D3 is probably the best single, quickly available metric regarding the caliber of an MLB manager and his team.
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What is D3?
To understand that, a few other definitions:
W, L : Actual team wins and losses.
First-order wins and losses: Expected wins and losses, based on a team's actual runs scored and runs allowed.
Equivalent average (EQA): A measure of total offensive value per out, with corrections for league offensive level, home park, and team pitching. EQA considers batting as well as baserunning, but not the value of a position player's defense. The EqA adjusted for all-time also has a correction for league difficulty. The scale is deliberately set to approximate that of batting average. League average EqA is always equal to .260. EqA is derived from Raw EqA, which is (H + TB + 1.5*(BB + HBP + SB) + SH + SF) divided by (AB + BB + HBP + SH + SF + CS + SB). REqA is then normalized to account for league difficulty and scale to create EqA.
Equivalent runs (EQR): EQR = 5 * OUT * EQA^2.5. In the fielding charts, the estimated number of EqR he had at the plate while playing this position in the field. In Adjusted Standings, EqR refers to the total number of equivalent runs scored by the team.
Second-order wins and losses: Expected wins and losses, based on a team's equivalent runs scored and equivalent runs allowed.
Adjusted equivalent runs (AEQR): EQR, adjusted for the exact strength of opposing teams' players.
Third-order wins and losses: Expected wins and losses, based on AEQR and AEQRA.
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What is D3? D3 is the difference between actual wins and third-order wins. That's the difference between how a team actually did and how it should have done, given
1) Its exact hits, walks and other contributions on offense;
2) Its exact hits and walks allowed, and other contributions on defense;
3) The strength of its opposition.
A good (or lucky) manager has a positive D3, getting more wins than expected, given how his players did.
The mean of D3 across MLB is, of course, zero. The standard deviation is 3.0. Let's look at the worst MLB managers by D3:
John Gibbons, Blue Jays (-4.1 games): John Gibbons' own grandmother reportedly asked him if he was going to be fired, given that he was doing so badly.
Clint Hurdle, Rockies (-4.0 games): Clint Hurdle has been known by stats guys, especially Chris Jaffe (who has studied this carefully), as one of the worst managers in MLB history, and probably the worst of this century.
Jim Leyland, Tigers (-3.7 games): Jim Leyland's team was supposed to be a contender, and they're ten games back in a weak division. Part of it is the players, but part is that they're winning less than they should, too.
OK, these make sense. Who are the best?
Mike Scioscia, Angels (+8.2 games): Yes, that's right. The Angels have won 38 games, and eight of those games can be credited either to good luck or to the managerial skill of Mike Scioscia. Given that Scioscia has a strong reputation, and that he's a perennial leader in this metric, and that 8.2 is almost three standard deviations above the mean, it's probably not just luck. Mike Scioscia is probably the best manager in MLB right now.
Ron Gardenhire, Twins (+5.0 games): Another perennial strong manager, taking a "rebuilding team" into contention in the AL Central, Gardenhire is doing a fine job this year.
Manny Acta, Nationals (+3.5 games): For some reason, Acta is highly regarded, even though his team stinks. This metric supports that.
Tony LaRussa, Cardinals (+3.5 games): A perennial contender for Manager of the Year, and certainly one of the great MLB managers of all time, LaRussa is, again, exceeding expectations.
No surprises here, either.
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Terry Francona is currently at -1.5 wins by D3. This isn't unusual; Terry Francona comes up short in most attempts at quantitative analysis. Chris Jaffe's work found him to be, along with Clint Hurdle, probably one of the two worst managers of his generation.
Let's see how things go for Terry Francona over the next few weeks with respect to D3. With the minor and major injuries on the ballclub, plus the recent suspensions, Terry Francona has a chance to make a difference. We'll see which way he makes that difference.