.15
31 to 50	0.16	0.12

Now, looking at teams individually, there's still some oddities.  Edin and Gushue are top of the rankings and have the highest HF by far (.33 and .39 respectively).  Howard was .3 at a ranking of 11 and Koe only .24 while being ranked 3rd.  In the womens, Jones and Hasselborg were .28 and .35  while Einarson at 14th had an HF = .27.  But for the most part, Hammer Factor seemed to drop with a teams ranking.

I haven't yet gone backwards to compare past season results and also haven't yet analyzed against W-L records (just rankings).  Perhaps HF could be used in a Bill James Pythagorean Expectation to estimate a team's winning percentage or a Bill James style log5 formula to estimate win probability head-to-head.   More to be done with this new calculation, but for now it's fair to say that the higher the Hammer Factor, the better.